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• How to Write a Research Proposal | Examples & Templates

How to Write a Research Proposal | Examples & Templates

Published on October 12, 2022 by Shona McCombes and Tegan George. Revised on November 21, 2023.

A research proposal describes what you will investigate, why it’s important, and how you will conduct your research.

The format of a research proposal varies between fields, but most proposals will contain at least these elements:

Introduction

Literature review.

• Research design

Reference list

While the sections may vary, the overall objective is always the same. A research proposal serves as a blueprint and guide for your research plan, helping you get organized and feel confident in the path forward you choose to take.

Table of contents

Research proposal purpose, research proposal examples, research design and methods, contribution to knowledge, research schedule, other interesting articles, frequently asked questions about research proposals.

Academics often have to write research proposals to get funding for their projects. As a student, you might have to write a research proposal as part of a grad school application , or prior to starting your thesis or dissertation .

In addition to helping you figure out what your research can look like, a proposal can also serve to demonstrate why your project is worth pursuing to a funder, educational institution, or supervisor.

Research proposal length

The length of a research proposal can vary quite a bit. A bachelor’s or master’s thesis proposal can be just a few pages, while proposals for PhD dissertations or research funding are usually much longer and more detailed. Your supervisor can help you determine the best length for your work.

One trick to get started is to think of your proposal’s structure as a shorter version of your thesis or dissertation , only without the results , conclusion and discussion sections.

Download our research proposal template

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Writing a research proposal can be quite challenging, but a good starting point could be to look at some examples. We’ve included a few for you below.

• Example research proposal #1: “A Conceptual Framework for Scheduling Constraint Management”
• Example research proposal #2: “Medical Students as Mediators of Change in Tobacco Use”

Like your dissertation or thesis, the proposal will usually have a title page that includes:

• The proposed title of your project
• Your supervisor’s name
• Your institution and department

The first part of your proposal is the initial pitch for your project. Make sure it succinctly explains what you want to do and why.

Your introduction should:

• Introduce your topic
• Give necessary background and context
• Outline your  problem statement  and research questions

To guide your introduction , include information about:

• Who could have an interest in the topic (e.g., scientists, policymakers)
• How much is already known about the topic
• What is missing from this current knowledge
• What new insights your research will contribute
• Why you believe this research is worth doing

As you get started, it’s important to demonstrate that you’re familiar with the most important research on your topic. A strong literature review  shows your reader that your project has a solid foundation in existing knowledge or theory. It also shows that you’re not simply repeating what other people have already done or said, but rather using existing research as a jumping-off point for your own.

In this section, share exactly how your project will contribute to ongoing conversations in the field by:

• Comparing and contrasting the main theories, methods, and debates
• Examining the strengths and weaknesses of different approaches
• Explaining how will you build on, challenge, or synthesize prior scholarship

Following the literature review, restate your main  objectives . This brings the focus back to your own project. Next, your research design or methodology section will describe your overall approach, and the practical steps you will take to answer your research questions.

To finish your proposal on a strong note, explore the potential implications of your research for your field. Emphasize again what you aim to contribute and why it matters.

For example, your results might have implications for:

• Improving best practices
• Informing policymaking decisions
• Strengthening a theory or model
• Challenging popular or scientific beliefs
• Creating a basis for future research

Last but not least, your research proposal must include correct citations for every source you have used, compiled in a reference list . To create citations quickly and easily, you can use our free APA citation generator .

Some institutions or funders require a detailed timeline of the project, asking you to forecast what you will do at each stage and how long it may take. While not always required, be sure to check the requirements of your project.

Here’s an example schedule to help you get started. You can also download a template at the button below.

Download our research schedule template

If you are applying for research funding, chances are you will have to include a detailed budget. This shows your estimates of how much each part of your project will cost.

Make sure to check what type of costs the funding body will agree to cover. For each item, include:

• Cost : exactly how much money do you need?
• Justification : why is this cost necessary to complete the research?
• Source : how did you calculate the amount?

To determine your budget, think about:

• Travel costs : do you need to go somewhere to collect your data? How will you get there, and how much time will you need? What will you do there (e.g., interviews, archival research)?
• Materials : do you need access to any tools or technologies?
• Help : do you need to hire any research assistants for the project? What will they do, and how much will you pay them?

If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples.

Methodology

• Sampling methods
• Simple random sampling
• Stratified sampling
• Cluster sampling
• Likert scales
• Reproducibility

 Statistics

• Null hypothesis
• Statistical power
• Probability distribution
• Effect size
• Poisson distribution

Research bias

• Optimism bias
• Cognitive bias
• Implicit bias
• Hawthorne effect
• Anchoring bias
• Explicit bias

Once you’ve decided on your research objectives , you need to explain them in your paper, at the end of your problem statement .

Keep your research objectives clear and concise, and use appropriate verbs to accurately convey the work that you will carry out for each one.

I will compare …

A research aim is a broad statement indicating the general purpose of your research project. It should appear in your introduction at the end of your problem statement , before your research objectives.

Research objectives are more specific than your research aim. They indicate the specific ways you’ll address the overarching aim.

A PhD, which is short for philosophiae doctor (doctor of philosophy in Latin), is the highest university degree that can be obtained. In a PhD, students spend 3–5 years writing a dissertation , which aims to make a significant, original contribution to current knowledge.

A PhD is intended to prepare students for a career as a researcher, whether that be in academia, the public sector, or the private sector.

A master’s is a 1- or 2-year graduate degree that can prepare you for a variety of careers.

All master’s involve graduate-level coursework. Some are research-intensive and intend to prepare students for further study in a PhD; these usually require their students to write a master’s thesis . Others focus on professional training for a specific career.

Critical thinking refers to the ability to evaluate information and to be aware of biases or assumptions, including your own.

Like information literacy , it involves evaluating arguments, identifying and solving problems in an objective and systematic way, and clearly communicating your ideas.

The best way to remember the difference between a research plan and a research proposal is that they have fundamentally different audiences. A research plan helps you, the researcher, organize your thoughts. On the other hand, a dissertation proposal or research proposal aims to convince others (e.g., a supervisor, a funding body, or a dissertation committee) that your research topic is relevant and worthy of being conducted.

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How to Determine Sample Size for a Research Study

Frankline kibuacha | apr. 06, 2021 | 3 min. read.

This article will discuss considerations to put in place when determining your sample size and how to calculate the sample size.

Confidence Interval and Confidence Level

As we have noted before, when selecting a sample there are multiple factors that can impact the reliability and validity of results, including sampling and non-sampling errors . When thinking about sample size, the two measures of error that are almost always synonymous with sample sizes are the confidence interval and the confidence level.

Confidence Interval (Margin of Error)

Confidence intervals measure the degree of uncertainty or certainty in a sampling method and how much uncertainty there is with any particular statistic. In simple terms, the confidence interval tells you how confident you can be that the results from a study reflect what you would expect to find if it were possible to survey the entire population being studied. The confidence interval is usually a plus or minus (±) figure. For example, if your confidence interval is 6 and 60% percent of your sample picks an answer, you can be confident that if you had asked the entire population, between 54% (60-6) and 66% (60+6) would have picked that answer.

Confidence Level

The confidence level refers to the percentage of probability, or certainty that the confidence interval would contain the true population parameter when you draw a random sample many times. It is expressed as a percentage and represents how often the percentage of the population who would pick an answer lies within the confidence interval. For example, a 99% confidence level means that should you repeat an experiment or survey over and over again, 99 percent of the time, your results will match the results you get from a population.

The larger your sample size, the more confident you can be that their answers truly reflect the population. In other words, the larger your sample for a given confidence level, the smaller your confidence interval.

Standard Deviation

Another critical measure when determining the sample size is the standard deviation, which measures a data set’s distribution from its mean. In calculating the sample size, the standard deviation is useful in estimating how much the responses you receive will vary from each other and from the mean number, and the standard deviation of a sample can be used to approximate the standard deviation of a population.

The higher the distribution or variability, the greater the standard deviation and the greater the magnitude of the deviation. For example, once you have already sent out your survey, how much variance do you expect in your responses? That variation in responses is the standard deviation.

Population Size

As demonstrated through the calculation below, a sample size of about 385 will give you a sufficient sample size to draw assumptions of nearly any population size at the 95% confidence level with a 5% margin of error, which is why samples of 400 and 500 are often used in research. However, if you are looking to draw comparisons between different sub-groups, for example, provinces within a country, a larger sample size is required. GeoPoll typically recommends a sample size of 400 per country as the minimum viable sample for a research project, 800 per country for conducting a study with analysis by a second-level breakdown such as females versus males, and 1200+ per country for doing third-level breakdowns such as males aged 18-24 in Nairobi.

How to Calculate Sample Size

As we have defined all the necessary terms, let us briefly learn how to determine the sample size using a sample calculation formula known as Andrew Fisher’s Formula.

• Determine the population size (if known).
• Determine the confidence interval.
• Determine the confidence level.
• Determine the standard deviation ( a standard deviation of 0.5 is a safe choice where the figure is unknown )
• Convert the confidence level into a Z-Score. This table shows the z-scores for the most common confidence levels:

• Put these figures into the sample size formula to get your sample size.

Here is an example calculation:

Say you choose to work with a 95% confidence level, a standard deviation of 0.5, and a confidence interval (margin of error) of ± 5%, you just need to substitute the values in the formula:

((1.96)2 x .5(.5)) / (.05)2

(3.8416 x .25) / .0025

.9604 / .0025

Your sample size should be 385.

Fortunately, there are several available online tools to help you with this calculation. Here’s an online sample calculator from Easy Calculation. Just put in the confidence level, population size, the confidence interval, and the perfect sample size is calculated for you.

GeoPoll’s Sampling Techniques

With the largest mobile panel in Africa, Asia, and Latin America, and reliable mobile technologies, GeoPoll develops unique samples that accurately represent any population. See our country coverage  here , or  contact  our team to discuss your upcoming project.

Related Posts

Sample Frame and Sample Error

Probability and Non-Probability Samples

How GeoPoll Conducts Nationally Representative Surveys

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Sample Size Determination: Definition, Formula, and Example

Are you ready to survey your research target? Research surveys help you gain insights from your target audience. The data you collect gives you insights to meet customer needs, leading to increased sales and customer loyalty. Sample size calculation and determination are imperative to the researcher to determine the right number of respondents, keeping in mind the research study’s quality.

So, how should you do the sample size determination? How do you know who should get your survey? How do you decide on the number of the target audience?

Sending out too many surveys can be expensive without giving you a definitive advantage over a smaller sample. But if you send out too few, you won’t have enough data to draw accurate conclusions. 

Knowing how to calculate and determine the appropriate sample size accurately can give you an edge over your competitors. Let’s take a look at what a good sample includes. Also, let’s look at the sample size calculation formula so you can determine the perfect sample size for your next survey.

What is Sample Size?

‘Sample size’ is a market research term used for defining the number of individuals included in conducting research. Researchers choose their sample based on demographics, such as age, gender questions , or physical location. It can be vague or specific. 

For example, you may want to know what people within the 18-25 age range think of your product. Or, you may only require your sample to live in the United States, giving you a wide population range. The total number of individuals in a particular sample is the sample size.

What is sample size determination?

Sample size determination is the process of choosing the right number of observations or people from a larger group to use in a sample. The goal of figuring out the sample size is to ensure that the sample is big enough to give statistically valid results and accurate estimates of population parameters but small enough to be manageable and cost-effective.

In many research studies, getting information from every member of the population of interest is not possible or useful. Instead, researchers choose a sample of people or events that is representative of the whole to study. How accurate and precise the results are can depend a lot on the size of the sample.

Choosing the statistically significant sample size depends on a number of things, such as the size of the population, how precise you want your estimates to be, how confident you want to be in the results, how different the population is likely to be, and how much money and time you have for the study. Statistics are often used to figure out how big a sample should be for a certain type of study and research question.

Figuring out the sample size is important in ensuring that research findings and conclusions are valid and reliable.

Why do you need to determine the sample size?

Let’s say you are a market researcher in the US and want to send out a survey or questionnaire . The survey aims to understand your audience’s feelings toward a new cell phone you are about to launch. You want to know what people in the US think about the new product to predict the phone’s success or failure before launch.

Hypothetically, you choose the population of New York, which is 8.49 million. You use a sample size determination formula to select a sample of 500 individuals that fit into the consumer panel requirement. You can use the responses to help you determine how your audience will react to the new product.

However, determining a sample size requires more than just throwing your survey at as many people as possible. If your estimated sample sizes are too big, it could waste resources, time, and money. A sample size that’s too small doesn’t allow you to gain maximum insights, leading to inconclusive results.

LEARN ABOUT: Survey Sample Sizes

What are the terms used around the sample size?

Before we jump into sample size determination, let’s take a look at the terms you should know:

1. Population size: 

Population size is how many people fit your demographic. For example, you want to get information on doctors residing in North America. Your population size is the total number of doctors in North America. 

Don’t worry! Your population size doesn’t always have to be that big. Smaller population sizes can still give you accurate results as long as you know who you’re trying to represent.

2. Confidence level: 

The confidence level tells you how sure you can be that your data is accurate. It is expressed as a percentage and aligned to the confidence interval. For example, if your confidence level is 90%, your results will most likely be 90% accurate.

3. The margin of error (confidence interval): 

There’s no way to be 100% accurate when it comes to surveys. Confidence intervals tell you how far off from the population means you’re willing to allow your data to fall. 

A margin of error describes how close you can reasonably expect a survey result to fall relative to the real population value. Remember, if you need help with this information, use our margin of error calculator .

4. Standard deviation: 

Standard deviation is the measure of the dispersion of a data set from its mean. It measures the absolute variability of a distribution. The higher the dispersion or variability, the greater the standard deviation and the greater the magnitude of the deviation. 

For example, you have already sent out your survey. How much variance do you expect in your responses? That variation in response is the standard deviation.

Sample size calculation formula – sample size determination

With all the necessary terms defined, it’s time to learn how to determine sample size using a sample calculation formula.

Your confidence level corresponds to a Z-score. This is a constant value needed for this equation. Here are the z-scores for the most common confidence levels:

90% – Z Score = 1.645

95% – Z Score = 1.96

99% – Z Score = 2.576

If you choose a different confidence level, various online tools can help you find your score.

Necessary Sample Size = (Z-score)2 * StdDev*(1-StdDev) / (margin of error)2

Here is an example of how the math works, assuming you chose a 90% confidence level, .6 standard deviation, and a margin of error (confidence interval) of +/- 4%.

((1.64)2 x .6(.6)) / (.04)2

( 2.68x .0.36) / .0016

.9648 / .0016

603 respondents are needed, and that becomes your sample size.

Free Sample Size Calculator

How is a sample size determined?

Determining the right sample size for your survey is one of the most common questions researchers ask when they begin a market research study. Luckily, sample size determination isn’t as hard to calculate as you might remember from an old high school statistics class.

Before calculating your sample size, ensure you have these things in place:

Goals and objectives: 

What do you hope to do with the survey? Are you planning on projecting the results onto a whole demographic or population? Do you want to see what a specific group thinks? Are you trying to make a big decision or just setting a direction? 

Calculating sample size is critical if you’re projecting your survey results on a larger population. You’ll want to make sure that it’s balanced and reflects the community as a whole. The sample size isn’t as critical if you’re trying to get a feel for preferences. 

For example, you’re surveying homeowners across the US on the cost of cooling their homes in the summer. A homeowner in the South probably spends much more money cooling their home in the humid heat than someone in Denver, where the climate is dry and cool. 

For the most accurate results, you’ll need to get responses from people in all US areas and environments. If you only collect responses from one extreme, such as the warm South, your results will be skewed.

Precision level: 

How close do you want the survey results to mimic the true value if everyone responded? Again, if this survey determines how you’re going to spend millions of dollars, then your sample size determination should be exact. 

The more accurate you need to be, the larger the sample you want to have, and the more your sample will have to represent the overall population. If your population is small, say, 200 people, you may want to survey the entire population rather than cut it down with a sample.

Confidence level: 

Think of confidence from the perspective of risk. How much risk are you willing to take on? This is where your Confidence Interval numbers become important. How confident do you want to be — 98% confident, 95% confident? 

Understand that the confidence percentage you choose greatly impacts the number of completions you’ll need for accuracy. This can increase the survey’s length and how many responses you need, which means increased costs for your survey. 

Knowing the actual numbers and amounts behind percentages can help make more sense of your correct sample size needs vs. survey costs. 

For example, you want to be 99% confident. After using the sample size determination formula, you find you need to collect an additional 1000 respondents. 

This, in turn, means you’ll be paying for samples or keeping your survey running for an extra week or two. You have to determine if the increased accuracy is more important than the cost.

Population variability: 

What variability exists in your population? In other words, how similar or different is the population?

If you are surveying consumers on a broad topic, you may have lots of variations. You’ll need a larger sample size to get the most accurate picture of the population. 

However, if you’re surveying a population with similar characteristics, your variability will be less, and you can sample fewer people. More variability equals more samples, and less variability equals fewer samples. If you’re not sure, you can start with 50% variability.

Response rate: 

You want everyone to respond to your survey. Unfortunately, every survey comes with targeted respondents who either never open the study or drop out halfway. Your response rate will depend on your population’s engagement with your product, service organization, or brand. 

The higher the response rate, the higher your population’s engagement level. Your base sample size is the number of responses you must get for a successful survey.

Consider your audience: 

Besides the variability within your population, you need to ensure your sample doesn’t include people who won’t benefit from the results. One of the biggest mistakes you can make in sample size determination is forgetting to consider your actual audience. 

For example, you don’t want to send a survey asking about the quality of local apartment amenities to a group of homeowners.

Select your respondents

Focus on your survey’s objectives: 

You may start with general demographics and characteristics, but can you narrow those characteristics down even more? Narrowing down your audience makes getting a more accurate result from a small sample size easier. 

For example, you want to know how people will react to new automobile technology. Your current population includes anyone who owns a car in a particular market. 

However, you know your target audience is people who drive cars that are less than five years old. You can remove anyone with an older vehicle from your sample because they’re unlikely to purchase your product.

Once you know what you hope to gain from your survey and what variables exist within your population, you can decide how to calculate sample size. Using the formula for determining sample size is a great starting point to get accurate results. 

After calculating the sample size, you’ll want to find reliable customer survey software to help you accurately collect survey responses and turn them into analyzed reports.

LEARN MORE: Population vs Sample

In sample size determination, statistical analysis plan needs careful consideration of the level of significance, effect size, and sample size. 

Researchers must reconcile statistical significance with practical and ethical factors like practicality and cost. A well-designed study with a sufficient sample size can improve the odds of obtaining statistically significant results.

To meet the goal of your survey, you may have to try a few methods to increase the response rate, such as:

• Increase the list of people who receive the survey.
• To reach a wider audience, use multiple distribution channels, such as SMS, website, and email surveys.
• Send reminders to survey participants to complete the survey.
• Offer incentives for completing the survey, such as an entry into a prize drawing or a discount on the respondent’s next order.
• Consider your survey structure and find ways to simplify your questions. The less work someone has to do to complete the survey, the more likely they will finish it. 
• Longer surveys tend to have lower response rates due to the length of time it takes to complete the survey. In this case, you can reduce the number of questions in your survey to increase responses.  

QuestionPro’s sample size calculator makes it easy to find the right sample size for your research based on your desired level of confidence, your margin of error, and the size of the population.

LEARN MORE         FREE TRIAL

Frequently Asked Questions (FAQ)

The four ways to determine sample size are: 1. Power analysis 2. Convenience sampling, 3. Random sampling , 4. Stratified sampling

The three factors that determine sample size are: 1. Effect size, 2. Level of significance 3. Power

Using statistical techniques like power analysis, the minimal detectable effect size, or the sample size formula while taking into account the study’s goals and practical limitations is the best way to calculate the sample size.

The sample size is important because it affects how precise and accurate the results of a study are and how well researchers can spot real effects or relationships between variables.

The sample size is the number of observations or study participants chosen to be representative of a larger group

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Determining sample size: how to make sure you get the correct sample size.

16 min read Sample size can make or break your research project. Here’s how to master the delicate art of choosing the right sample size.

What is sample size?

Sample size is the beating heart of any research project. It’s the invisible force that gives life to your data, making your findings robust, reliable and believable.

Sample size is what determines if you see a broad view or a focus on minute details; the art and science of correctly determining it involves a careful balancing act. Finding an appropriate sample size demands a clear understanding of the level of detail you wish to see in your data and the constraints you might encounter along the way.

Remember, whether you’re studying a small group or an entire population, your findings are only ever as good as the sample you choose.

Free eBook: Empower your market research efforts today

Let’s delve into the world of sampling and uncover the best practices for determining sample size for your research.

How to determine sample size

“How much sample do we need?” is one of the most commonly-asked questions and stumbling points in the early stages of  research design . Finding the right answer to it requires first understanding and answering two other questions:

How important is statistical significance to you and your stakeholders?

What are your real-world constraints.

At the heart of this question is the goal to confidently differentiate between groups, by describing meaningful differences as statistically significant.  Statistical significance  isn’t a difficult concept, but it needs to be considered within the unique context of your research and your measures.

First, you should consider when you deem a difference to be meaningful in your area of research. While the standards for statistical significance are universal, the standards for “meaningful difference” are highly contextual.

For example, a 10% difference between groups might not be enough to merit a change in a marketing campaign for a breakfast cereal, but a 10% difference in efficacy of breast cancer treatments might quite literally be the difference between life and death for hundreds of patients. The exact same magnitude of difference has very little meaning in one context, but has extraordinary meaning in another. You ultimately need to determine the level of precision that will help you make your decision.

Within sampling, the lowest amount of magnification – or smallest sample size – could make the most sense, given the level of precision needed, as well as timeline and budgetary constraints.

If you’re able to detect statistical significance at a difference of 10%, and 10% is a meaningful difference, there is no need for a larger sample size, or higher magnification. However, if the study will only be useful if a significant difference is detected for smaller differences – say, a difference of 5% — the sample size must be larger to accommodate this needed precision. Similarly, if 5% is enough, and 3% is unnecessary, there is no need for a larger statistically significant sample size.

You should also consider how much you expect your responses to vary. When there isn’t a lot of variability in response, it takes a lot more sample to be confident that there are statistically significant differences between groups.

For instance, it will take a lot more sample to find statistically significant differences between groups if you are asking, “What month do you think Christmas is in?” than if you are asking, “How many miles are there between the Earth and the moon?”. In the former, nearly everybody is going to give the exact same answer, while the latter will give a lot of variation in responses. Simply put, when your variables do not have a lot of variance, larger sample sizes make sense.

Statistical significance

The likelihood that the results of a study or experiment did not occur randomly or by chance, but are meaningful and indicate a genuine effect or relationship between variables.

Magnitude of difference

The size or extent of the difference between two or more groups or variables, providing a measure of the effect size or practical significance of the results.

Actionable insights

Valuable findings or conclusions drawn from  data analysis  that can be directly applied or implemented in decision-making processes or strategies to achieve a particular goal or outcome.

It’s crucial to understand the differences between the concepts of “statistical significance”, “magnitude of difference” and “actionable insights” – and how they can influence each other:

• Even if there is a statistically significant difference, it doesn’t mean the magnitude of the difference is large: with a large enough sample, a 3% difference could be statistically significant
• Even if the magnitude of the difference is large, it doesn’t guarantee that this difference is statistically significant: with a small enough sample, an 18% difference might not be statistically significant
• Even if there is a large, statistically significant difference, it doesn’t mean there is a story, or that there are actionable insights

There is no way to guarantee statistically significant differences at the outset of a study – and that is a good thing.

Even with a sample size of a million, there simply may not be any differences – at least, any that could be described as statistically significant. And there are times when a lack of significance is positive.

Imagine if your main competitor ran a multi-million dollar ad campaign in a major city and a huge pre-post study to detect campaign effects, only to discover that there were no statistically significant differences in  brand awareness . This may be terrible news for your competitor, but it would be great news for you.

With Stats iQ™ you can analyze your research results and conduct significance testing

As you determine your sample size, you should consider the real-world constraints to your research.

Factors revolving around timings, budget and target population are among the most common constraints, impacting virtually every study. But by understanding and acknowledging them, you can definitely navigate the practical constraints of your research when pulling together your sample.

Timeline constraints

Gathering a larger sample size naturally requires more time. This is particularly true for elusive audiences, those hard-to-reach groups that require special effort to engage. Your timeline could become an obstacle if it is particularly tight, causing you to rethink your sample size to meet your deadline.

Budgetary constraints

Every sample, whether large or small, inexpensive or costly, signifies a portion of your budget. Samples could be like an open market; some are inexpensive, others are pricey, but all have a price tag attached to them.

Population constraints

Sometimes the individuals or groups you’re interested in are difficult to reach; other times, they’re a part of an extremely small population. These factors can limit your sample size even further.

What’s a good sample size?

A good sample size really depends on the context and goals of the research. In general, a good sample size is one that accurately represents the population and allows for reliable statistical analysis.

Larger sample sizes are typically better because they reduce the likelihood of  sampling errors  and provide a more accurate representation of the population. However, larger sample sizes often increase the impact of practical considerations, like time, budget and the availability of your audience. Ultimately, you should be aiming for a sample size that provides a balance between statistical validity and practical feasibility.

4 tips for choosing the right sample size

Choosing the right sample size is an intricate balancing act, but following these four tips can take away a lot of the complexity.

1) Start with your goal

The foundation of your research is a clearly defined goal. You need to determine what you’re trying to understand or discover, and use your goal to guide your  research methods  – including your sample size.

If your aim is to get a broad overview of a topic, a larger, more diverse sample may be appropriate. However, if your goal is to explore a niche aspect of your subject, a smaller, more targeted sample might serve you better. You should always align your sample size with the objectives of your research.

2) Know that you can’t predict everything

Research is a journey into the unknown. While you may have hypotheses and predictions, it’s important to remember that you can’t foresee every outcome – and this uncertainty should be considered when choosing your sample size.

A larger sample size can help to mitigate some of the risks of unpredictability, providing a more diverse range of data and potentially more accurate results. However, you shouldn’t let the fear of the unknown push you into choosing an impractically large sample size.

3) Plan for a sample that meets your needs and considers your real-life constraints

Every research project operates within certain boundaries – commonly budget, timeline and the nature of the sample itself. When deciding on your sample size, these factors need to be taken into consideration.

Be realistic about what you can achieve with your available resources and time, and always tailor your sample size to fit your constraints – not the other way around.

4) Use best practice guidelines to calculate sample size

There are many established guidelines and formulas that can help you in determining the right sample size.

The easiest way to define your sample size is using a  sample size calculator , or you can use a manual sample size calculation if you want to test your math skills. Cochran’s formula is perhaps the most well known equation for calculating sample size, and widely used when the population is large or unknown.

Beyond the formula, it’s vital to consider the confidence interval, which plays a significant role in determining the appropriate sample size – especially when working with a  random sample  – and the sample proportion. This represents the expected ratio of the target population that has the characteristic or response you’re interested in, and therefore has a big impact on your correct sample size.

If your population is small, or its variance is unknown, there are steps you can still take to determine the right sample size. Common approaches here include conducting a small pilot study to gain initial estimates of the population variance, and taking a conservative approach by assuming a larger variance to ensure a more representative sample size.

Empower your market research

Conducting meaningful research and extracting actionable intelligence are priceless skills in today’s ultra competitive business landscape. It’s never been more crucial to stay ahead of the curve by leveraging the power of market research to identify opportunities, mitigate risks and make informed decisions.

Equip yourself with the tools for success with our essential eBook,  “The ultimate guide to conducting market research” .

With this front-to-back guide, you’ll discover the latest strategies and best practices that are defining effective market research. Learn about practical insights and real-world applications that are demonstrating the value of research in driving business growth and innovation.

Learn how to determine sample size

To choose the correct sample size, you need to consider a few different factors that affect your research, and gain a basic understanding of the statistics involved. You’ll then be able to use a sample size formula to bring everything together and sample confidently, knowing that there is a high probability that your survey is statistically accurate.

The steps that follow are suitable for finding a sample size for continuous data – i.e. data that is counted numerically. It doesn’t apply to categorical data – i.e. put into categories like green, blue, male, female etc.

Stage 1: Consider your sample size variables

Before you can calculate a sample size, you need to determine a few things about the target population and the level of accuracy you need:

1. Population size

How many people are you talking about in total? To find this out, you need to be clear about who does and doesn’t fit into your group. For example, if you want to know about dog owners, you’ll include everyone who has at some point owned at least one dog. (You may include or exclude those who owned a dog in the past, depending on your research goals.) Don’t worry if you’re unable to calculate the exact number. It’s common to have an unknown number or an estimated range.

2. Margin of error (confidence interval)

Errors are inevitable – the question is how much error you’ll allow. The margin of error , AKA confidence interval, is expressed in terms of mean numbers. You can set how much difference you’ll allow between the mean number of your sample and the mean number of your population. If you’ve ever seen a political poll on the news, you’ve seen a confidence interval and how it’s expressed. It will look something like this: “68% of voters said yes to Proposition Z, with a margin of error of +/- 5%.”

3. Confidence level

This is a separate step to the similarly-named confidence interval in step 2. It deals with how confident you want to be that the actual mean falls within your margin of error. The most common confidence intervals are 90% confident, 95% confident, and 99% confident.

4. Standard deviation

This step asks you to estimate how much the responses you receive will vary from each other and from the mean number. A low standard deviation means that all the values will be clustered around the mean number, whereas a high standard deviation means they are spread out across a much wider range with very small and very large outlying figures. Since you haven’t yet run your survey, a safe choice is a standard deviation of .5 which will help make sure your sample size is large enough.

Stage 2: Calculate sample size

Now that you’ve got answers for steps 1 – 4, you’re ready to calculate the sample size you need. This can be done using an  online sample size calculator  or with paper and pencil.

1. Find your Z-score

Next, you need to turn your confidence level into a Z-score. Here are the Z-scores for the most common confidence levels:

• 90% – Z Score = 1.645
• 95% – Z Score = 1.96
• 99% – Z Score = 2.576

If you chose a different confidence level, use this  Z-score table  (a resource owned and hosted by SJSU.edu) to find your score.

2. Use the sample size formula

Plug in your Z-score, standard of deviation, and confidence interval into the  sample size calculator  or use this sample size formula to work it out yourself:

This equation is for an unknown population size or a very large population size. If your population is smaller and known, just  use the sample size calculator.

What does that look like in practice?

Here’s a worked example, assuming you chose a 95% confidence level, .5 standard deviation, and a margin of error (confidence interval) of +/- 5%.

((1.96)2 x .5(.5)) / (.05)2

(3.8416 x .25) / .0025

.9604 / .0025

385 respondents are needed

Voila! You’ve just determined your sample size.

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How to calculate sample size using a sample size formula.

Learn how to calculate sample size with a margin of error using these simple sample size formulas for your market research.

Anika Nishat

March 22, 2024

What is sample size determination and why is it important

Finding an appropriate sample size, otherwise known as sample size determination, is a crucial first step in market research. Understanding why sample size is important is equally crucial. The answer: it ensures the robustness, reliability, and believability of your research findings. But how is sample size determined?

Calculating your sample size

During the course of your market research , you may be unable to reach the entire population you want to gather data about. While larger sample sizes bring you closer to a 1:1 representation of your target population, working with them can be time-consuming, expensive, and inconvenient. However, small samples risk yielding results that aren’t representative of the target population. It can be tricky because determining the ideal sample size for statistical significance ensures your research yields reliable and actionable insights.

Luckily, you can easily identify an ideal subset that represents the population and produces strong, statistically significant results that don’t gobble up all of your resources. In this article, we’ll teach you how to calculate sample size with a margin of error to identify that subset.

Five steps to finding your sample size

• Define population size or number of people

Designate your margin of error

• Determine your confidence level
• Predict expected variance
• Finalize your sample size

What is a good statistical sample size can vary depending on your research goals. But by following these five steps, you'll ensure you get the right selection size for your research needs.

Download: The State of AI in Market Research

Define the size of your population.

Your sample size needs will differ depending on the true population size or the total number of people you're looking to conclude on. That's why determining the minimum sample size for statistical significance is an important first step.

Defining the size of your population can be easier said than done. While there is a lot of population data available, you may be targeting a complex population or for which no reliable data currently exists.

Knowing the size of your population is more important when dealing with relatively small, easy-to-measure groups of people. If you're dealing with a larger population, take your best estimate, and roll with it.

This is the first step in a sample size formula, yielding more accurate results than a simple estimate – and accurately reflecting the population.

Random sample errors are inevitable whenever you're using a subset of your total population. Be confident that your results are accurate by designating how much error you intend to permit: that's your margin of error.

Sometimes called a "confidence interval," a margin of error indicates how much you're willing for your sample mean to differ from your population mean . It's often expressed alongside statistics as a plus-minus (±) figure, indicating a range which you can be relatively certain about.

For example, say you take a sample proportion of your colleagues with a designated 3% margin of error and find that 65% of your office uses some form of voice recognition technology at home. If you were to ask your entire office, you could be sure that in reality, as low as 62% and as high as 68% might use some form of voice recognition technology at home.

Determine how confident you can be

Your confidence level reveals how certain you can be that the true proportion of the total population would pick an answer within a particular range. The most common confidence levels are 90%, 95%, and 99%. Researchers most often employ a 95% confidence level.

Don't confuse confidence levels for confidence intervals (i.e., mean of error). Remember the distinction by thinking about how the concepts relate to each other to sample more confidently.

In our example from the previous step, when you put confidence levels and intervals together, you can say you're 95% certain that the true percentage of your colleagues who use voice recognition technology at home is within ± three percentage points from the sample mean of 65%, or between 62% and 68%.

Your confidence level corresponds to something called a "z-score." A z-score is a value that indicates the placement of your raw score (meaning the percent of your confidence level) in any number of standard deviations below or above the population mean.

Z-scores for the most common confidence intervals are:

• 90% = 2.576
• 99% = 2.576

While not as commonly used, the z-score for an 80% confidence interval is approximately 1.28. If you're using a different confidence interval, use this z-score table . A z-score sample calculator like this will quickly determine the appropriate value for your chosen confidence level.

Predict variance by calculating standard deviation in a sample

The last thing you'll want to consider when calculating your sample size is the amount of variance you expect to see among participant responses.

The standard deviation in a sample measures how much individual sample data points deviate from the average population.

Don't know how much variance to expect? Use the standard deviation of 0.5 to make sure your group is large enough.

Read: Best Practices for Writing Discussion Guides (eBook)

Finding your ideal sample size.

Now that you know what goes into determining sample size, you can easily calculate sample size online. Consider using a sample size calculator to ensure accuracy. Or, calculate it the old-fashioned way: by hand.

Below, find two sample size calculations - one for the known population proportion and one for the unknown population.

Sample size for known population

Sample size for unknown population

Here’s how the calculations work out for our voice recognition technology example in an office of 500 people, with a 95% confidence level and 5% margin of error:

There you have it! 197 respondents are needed.

You can tweak some things if that number is too big to swallow.

Try increasing your margin of error or decreasing your confidence level. This will reduce the number of respondents necessary but, unfortunately, increase the chances of errors. Even so, understanding why trade-offs are necessary in sample size determination can help you make informed decisions.

Summing Up Sample Size

Calculating sample size sounds complicated - but, utilizing an easy sample size formula and even calculators are now available to make this tedious part of market research faster!

Once you've determined your sample size, you're ready to create and distribute your sample market research survey. This can be done through methods like running a focus group or even a customer satisfaction survey . Whatever you decide, you now have the information needed to make decisions with confidence.

Want to whip your research skills into shape? Check out our go-to eBook on writing discussion guides !

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Dive Deeper

Calculate your ideal sample size

Last updated

11 May 2023

Reviewed by

Miroslav Damyanov

Whether you're conducting market research , medical trials, or social science studies, understanding how to calculate your ideal sample size is essential for a successful research project .

Make research less tedious

Dovetail streamlines research to help you uncover and share actionable insights

• What is a sample size?

The sample size is the number of participants or data points a researcher needs to collect to make inferences about a larger population. Researchers use sample size to conclude a population. 

For example, if a researcher wants to know the average height of adult males in the United States, the population would be all adult males in the US. The researcher would collect a sample of adult males, measure their height, and use this information to estimate the average size of all adult males in the US. 

• Understanding sample size

Comprehending sample size is vital for conducting meaningful research that provides reliable and accurate results. Here are some key concepts that can help you better understand this critical aspect of research:

Representativeness

A sample is considered emblematic if it accurately reflects the population characteristics from which it’s drawn. To ensure representativeness, researchers should use appropriate sampling methods , such as random or stratified sampling .

Confidence level

This is the degree of certainty the results obtained from a sample accurately represent the population. A confidence level of 95% means there is a 95% chance the population parameter falls within the confidence interval .

The margin of error

The margin of error is the sampling error expected in the results due to using a cross-section instead of the entire population. 

This refers to the ability of a study to detect an actual effect—if it exists. A study with high power has a greater chance of detecting a significant impact, while a study with low power may fail to see the effect, even if it exists.

Effect size

This is the magnitude of the difference between groups or the strength of the relationship between variables. The larger the effect size, the stronger the relationship.

By selecting an appropriate sample size, researchers can ensure their findings represent the population being studied and have the necessary level of precision and confidence.

Does having a statistically significant sample size matter?

A statistically significant sample size is the minimum number of participants required to detect a meaningful difference in the studied population. Statistical significance doesn't guarantee the validity or importance of the study results. 

However, it provides evidence that the observed differences in the sample are unlikely coincidental. Therefore, a statistically significant sample size is vital in drawing valid conclusions and making informed decisions based on the study results.

• How to calculate sample size

Quantifying the ideal sample size requires careful consideration of several factors, including the research question , the desired accuracy, and the confidence level. Here's a general overview of how to calculate sample size:

Power analysis is a statistical method used to determine the ideal sample size based on the effect size, the significance level, and the study's desired power. 

Confidence intervals are an analytical method used to estimate the range of values probable to contain the actual population variable with a certain confidence level. 

The margin of error is a demographic method used to gauge the scope of values likely to have the true population parameter with a certain precision level. 

The sample size calculation may differ depending on the statistical method and study design.

Sample size calculator

Maximize your research’s impact with the right sample size and get an accurate representation of your target audience.

Sample size

The total number of people whose opinion or behavior your sample will represent.

The probability that your sample accurately reflects the attitudes of your population. The industry standard is 95%.

The range (measured as a percentage) that your population’s responses may deviate from your sample’s.

Sample size formula

The formulas for calculating sample size depend on the statistical method used. Here are the commonly used formulas:

Power analysis : N = [(Zα/2 + Zβ) / ES] ^ 2

N = sample size

Zα/2 = the critical value of the standard normal distribution for a specified level of significance

Zβ = the critical value of the standard normal distribution for a particular power of the study

ES = the effect size, representing the magnitude of the difference or effect the study tries to detect

Confidence intervals :  n = [(z * σ) / E] ^ 2

z = the critical value of the standard normal distribution for a specified level of confidence

σ = the standard deviation of the population

E = the desired margin of error

The margin of error : MOE = Z * (σ / √n)

Z = the z-score associated with the desired level of confidence (e.g., for 95% confidence, Z = 1.96)

n = the sample size

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Optimize your research’s impact when you improve the margin of error.

Margin of error

The number of people who took your survey.

These formulas are general guidelines, and researchers should consult with a statistician or use statistical software to ensure the sample size calculation is appropriate for their particular research question and study design.

Is a larger sample size better?

Yes, a larger sample size is better. A larger sample size increases the statistical power of a study, meaning it's more likely to detect actual effects or differences between groups.

Why use a sample size calculator?

A sample size calculator is used to determine the optimal sample size needed to obtain reliable and valid results in a study. It considers several factors, including the desired level of statistical power, the expected effect size, and the significance level.

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How to Write a Research Proposal: (with Examples & Templates)

Table of Contents

Before conducting a study, a research proposal should be created that outlines researchers’ plans and methodology and is submitted to the concerned evaluating organization or person. Creating a research proposal is an important step to ensure that researchers are on track and are moving forward as intended. A research proposal can be defined as a detailed plan or blueprint for the proposed research that you intend to undertake. It provides readers with a snapshot of your project by describing what you will investigate, why it is needed, and how you will conduct the research.  

Your research proposal should aim to explain to the readers why your research is relevant and original, that you understand the context and current scenario in the field, have the appropriate resources to conduct the research, and that the research is feasible given the usual constraints.  

This article will describe in detail the purpose and typical structure of a research proposal , along with examples and templates to help you ace this step in your research journey.  

What is a Research Proposal ?  

A research proposal¹ ,²  can be defined as a formal report that describes your proposed research, its objectives, methodology, implications, and other important details. Research proposals are the framework of your research and are used to obtain approvals or grants to conduct the study from various committees or organizations. Consequently, research proposals should convince readers of your study’s credibility, accuracy, achievability, practicality, and reproducibility.   

With research proposals , researchers usually aim to persuade the readers, funding agencies, educational institutions, and supervisors to approve the proposal. To achieve this, the report should be well structured with the objectives written in clear, understandable language devoid of jargon. A well-organized research proposal conveys to the readers or evaluators that the writer has thought out the research plan meticulously and has the resources to ensure timely completion.  

Purpose of Research Proposals  

A research proposal is a sales pitch and therefore should be detailed enough to convince your readers, who could be supervisors, ethics committees, universities, etc., that what you’re proposing has merit and is feasible . Research proposals can help students discuss their dissertation with their faculty or fulfill course requirements and also help researchers obtain funding. A well-structured proposal instills confidence among readers about your ability to conduct and complete the study as proposed.  

Research proposals can be written for several reasons:³  

• To describe the importance of research in the specific topic  
• Address any potential challenges you may encounter  
• Showcase knowledge in the field and your ability to conduct a study  
• Apply for a role at a research institute  
• Convince a research supervisor or university that your research can satisfy the requirements of a degree program  
• Highlight the importance of your research to organizations that may sponsor your project  
• Identify implications of your project and how it can benefit the audience  

What Goes in a Research Proposal?    

Research proposals should aim to answer the three basic questions—what, why, and how.  

The What question should be answered by describing the specific subject being researched. It should typically include the objectives, the cohort details, and the location or setting.  

The Why question should be answered by describing the existing scenario of the subject, listing unanswered questions, identifying gaps in the existing research, and describing how your study can address these gaps, along with the implications and significance.  

The How question should be answered by describing the proposed research methodology, data analysis tools expected to be used, and other details to describe your proposed methodology.   

Research Proposal Example  

Here is a research proposal sample template (with examples) from the University of Rochester Medical Center. 4 The sections in all research proposals are essentially the same although different terminology and other specific sections may be used depending on the subject.  

Structure of a Research Proposal  

If you want to know how to make a research proposal impactful, include the following components:¹  

1. Introduction  

This section provides a background of the study, including the research topic, what is already known about it and the gaps, and the significance of the proposed research.  

2. Literature review  

This section contains descriptions of all the previous relevant studies pertaining to the research topic. Every study cited should be described in a few sentences, starting with the general studies to the more specific ones. This section builds on the understanding gained by readers in the Introduction section and supports it by citing relevant prior literature, indicating to readers that you have thoroughly researched your subject.  

3. Objectives  

Once the background and gaps in the research topic have been established, authors must now state the aims of the research clearly. Hypotheses should be mentioned here. This section further helps readers understand what your study’s specific goals are.  

4. Research design and methodology  

Here, authors should clearly describe the methods they intend to use to achieve their proposed objectives. Important components of this section include the population and sample size, data collection and analysis methods and duration, statistical analysis software, measures to avoid bias (randomization, blinding), etc.  

5. Ethical considerations  

This refers to the protection of participants’ rights, such as the right to privacy, right to confidentiality, etc. Researchers need to obtain informed consent and institutional review approval by the required authorities and mention this clearly for transparency.  

6. Budget/funding  

Researchers should prepare their budget and include all expected expenditures. An additional allowance for contingencies such as delays should also be factored in.  

7. Appendices  

This section typically includes information that supports the research proposal and may include informed consent forms, questionnaires, participant information, measurement tools, etc.  

8. Citations  

Important Tips for Writing a Research Proposal  

Writing a research proposal begins much before the actual task of writing. Planning the research proposal structure and content is an important stage, which if done efficiently, can help you seamlessly transition into the writing stage. 3,5  

The Planning Stage  

• Manage your time efficiently. Plan to have the draft version ready at least two weeks before your deadline and the final version at least two to three days before the deadline.
• What is the primary objective of your research?  
• Will your research address any existing gap?  
• What is the impact of your proposed research?  
• Do people outside your field find your research applicable in other areas?  
• If your research is unsuccessful, would there still be other useful research outcomes?  

  The Writing Stage  

• Create an outline with main section headings that are typically used.  
• Focus only on writing and getting your points across without worrying about the format of the research proposal , grammar, punctuation, etc. These can be fixed during the subsequent passes. Add details to each section heading you created in the beginning.   
• Ensure your sentences are concise and use plain language. A research proposal usually contains about 2,000 to 4,000 words or four to seven pages.  
• Don’t use too many technical terms and abbreviations assuming that the readers would know them. Define the abbreviations and technical terms.  
• Ensure that the entire content is readable. Avoid using long paragraphs because they affect the continuity in reading. Break them into shorter paragraphs and introduce some white space for readability.  
• Focus on only the major research issues and cite sources accordingly. Don’t include generic information or their sources in the literature review.  
• Proofread your final document to ensure there are no grammatical errors so readers can enjoy a seamless, uninterrupted read.  
• Use academic, scholarly language because it brings formality into a document.  
• Ensure that your title is created using the keywords in the document and is neither too long and specific nor too short and general.  
• Cite all sources appropriately to avoid plagiarism.  
• Make sure that you follow guidelines, if provided. This includes rules as simple as using a specific font or a hyphen or en dash between numerical ranges.  
• Ensure that you’ve answered all questions requested by the evaluating authority.  

Key Takeaways   

Here’s a summary of the main points about research proposals discussed in the previous sections:  

• A research proposal is a document that outlines the details of a proposed study and is created by researchers to submit to evaluators who could be research institutions, universities, faculty, etc.  
• Research proposals are usually about 2,000-4,000 words long, but this depends on the evaluating authority’s guidelines.  
• A good research proposal ensures that you’ve done your background research and assessed the feasibility of the research.  
• Research proposals have the following main sections—introduction, literature review, objectives, methodology, ethical considerations, and budget.  

Frequently Asked Questions  

Q1. How is a research proposal evaluated?  

A1. In general, most evaluators, including universities, broadly use the following criteria to evaluate research proposals . 6  

• Significance —Does the research address any important subject or issue, which may or may not be specific to the evaluator or university?  
• Content and design —Is the proposed methodology appropriate to answer the research question? Are the objectives clear and well aligned with the proposed methodology?  
• Sample size and selection —Is the target population or cohort size clearly mentioned? Is the sampling process used to select participants randomized, appropriate, and free of bias?  
• Timing —Are the proposed data collection dates mentioned clearly? Is the project feasible given the specified resources and timeline?  
• Data management and dissemination —Who will have access to the data? What is the plan for data analysis?  

Q2. What is the difference between the Introduction and Literature Review sections in a research proposal ?  

A2. The Introduction or Background section in a research proposal sets the context of the study by describing the current scenario of the subject and identifying the gaps and need for the research. A Literature Review, on the other hand, provides references to all prior relevant literature to help corroborate the gaps identified and the research need.  

Q3. How long should a research proposal be?  

A3. Research proposal lengths vary with the evaluating authority like universities or committees and also the subject. Here’s a table that lists the typical research proposal lengths for a few universities.  

Q4. What are the common mistakes to avoid in a research proposal ?  

A4. Here are a few common mistakes that you must avoid while writing a research proposal . 7  

• No clear objectives: Objectives should be clear, specific, and measurable for the easy understanding among readers.  
• Incomplete or unconvincing background research: Background research usually includes a review of the current scenario of the particular industry and also a review of the previous literature on the subject. This helps readers understand your reasons for undertaking this research because you identified gaps in the existing research.  
• Overlooking project feasibility: The project scope and estimates should be realistic considering the resources and time available.   
• Neglecting the impact and significance of the study: In a research proposal , readers and evaluators look for the implications or significance of your research and how it contributes to the existing research. This information should always be included.  
• Unstructured format of a research proposal : A well-structured document gives confidence to evaluators that you have read the guidelines carefully and are well organized in your approach, consequently affirming that you will be able to undertake the research as mentioned in your proposal.  
• Ineffective writing style: The language used should be formal and grammatically correct. If required, editors could be consulted, including AI-based tools such as Paperpal , to refine the research proposal structure and language.  

Thus, a research proposal is an essential document that can help you promote your research and secure funds and grants for conducting your research. Consequently, it should be well written in clear language and include all essential details to convince the evaluators of your ability to conduct the research as proposed.  

This article has described all the important components of a research proposal and has also provided tips to improve your writing style. We hope all these tips will help you write a well-structured research proposal to ensure receipt of grants or any other purpose.  

References  

• Sudheesh K, Duggappa DR, Nethra SS. How to write a research proposal? Indian J Anaesth. 2016;60(9):631-634. Accessed July 15, 2024. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5037942/  
• Writing research proposals. Harvard College Office of Undergraduate Research and Fellowships. Harvard University. Accessed July 14, 2024. https://uraf.harvard.edu/apply-opportunities/app-components/essays/research-proposals  
• What is a research proposal? Plus how to write one. Indeed website. Accessed July 17, 2024. https://www.indeed.com/career-advice/career-development/research-proposal  
• Research proposal template. University of Rochester Medical Center. Accessed July 16, 2024. https://www.urmc.rochester.edu/MediaLibraries/URMCMedia/pediatrics/research/documents/Research-proposal-Template.pdf  
• Tips for successful proposal writing. Johns Hopkins University. Accessed July 17, 2024. https://research.jhu.edu/wp-content/uploads/2018/09/Tips-for-Successful-Proposal-Writing.pdf  
• Formal review of research proposals. Cornell University. Accessed July 18, 2024. https://irp.dpb.cornell.edu/surveys/survey-assessment-review-group/research-proposals  
• 7 Mistakes you must avoid in your research proposal. Aveksana (via LinkedIn). Accessed July 17, 2024. https://www.linkedin.com/pulse/7-mistakes-you-must-avoid-your-research-proposal-aveksana-cmtwf/  

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Get accurate academic translations, rewriting support, grammar checks, vocabulary suggestions, and generative AI assistance that delivers human precision at machine speed. Try for free or upgrade to Paperpal Prime starting at US$19 a month to access premium features, including consistency, plagiarism, and 30+ submission readiness checks to help you succeed.  

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Related Reads:

• How to Paraphrase Research Papers Effectively
• How to Cite Social Media Sources in Academic Writing? 
• What is the Importance of a Concept Paper and How to Write It 

APA format: Basic Guide for Researchers

The future of academia: how ai tools are changing the way we do research, you may also like, the ai revolution: authors’ role in upholding academic..., the future of academia: how ai tools are..., how to choose a dissertation topic, how to write a phd research proposal, how to write an academic paragraph (step-by-step guide), five things authors need to know when using..., 7 best referencing tools and citation management software..., maintaining academic integrity with paperpal’s generative ai writing..., research funding basics: what should a grant proposal....

Sample size estimation for health and social science researchers: The principles and considerations for different study designs

• Nigerian Postgraduate Medical Journal 27(2):67
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Sample Size Estimation for Health and Social Science Researchers

The principles and considerations for different study designs.

Bolarinwa, Oladimeji Akeem

Department of Epidemiology and Community Health, Faculty of Clinical Sciences, University of Ilorin, Ilorin, Nigeria

Address for correspondence: Dr. Oladimeji Akeem Bolarinwa, Department of Epidemiology and Community Health, Faculty of Clinical Sciences, University of Ilorin, Ilorin, Nigeria. E-mail: [email protected]

Received February 01, 2020

Received in revised form February 29, 2020

Accepted March 16, 2020

Sample size is one of the important considerations at the planning phase of a research proposal, but researchers are often faced with challenges of estimating valid sample size. Many researchers frequently use inadequate sample size and this invariably introduces errors into the final findings. Many reviews on sample size estimation have focused more on specific study designs which often present technical equations and formula that are boring to statistically naïve health researchers. Therefore, this compendium reviews all the common sample size estimation formula in social science and health research with the aim of providing basic guidelines and principles to achieve valid sample size estimation. The simplification of the sample size formula and detailed explanation in this review will demystify the difficulties many students as well as some researchers have with statistical formulae for sample size estimation.

Every scientific research requires carefully designed methods to produce valid and relevant results. In achieving such results, a scientifically proven sample size estimation must be adopted. In almost all quantitative researches, sample size will be required to provide credible findings. Therefore, sample size estimation is a vital consideration at the concept development and proposal phase in research. One of the key questions health researchers are likely to ask is, how much of a population is needed for valid and reliable study? In some instances, researchers may choose to study all those within a target population. This is possible when the entire population of interest is small and there are resources to study them. This scenario is called exhaustive survey,[ 1 ] and in this instance, a sample size calculation may not be required or may not be applicable even when estimated. In most instances, it is not feasible to study the entire subjects or respondents in a population of interest. Therefore, a sample or sub-set of the population will be required.[ 1 2 ] It will be impractical to study the entire population of interest, when there is large geographical spread of the population, when the subjects within the population are too large and when there are limited resources to study the whole population. In all these situations, a scientific method of selecting representatives of the population will be vital.

In health and social science research, scientists are often faced with challenges of estimating valid sample sizes. Many researchers frequently use inadequate sample size and this invariably introduces errors into the final findings. Taking ‘too much’ or ‘too small’ of a population sample is not only a waste of scarce resources but the researcher is also working with wrong research assumptions[ 3 ] which could possibly have ethical concerns as well. This will undermine the integrity of the outcome of the study with spurious effects on future researches that may use such outcomes. In essence, sample size should be ‘large enough’ that an effect or precision of such magnitude as to be of scientific or clinical significance will also be statistically significant. Sample size is so important that it has evidential link with previous studies, characteristics of the population of interest, scientific assumptions, allowable study errors, sampling methods, analysis methods and study designs. Available literatures on sample size focused more on specific study designs and often present technical equations and formula that are boring to statistically naïve health researchers. This compendium reviews all the common sample size estimation formulae in social science and health research. In addition, it provides basic guidelines and principles to achieve valid estimation. The simplification of the sample size formula and detailed explanation in this review will demystify statistical formulae in sample size estimation for researchers.

IMPORTANCE OF SAMPLE SIZE DETERMINATION IN HEALTH RESEARCH

Both internal and external validities of the research are ensured with an accurately estimated sample size that leveraged on previous studies or evidences. When representativeness in a study is accurately determined, it ensures that it measured the population attributes it purports to study. In human and animal experiment, sample size is a pivotal issue for ethical reasons. Inadequate sample size will produce scientific inference with small power. This will expose subjects to potentially harmful treatments without advancing knowledge. On the other hand, oversized experiments will recruit an unnecessarily large number of subjects into the study. This will in turn expose them to unnecessary harmful treatment. The volunteer in the study will be needlessly troubled without the study adding significant contribution to scientific knowledge.

DYNAMICS OF SAMPLE SIZE DETERMINATION

Some researchers have classified sample size determination into four depending on the aim and procedure involved.[ 2 ] These are; sample size estimation/determination, sample size justification, sample size adjustment and sample size re-estimation. Sample size estimation/determination requires the actual calculation using scientific assumption and evidence to achieve desired statistical significance of valid and reliable outcome. This is the most common method which requires attributes such as prevalence, proportion and means from previous studies. Predetermined assumptions for validity and reliability such as power of study, level of significance and design effect (Deff) may be needed in sample size estimation.[ 2 ] Sample size justification is necessary when a sample size is already chosen. It becomes expedient for the researcher to provide a ‘statistical justification’ for the selected sample size.[ 2 ] Usually, a small size of the population will be recruited initially due to budgetary constraints or for medical consideration. A good example of this is the sample size in the first phase of clinical trials. Various methods for sample size adjustment have been described in the literature.[ 1 ][ 2 ][ 3 4 ] For reasons like small study population, e.g., for instance a population <10,000, expected attrition or dropouts, non-response, covariates, e.g., controlling for confounders[ 2 3 ] and Deff in cluster sampling.[ 1 4 ] These adjustments are for the purpose of yielding sufficient number of analysable subjects for valid statistical findings of the health research.[ 2 ] In sample size re-estimation, there is no known or little evidence in the literature about some attributes to be studied, especially past prevalence, incidence and means. In some other instances, certain aspect of the study needs to be monitored for safety and relevance before exposing more participants to the intervention. Therefore, there may be a need for a pilot study or interim study (in clinical trials).[ 2 ] In these situations, sample size re-estimation is required to adjust for the initial sample size calculated for the pilot study and to confirm the preliminary study assumptions such as power. In this manuscript, sample size estimation, calculation and determination will be used exchangeable. Of all the four methods, sample size estimation will be discussed extensively in this review. A little note will be added towards the end of the review on sample size adjustment.

GENERAL CONSIDERATIONS IN SAMPLE SIZE DETERMINATION

It is very important to understand the dimensions of the research to be conducted in terms of characteristics of the proposed study population, the appropriate study designs and the intended methods of analysis.[ 5 ] Characteristics of the population are relevant consideration in sample size determination. These characteristics could be human sociodemography, animal species, human body parts or system to be studied and type of health records available. Study sites' characteristics should also be considered. Some of the study site characteristics are community setup, household, hospital or institutional-based study sites, geographic spread, confinement and security considerations. The study designs have great influence on analysis methods. As will be shown later, a good idea of the proposed study design that is appropriate for the study concept and analysis method will help define the appropriate sample size estimation for the study. Explicitly, the following study characteristics are essential to the validity of sample size determination.

Objectives or hypothesis

The objectives, research question and hypothesis are interrelated considerations to choosing the best sample size determination.[ 2 ] For some studies, these considerations may have more than one attributes (prevalence, incidence and means) which needed to be well thought-out before estimating the sample size. For instance, the prevalence in a study that aimed at assessing the treatment outcomes and health-related quality of life of hypertensive patients attending a local hospital has more than one dependent variables, e.g., clinical outcomes and quality of life, to consider when estimating sample size. Literatures agreed that researchers should calculate for all the attributes and choose the higher or highest sample size.[ 2 5 ] Another consideration is the direction of the null hypothesis stated. Is the hypothesis one-tail or two-tail test? This is more relevant in analytical study types, especially experimental studies and some descriptive studies. As would be discussed later, the hypothesis connects sample size and the methods of analysis of the study.

Study designs

A properly applied study design will need appropriate sample size based on whether the study is descriptive (cross-sectional, surveys or case studies types) or analytical (observational or experimental types).[ 2 5 ] A good study requires that each of the study design has specific sample size estimation consideration. For example, a cross-sectional study that aimed at assessing the health-care utilisation pattern in a community will need not set power (1-type 2 error) for the sample size estimation. Whereas, a clinical trial that aims at assessing the effectiveness of drug X as against drug Y will be interested in setting a stringent power.

ELEMENTS REQUIRED FOR SAMPLE SIZE DETERMINATION

Outcome variable/parameter/endpoints.

In health research, units of measuring variables are of two classes. It is either numeric or categorical. These two categories have other sub-types of units of measurement. The unit of measurement in categorical variables is in proportion (percentages and rates) and at times could be in ratio. The numeric variables are presented as means and median mostly (measures of central tendency). In some health researches, odd ratio (OR) and relative risk are also measured as outcome variables. The chosen unit of measurement in sample size estimation should be taken into consideration at all time.[ 4 6 ] A previous literature that uses the same or similar unit of measurement for the variable should be adopted for the sample size estimation. However, in some instances, a variable could be interpreted in more than one unit of measurement in health research. For example, blood pressure (BP) can be expressed as a mean value in mmHg. It can also be reported as controlled BP or uncontrolled BP. Another classification of BP could be optimal, Grade I, Grade II or Grade III.

Variability of the parameter

This is the measure of how spread out or dispersed individual unit in a variable is from the middle. The wider the variability, the more sample size that will be required to achieve a significant effect size if any. The reason is that any two highly dispersed variables being compared will overlap.[ 5 ] For the numeric parameters, the measures of dispersion for a sample mean is variance (standard deviation), whereas for median is range (interquartile range). These are usually reported by previous literatures and available for the researcher to leverage on to estimate the study sample size. However, for categorical parameter, the variability for sample proportions is based on spread towards 0.5 (or 50%). If a previous study reported a prevalence of 0.5 (50%), the dispersion will also equal 0.5 (that is 1–0.5). A prevalence tending towards 50% indicates maximum variability.[ 7 ] The prevalence moving towards extreme of the spectrum 100% (or 1) and 0 will not have as much variability. This simply means that majority of the sample population possess or do not possess the attribute of interest.[ 7 ]

Detectable difference (effect size) of the parameter

This is the smallest clinical effect that is detectable in the finding.[ 5 8 ] It is a parameter that elicits the difference in the outcome of one arm of study (intervention, experimental or study group) to the other arm (control or comparator). It is the attribute of analytical studies which determines the probability that an independent factor will be strongly associated with an outcome or dependent variable.[ 5 ] Depending on the unit of measuring the outcome variables, effect size could be mean difference or change in the proportion. It is expedient to mention that effect size is interrelated to the hypothesis set at the beginning of the research, the outcome measurement and clinically detectable difference in the outcome measurement. As a general rule of thumb, a small effect size will require a large sample size to be able to detect a clinically meaningful difference, whereas a large effect size will require a small sample size.[ 4 5 ] The effect sizes to input in sample size estimation are often obtained from previous research.

Three variants of detectable difference have been described in the literature.[ 2 ] Absolute difference means that a clinically acceptable effect size can be presumably set for the study. For instance, a difference of 5 mmHg can be presumed to be clinically acceptable between a new and the existing drug for hypertension treatment. Relative difference requires that researcher set the study to detect certain change in proportion of a clinical outcome. For example, a 10% decrease in systolic BP can be set to be of practical importance (20%–30% is usually taken as clinically acceptable). Cohen, decades ago, established that for an experimental (interventional) study with 2 arms of comparison, a ratio of effect size and standard deviation termed standardised effect size or standard difference can be applied.[ 8 9 ] The standardised effect size was classified as small, medium or big if this ratio is 0.2, 0.5 and 0.8, respectively.[ 8 ]

Error rates

The concept of error assumption in research stemmed from the hypothesis testing.[ 2 5 8 ] The type of error committed when researcher wrongly rejects a null hypothesis that is true is called type I or alpha (α) error. This is also described as ' failure to accept a true null hypothesis ' .[ 2 5 8 ] On the other hand, type II or beta (β) error means to wrongly accept a false null hypothesis. It is also described as ' failure to reject a false null hypothesis'.[ 2 5 8 ] The implication of type I error (α) is that the researcher has to set an assumption for the level of type I error he/she wishes to allow in the study. This assumption of type I error is also called setting 'level of significance ( P value)'. It is frequently set at 5% which means the researcher is willing to allow the 5% probability of 'failure to accept a true null hypothesis ' . However, some researches such as clinical trials can set a very small α-error. The smaller the α-error, the larger the sample size required.[ 8 ] The level of significant thereby means that at less than 5% ( P = 0.05) or 1% ( P = 0.01 in stringent trials) of error, the variations observed in the outcome are due to chance and not due to ' too much error'.[ 10 ] An important caution here is that majority of the analysis software like SPSS, set P -value at 0.05 as a default. Consequently, if there is a need to use P value lower than 5%, the researcher needs to change this from the software setting to the desired value. Otherwise, the researcher's assumption of P value of 1% could be erroneously presenting the result at P value of 5%. Another note of relevance is that when researcher fails to reject null hypothesis, it does not mean that it is true, it is just that there is not enough evidence to reject the null hypothesis.[ 10 ]

Type II error (β, beta error) on the other hand gives rise to ' power ' of the study which is 1-β.[ 2 5 8 10 ] The power of the study therefore means the other proportion left behind after removing the errors committed by wrongly accepting a false null hypothesis [ Figure 1 ]. This connotes a proportion of rightly rejected false null hypothesis.[ 2 5 ] Power of the study is often assumed or set at the proposal stage similar to the level of significance. For example, suppose a researcher assumes a 20% β-error, the power of the study will be set at 80%.[ 2 5 8 ] Random values of 0.05 for α and 0.2 for β (power, 0.8) are often used by researchers, but conventionally, α values could range from 0.01 to 0.10, whereas β can be set between 0.05 (power, 0.95) and 0.20 (power, 0.80).[ 5 ] Like the α error, the lower the β (higher power), the larger the sample size is required to achieve clinically detectable changes in the outcome.[ 2 5 8 ] As applicable to the actual sample size estimation formula, the values of α and β cannot be used directly. This required conversion on the standard normal deviate in the Gaussian curve.[ 8 ] This is called the Z -scores denoted as Z α and Z β for α and β errors, respectively [ Table 1 ]. Fianlly, a few clarification need to be stated about the relationship between confidence level and α-error. Similar to the power of the study, confidence level simply means the other proportion left behind after removing the α-error (1− α) usually set as 0.95 as shown in Figure 1 .[ 11 ] It is the precision of the study which means the confidence of not rejecting a true null hypothesis.[ 2 ] For analytical studies, setting a confidence interval (CI) means that the interval of the width of the confidence level will be estimated during analysis.[ 2 ] The CI like the P value indicates the statistical significance of the study outcomes.

SAMPLE SIZE ESTIMATION FOR DIFFERENT STUDY DESIGNS AND STATISTICAL ANALYSIS

Cross-sectional studies and surveys.

Prevalence studies and surveys are descriptive in nature. They are employed to show the associations between factors and generated hypothesis for future researches.[ 4 ] Estimating sample size for these type of research requires outcomes/variables/parameters such as prevalence, incidence, means, rates and ratios. Out of all these, prevalence ( p ) and means (μ) are commonly used for outcomes that are categorical (qualitative) or numeric (quantitative) in nature. The variability for each of P (1 − p ) and μ (variance = σ), normal standard deviate for α-error ( Z α ) and a precision level (δ) usually assumed at 5% (0.05) are all required. The followings depict the formula for both the categorical and numeric outcome variable cross-sectional studies:[ 4 6 8 12 ]

a. Categorical outcome (proportion)

b. Numeric outcome (mean).

Analytical studies: Independent case–control and cohort studies

In this type of studies, there are comparator groups called 'controls ' that are weighed against the group with the attributes been studied called ‘cases’. While the case–control study captures the cases with outcome (disease or other health related issue) and search retrospectively to determine the exposed factors, the cohort study starts from exposed factors and follow the cohort prospectively to determine the associated outcomes. Only few studies have extensively documented sample size formula for case–control and cohort studies.[ 6 7 13 ] Other study variants' formula (such as matched and paired studies) can be found in some other literature[ 7 ] and internet sources. Formulae for independent studies are shown in this review.

c. Independent case–control (retrospective study).[ 7 13 ]

In equation C (1), N is the estimated sample size for the independent case–control, Z α is the standard normal deviate for α error and Z β is the standard normal deviate for power (1−β error ). P * is the average probability of the exposure (similar to pooled variance or proportion) calculated as shown in formula C (2). m is ratio of control subjects to case subjects desired, while P 1 is the probability of exposure in the control group, calculated in equation C (3) f rom known prevalence of the exposure from the population ( P 0 ) and OR (ω) of the exposure between cases and control.[ 7 ] As shown in C (4) formula, N c is the continuity-adjusted sample size for further analysis such as Chi-square and Fisher's exact, taking into consideration the ratio of control to case, prevalence in the population and probability of the exposure.[ 7 ] When OR (ω) is not available but only prevalence is available, a more simple alternative formula is prescribed:[ 13 ]

d. Independent cohort (prospective study)[ 7 13 ]

In equation d (1), N is the estimated sample size for the independent case–control, Z α is the standard normal deviate for α error and Z β is the standard normal deviate for power (1−β error ). P * is the average probability of the exposure calculated as shown in formula d (2). m is the ratio of control subjects to cohort or experimental subjects desired, while P 0 is the probability of event in the control group and P 1 is the probability of the event in the study or experimental group.[ 7 ] As shown in d (3) formula, N c is the continuity-adjusted sample size for further analysis such as Chi-square and Fisher's exact.[ 7 ]

Analytical studies: Cross-sectional analytical comparative) studies

These are various types of observational study that compare population proportions ( P 1 and P 2 ) and means (μ 1 and μ 2 ). It is formerly known as ‘comparative study’. In this study, there is no form of intervention or experimentation. For instance, a study that aimed at comparing the cardiovascular risk score between the residents in rural and urban communities. The formula for cross-sectional analytical study can be applied to categorical and numerical variables as shown below:[ 4 8 12 ][ 13 ][ 14 ]

d. Comparing two proportions

f. Comparing two means

Analytical studies: Randomised controlled trials

There are four variants of randomised control trials (RCT) described in the literature[ 10 15 ] as shown in Table 2 :

• Equality trial: (H o : μ T − μ S = 0). This trial is designed to hypothesise that there is no clinical difference or effect between the mean of the new treatment/intervention (μ T ) and the mean of the comparator (μ S )
• Equivalence trial: (H o :|μ T − μ S |= δ). This trial hypothesises that both the treatment/intervention and the comparator (μ T and μ S ) are equally effective
• Non-inferior trial: (H o : μ T − μ S ≥ δ). It is a design to prove that the treatment/intervention is as effective as the comparator and not necessary better than comparator (standard or usual or placebo)
• Superiority trial: (H o : μ T − μ S ≤ δ). The purpose of this design is to prove that the treatment/intervention is more effective (statistically or clinically) than the comparator (standard or usual or placebo).

The trials can also be one-sided (one-tail) hypothesis. This means that the direction of the difference or the effect is stated (more/greater or less/lower than). More commonly, many researchers prefer to adopt two-sided (two-tail) hypothesis which usually do not state the direction of the differences or effects expected. This states that there is no difference between the effect of the treatment/intervention and the comparator (standard/usual/placebo), and the common analysis method is independent t -test. In addition to the direction of the hypothesis, the design variants of the trials such as the parallel, cross-over and cluster RCTs also have effects on the sample size calculation as shown in Table 2 .[ 2 6 10 15 ]

σ 2 = pooled variance =

where σ T is the variance of the treatment group and the σ S is the variance of the comparator group or

if standard deviation is given for the treatment ( S T ) and comparator ( S S ) groups. Alternatively, a more comprehensive pooled standard variation ( S pooled ) calculation has been suggested[ 11 ] =

keeping in view the standard deviations ( s 1 , s 2 ….) and sample sizes ( n 1 , n 2 …) of the groups. P is also a pooled prevalence and is simply P T + P S /2. P T and P S are the prevalence of the outcomes in the treatment and the comparators, while μ T and μ S are the mean outcomes in the treatment and the comparator groups. Clinically acceptable margin effect is denoted as δ in the above equation.

OTHER SAMPLE SIZE CONSIDERATION IN RANDOMISED CONTROL TRIALS AND INTERVENTIONAL STUDIES

Cluster randomised control trials designs.

For a detailed explanation on sample size considerations on cluster RCTs, standard reviews should be consulted.[ 15 16 ] However, a brief and helpful explanation is provided here from existing literature.[ 15 16 ]

The initial step is to follow the appropriate sample size estimation N for RCT over individuals as shown in Table 1 , and then corrections will be considered for the κ number of clusters in each arm of size ď. This will produce a total number of N c = ďκ individuals in each arm. As a rule of thumb, to compensate for the selection error inherent in cluster sampling, there is a need to inflate the variance of the difference (δ c ) to be detected by a variance inflation factor (VIF). How well individuals in the clusters are correlated to each other known as the intra-cluster correlation coefficient (ρ) is important when multiplying with VIF. This is called Deff.

Therefore, VIF = [1+ (ď-1)ρ].

There are times that the cluster sizes are not equal, then VIF = [1+ ((δ v 2 + 1)ď*-1)ρ].

The δ v means the coefficient of variation of the cluster sizes and ď* represents average cluster size. Substituting the multiplier for VIF in any of the individual RCT formula is:

N c = N [1+ (ď-1)ρ] = N [VIF] – for equal cluster size

= N [1+ ((δ v 2 + 1)ď*-1)ρ] – for unequal cluster sizes.

QUASI-EXPERIMENTAL STUDIES

One good example of quasi-experimental study is pre- and post-test or before and after test. This is also described as repeated measure. Another description of this situation is that each subject is serving as his/her own control. Repeated measures analyses such as paired t -test (for numeric) and McNemar test (categorical) are employed for the analysis of these forms of study as shown below:[ 11 12 ]

Categorical

It looks very similar to the two-sample situation, but with two important changes. First, there is no multiplier of ‘2’. Second, the σ is the standard deviation of the differences within pairs, while δ = μ 1 and μ 2 are the means before and after intervention, respectively.[ 11 12 ] Similarly, p 1 and p 2 are the proportion/prevalence before and after intervention. The P is the pooled prevalence of the before and after prevalence. The σ is the variance of the difference in the repeated measure = σ 1 2 + σ 2 2 − ρσ 1 σ2[ 11 12 ] where ρ is the correlation between baseline and post-intervention values on the same group. If only one σ 1 is reported, then σ =2 σ 1 (1−ρ).

SURVIVAL ANALYSIS (OUTCOME) STUDY

This type of study is carry out when research subjects are followed up over a time to generate outcome variable that is of time-to-event type.[ 12 ] A good example of this is in the clinical trial that set out to compare the survival rates of the experimental drug or an intervention group compared to the control (non-experimental) group. One striking feature of survival study is that by design, it is not every research subject that survive to the end of the study.[ 12 ] Hence, research subjects exit at different points along the follow-up period. Log-rank test is mostly applied to this type of analysis, thereby making it expedient to take differential total number of events into consideration.[ 12 ] Therefore, both the sample size estimation and duration of stay in the study are important considerations for this type of study design.[ 12 ] The first consideration is the number of events ( d ) estimated using the α-error, the power (1−β) and effect size or the treatment effect (δ). However, the treatment effect is embodied by the probability of the occurrence of the events in the two study groups.[ 12 ] This probability is termed ‘hazard ratio’ (HR).

The total number of events can be estimated as:

The p e and p c are the estimated survival probability in the experimental and control groups, respectively.

SAMPLE SIZE CONSIDERATION IN CORRELATION AND DIAGNOSTIC TESTS

Correlational studies.

Despite being a common descriptive study, only few literature[ 5 ] have described sample size estimation in correlational study. In this study type, the main focus is the correlational coefficient (r) and the Fisher's transformation of the correlation coefficient ( C r ).

One sample correlation formula:

Two sample correlation formula:

Accuracy tests (sensitivity/specificity)

Further detail reading can be found in the literature.[ 17 ] For the purpose of this review, a simple and an all-purpose formula is given here:[ 17 ] the sensitivity ( S e ), specificity ( S p ), disease prevalence ( P ) and precision (δ) are all required.

Sample size when the aim of the accuracy test is for single sensitivity or specificity:

Sensitivity .

Specificity

Sample size for sensitivity (or specificity) of a single diagnostic test in comparison with a standard: The comparison is of the value of the sensitivity/specificity ( P 1 ) of a diagnostic test been compared with a predetermined or a gold standard sensitivity/specificity ( P 0 ).

Sample size for a Sensitivity (or specificity) of more than one diagnostic tests: the comparison in this design involves two alternative diagnostic tests ( P 1 and P 2 )

Sample size adjustments

There are various reasons that can warrant adjustment for an initially estimated sample size.

Multiple outcome variables

When there are more than one outcome variables of interest in a study, sample size of each of all these variables should be estimated and the highest of them should be applied for the study.[ 8 15 ]

Unequal comparison group

Some researches have comparison group which may have equal or unequal subjects per group. In this instance that the arms of the study have unequal subjects in the group, it become expedient to adjust the initially calculated sample size ( N ) that assumed that the arms of study are equal,[ 8 ] using the actual ratio between the unequal arms of the research (ď). The adjusted sample size

Non-consent, missing response, withdrawal from study and dropout

Sample size is calculated as a minimum number required to achieve research aim. In practice, reasons ranging from incomplete response to loss to follow-up ( N *) can adversely affect the final sample size that is useful for the research.[ 8 15 ] Researcher should have adequate knowledge of these losses and have good idea of the proportion ( P ) that may be lost to any of these in a study.

Finite population correction

Logically, searching for a few coloured grains of corn in a large bowl will take longer than finding same coloured grains in a handful scoop of corn. After estimation of sample size for a population of less than 10,000 ( N 0 ), need arises for the researcher to correct the sample size ( N ) for the small study population.[ 7 ]

Design effects

The cluster trials design and the VIF have been discussed in detail in the preceding section. It should be noted that stratified sampling has similarly Deff like cluster randomisation and should be corrected as well.[ 8 ]

Multivariate analysis and covariates

More advanced analysis and modelling are being frequently used in health research nowadays; some of these analyses such as analysis of covariance, log-linear analysis and cox's proportional hazard analysis will require sample size adjustments.[ 8 ] Proper methods of doing these are still evolving.[ 8 ]

This review discussed common sample size estimation formula in health research and offers basic guidelines and principles to achieve valid estimation. The simplification of the sample size formula and detail explanation were also provided. Sample size estimation is an important step in conducting a valid and generalisable research. The variable of outcomes, research designs, analysis methods, error assumptions and effect size among other important elements are cardinal to estimating a scientifically correct sample size. Certain situations require adjustment for the sample size and they are to be considered at all times in health research. This compendium will ease the struggles student and young researchers go through to deploy scientifically strong sample size estimation in their studies.

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• A Researcher’s Guide To Statistical Significance And Sample Size Calculations

Determining Sample Size: How Many Survey Participants Do You Need?

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How to calculate a statistically significant sample size in research, determining sample size for probability-based surveys and polling studies, determining sample size for controlled surveys, determining sample size for experiments, how to calculate sample size for simple experiments, an example sample size calculation for an a/b test, what if i don’t know what size difference to expect, part iii: sample size: how many participants do i need for a survey to be valid.

In the U.S., there is a Presidential election every four years. In election years, there is a steady stream of polls in the months leading up to the election announcing which candidates are up and which are down in the horse race of popular opinion.

If you have ever wondered what makes these polls accurate and how each poll decides how many voters to talk to, then you have thought like a researcher who seeks to know how many participants they need in order to obtain statistically significant survey results.

Statistically significant results are those in which the researchers have confidence their findings are not due to chance . Obtaining statistically significant results depends on the researchers’ sample size (how many people they gather data from) and the overall size of the population they wish to understand (voters in the U.S., for example).

Calculating sample sizes can be difficult even for expert researchers. Here, we show you how to calculate sample size for a variety of different research designs.

Before jumping into the details, it is worth noting that formal sample size calculations are often based on the premise that researchers are conducting a representative survey with probability-based sampling techniques. Probability-based sampling ensures that every member of the population being studied has an equal chance of participating in the study and respondents are selected at random.

For a variety of reasons, probability sampling is not feasible for most behavioral studies conducted in industry and academia . As a result, we outline the steps required to calculate sample sizes for probability-based surveys and then extend our discussion to calculating sample sizes for non-probability surveys (i.e., controlled samples) and experiments.

Determining how many people you need to sample in a survey study can be difficult. How difficult? Look at this formula for sample size.

No one wants to work through something like that just to know how many people they should sample. Fortunately, there are several sample size calculators online that simplify knowing how many people to collect data from.

Even if you use a sample size calculator, however, you still need to know some important details about your study. Specifically, you need to know:

• What is the population size in my research?

Population size is the total number of people in the group you are trying to study. If, for example, you were conducting a poll asking U.S. voters about Presidential candidates, then your population of interest would be everyone living in the U.S.—about 330 million people.

Determining the size of the population you’re interested in will often require some background research. For instance, if your company sells digital marketing services and you’re interested in surveying potential customers, it isn’t easy to determine the size of your population. Everyone who is currently engaged in digital marketing may be a potential customer. In situations like these, you can often use industry data or other information to arrive at a reasonable estimate for your population size.

• What margin of error should you use?

Margin of error is a percentage that tells you how much the results from your sample may deviate from the views of the overall population. The smaller your margin of error, the closer your data reflect the opinion of the population at a given confidence level.

Generally speaking, the more people you gather data from the smaller your margin of error. However, because it is almost never feasible to collect data from everyone in the population, some margin of error is necessary in most studies.

• What is your survey’s significance level?

The significance level  is a percentage that tells you how confident you can be that the true population value lies within your margin of error. So, for example, if you are asking people whether they support a candidate for President, the significance level tells you how likely it is that the level of support for the candidate in the population (i.e., people not in your sample) falls within the margin of error found in your sample.

Common significance levels in survey research are 90%, 95%, and 99%.

Once you know the values above, you can plug them into a sample size formula or more conveniently an online calculator to determine your sample size.

The table below displays the necessary sample size for different sized populations and margin of errors. As you can see, even when a population is large, researchers can often understand the entire group with about 1,000 respondents.

• How Many People Should I Invite to My Study?

Sample size calculations tell you how many people you need to complete your survey. What they do not tell you, however, is how many people you need to invite to your survey. To find that number, you need to consider the response rate.

For example, if you are conducting a study of customer satisfaction and you know from previous experience that only about 30% of the people you contact will actually respond to your survey, then you can determine how many people you should invite to the survey to wind up with your desired sample size.

All you have to do is take the number of respondents you need, divide by your expected response rate, and multiple by 100. For example, if you need 500 customers to respond to your survey and you know the response rate is 30%, you should invite about 1,666 people to your study (500/30*100 = 1,666).

Sample size formulas are based on probability sampling techniques—methods that randomly select people from the population to participate in a survey. For most market surveys and academic studies, however, researchers do not use probability sampling methods. Instead they use a mix of convenience and purposive sampling methods that we refer to as controlled sampling .

When surveys and descriptive studies are based on controlled sampling methods, how should researchers calculate sample size?

When the study’s aim is to measure the frequency of something or to describe people’s behavior, we recommend following the calculations made for probability sampling. This often translates to a sample of about 1,000 to 2,000 people. When a study’s aim is to investigate a correlational relationship, however, we recommend sampling between 500 and 1,000 people. More participants in a study will always be better, but these numbers are a useful rule of thumb for researchers seeking to find out how many participants they need to sample.

If you look online, you will find many sources with information for calculating sample size when conducting a survey, but fewer resources for calculating sample size when conducting an experiment. Experiments involve randomly assigning people to different conditions and manipulating variables in order to determine a cause-and-effect relationship. The reason why sample size calculators for experiments are hard to find is simple: experiments are complex and sample size calculations depend on several factors.

The guidance we offer here is to help researchers calculate sample size for some of the simplest and most common experimental designs: t -tests, A/B tests, and chi square tests.

Many businesses today rely on A/B tests. Especially in the digital environment, A/B tests provide an efficient way to learn what kinds of features, messages, and displays cause people to spend more time or money on a website or an app.

For example, one common use of A/B testing is marketing emails. A marketing manager might create two versions of an email, randomly send one to half the company’s customers and randomly send the second to the other half of customers and then measure which email generates more sales.

In many cases , researchers may know they want to conduct an A/B test but be unsure how many people they need in their sample to obtain statistically significant results. In order to begin a sample size calculation, you need to know three things.

1. The significance level .

The significance level represents how sure you want to be that your results are not due to chance. A significance level of .05 is a good starting point, but you may adjust this number up or down depending on the aim of your study.

2. Your desired power.

Statistical tests are only useful when they have enough power to detect an effect if one actually exists. Most researchers aim for 80% power—meaning their tests are sensitive enough to detect an effect 8 out of 10 times if one exists.

3. The minimum effect size you are interested in.

The final piece of information you need is the minimum effect size, or difference between groups, you are interested in. Sometimes there may be a difference between groups, but if the difference is so small that it makes little practical difference to your business, it probably isn’t worth investigating. Determining the minimum effect size you are interested in requires some thought about your goals and the potential impact on your business. 

Once you have decided on the factors above, you can use a sample size calculator to determine how many people you need in each of your study’s conditions.

Let’s say a marketing team wants to test two different email campaigns. They set their significance level at .05 and their power at 80%. In addition, the team determines that the minimum response rate difference between groups that they are interested in is 7.5%. Plugging these numbers into an effect size calculator reveals that the team needs 693 people in each condition of their study, for a total of 1,386.

Sending an email out to 1,386 people who are already on your contact list doesn’t cost too much. But for many other studies, each respondent you recruit will cost money. For this reason, it is important to strongly consider what the minimum effect size of interest is when planning a study.    

When you don’t know what size difference to expect among groups, you can default to one of a few rules of thumb. First, use the effect size of minimum practical significance. By deciding what the minimum difference is between groups that would be meaningful, you can avoid spending resources investigating things that are likely to have little consequences for your business.

A second rule of thumb that is particularly relevant for researchers in academia is to assume an effect size of d = .4. A d = .4 is considered by some to be the smallest effect size that begins to have practical relevance . And fortunately, with this effect size and just two conditions, researchers need about 100 people per condition.

After you know how many people to recruit for your study, the next step is finding your participants. By using CloudResearch’s Prime Panels or MTurk Toolkit, you can gain access to more than 50 million people worldwide in addition to user-friendly tools designed to make running your study easy. We can help you find your sample regardless of what your study entails. Need people from a narrow demographic group? Looking to collect data from thousands of people? Do you need people who are willing to engage in a long or complicated study? Our team has the knowledge and expertise to match you with the right group of participants for your study. Get in touch with us today and learn what we can do for you.

Continue Reading: A Researcher’s Guide to Statistical Significance and Sample Size Calculations

Part 1: What Does It Mean for Research to Be Statistically Significant?

Part 2: How to Calculate Statistical Significance

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8 Research Proposal Examples & Template to Use

Written by: Raja Mandal

So you have a groundbreaking research idea you've spent months or even years developing, and now you're ready to take the next step.

How do you get funding for your research, and how should you approach potential funders? The answer is to create a convincing research proposal.

Unfortunately, most research proposals often get rejected. According to the European Research Council, the success rate for repeat proposal applications was only 14.8% in 2023 .

Pitching a novel research concept isn’t enough. To increase your chances of securing funding, your research proposal must check the right boxes in terms of clarity, feasibility, aesthetic appeal and other factors.

If you’re looking for inspiration to create a persuasive and feasible proposal, you’re in the right place. In this article, we have compiled a list of research proposal examples to help you create yours.

These examples will help you understand how to organize your proposal, what information to include and how to present it in a way that encourages others to support your project.

Let's dive in!

Table of Contents

What is a research proposal, what to include in a research proposal, 8 research proposal examples & templates, research proposal faqs.

• A research proposal is a document that outlines your proposed research project, explaining what you plan to study, why it's important and how you will conduct your research.
• A well-structured research proposal includes a title page, abstract and table of contents, introduction, literature review, research design and methodology, contribution to knowledge, research schedule, timeline and budget.
• Visme's research proposal examples and templates offer a great starting point for creating engaging and well-structured proposals.
• Choose a template from Visme's research proposal examples and customize it to fit your needs.
• With Visme’s proposal maker , you can create a research proposal that stands out. Access a drag-and-drop editor and advanced features like AI tools , collaboration features, brand wizard and more.

A research proposal is a structured document that outlines the core idea of your research, the methods you intend to use, the required resources and the expected results.

Think of it as a sales pitch for your research. It answers some big questions: What are you planning to explore? Why is it important to conduct the research? What are your research objectives and the methods you’ll use to achieve them? What are the potential outcomes or contributions of this research to the field?

A research proposal serves two primary purposes. First, it convinces funding bodies or academic committees to support your research project expected to bring new ideas and insights. Second, it provides a roadmap for your research journey, helping you stay focused, organized and on track.

Now, we'll discuss what to include in a research proposal. You'll learn about the important parts of a research proposal template and how they help present your research idea clearly.

Here’s an infographic that you can use to understand the elements of a research proposal quickly.

1. Title Page

Start your research proposal with a title page that clearly states your research. The title page is like a book cover, giving the first impression of your project. Therefore, you must ensure the design is engaging enough to attract your audience at first glance.

Include the following details on your title page:

• Title of your research
• Contact Details
• Name of the department or organization
• Date of submission

2. Abstract and Table of Contents

After the title page comes the abstract and the table of contents.

The abstract is a concise summary of your project that briefly outlines your research question, the reasons behind the study and the methods you intend to use. It is a quick way for readers to understand your proposal without reading the entire document.

The table of contents is a detailed list of the sections and subsections in your proposal, with page numbers. It helps readers navigate through your document and quickly locate different parts they're interested in.

3. Introduction

The introduction of your research proposal sets the tone for the rest of the document. It should grab the reader's attention and make them want to learn more. It's your chance to make a strong case for why your research is worth investigating and how it can fill a gap in current knowledge or solve a specific problem.

Make sure that your introduction covers the following:

• Background Information: Set the stage with a brief snapshot of existing research and why your topic is relevant.
• Research Problem: Identify the specific problem or knowledge gap that your study will address.
• Research Questions or Hypotheses: Present the central question or hypothesis that guides your research focus.
• Aims and Objectives: Outline your research's main goal and the steps you'll take to achieve it.
• Significance and Contribution: Explain how your research will add value to the field and what impact it could have.

4. Literature Review

A literature review is a list of the scholarly works you used to conduct your research. It helps you demonstrate your current knowledge about the topic.

Here's how this part works:

• Summary of Sources: Talk about the main ideas or findings from your research materials and explain how they connect to your research questions.
• Finding Gaps: Show where the current research falls short or doesn't give the full picture—this is where your research comes in!
• Key Theories: Tell the readers about any theories or ways of thinking that help shape your research.
• Learning from Methods: Discuss what previous researchers worked on and how their methods might guide your research.
• Recognizing Authors and Studies: Honor the pioneers whose work has had a major influence on your topic.

5. Research Design and Methodology

This section outlines your plan for answering your research question. It explains how you intend to gather and analyze information, providing a clear roadmap of the investigation process.

Here are the key components:

Population and Sample

Describe the entire group you're interested in (the population). This could be all teachers in a specific state or all social media platform users. After that, you will need to explain how you will choose a smaller group, known as a sample, to study directly. This sample should be selected to accurately represent the larger population you are interested in studying.

To choose the right sampling method, you need to assess your population properly. For instance, to obtain general insights, you can use random sampling to select individuals without bias. If the population consists of different categories, such as professionals and students, you can use stratified sampling to ensure that each category is represented in the sample.

Other popular sampling methods include systematic, convenience, purposive, cluster, and probability sampling techniques.

Research Approach

There are three main approaches for the research: qualitative (focusing on experiences and themes), quantitative (using numbers and statistics), or mixed methods (combining both). Your choice will depend on your research question and the kind of data you need.

Data Collection

This section details the specific methods you'll use to gather information. Will you distribute surveys online or in person? Conduct interviews? Perhaps you'll use existing data sets. Here, you'll also explain how you'll ensure the data collection process is reliable and ethical.

Data Analysis

Once you have collected your data, the next step is to analyze it to obtain meaningful insights. The method you choose depends on the available data type.

If you have quantitative data, you can employ statistical tests to analyze it. And if you're dealing with qualitative data, coding techniques can help you spot patterns and themes in your collected data.

6. Contribution to Knowledge

In this section, you need to explain how your research will contribute to the existing knowledge in your field. You should describe whether your study will fill a knowledge gap, challenge conventional ideas or beliefs or offer a fresh perspective on a topic.

Clearly outline how your work will advance your field of study and why this new knowledge is essential.

7. Research Schedule and Timeline

Create a timeline with important milestones, such as finishing your literature review, completing data collection and finalizing your analysis.

This shows that you've carefully considered the scope of your project and can manage your time effectively. Furthermore, account for possible delays and be prepared to adapt your schedule accordingly.

To create this timeline, consider using a visual tool like a Gantt chart or a simple spreadsheet. These tools will help you organize individual tasks, assign deadlines, and visualize the project's overall progress.

Choose a Gantt chart template from Visme's library and customize it to create your timeline quickly. Here's an example template:

The budget section is your opportunity to show them that you've carefully considered all necessary expenses and that your funding request is justified.

Here's how you can approach this part:

• Understand the Rules: Before making calculations, thoroughly review the funding agency's guidelines. Pay attention to what types of expenses are allowed or excluded and whether there are any budget caps.
• Personnel: Salaries and benefits for yourself, research assistants, or collaborators.
• Equipment: Specialized tools, software, or lab supplies.
• Travel: Transportation, lodging and meals if data collection requires travel.
• Dissemination: Costs for publishing results or presenting at conferences.
• Provide Justifications: Don't just list a cost. Briefly explain why each expense is crucial for completing your research.
• Be Thorough and Realistic: Research prices for specific items using quotes or online comparisons. Don't underestimate expenses, as this can raise troubles about the project's feasibility.
• Don't Forget Contingencies: Include a small buffer (around 5% of your total budget) for unexpected costs that might arise.

Using these research proposal examples and templates, you can create a winning proposal in no time. You will find templates for various topics and customize every aspect of them to make them your own.

Visme’s drag-and-drop editor, advanced features and a vast library of templates help organizations and individuals worldwide create engaging documents.

Here’s what a research student who uses Visme to create award-winning presentations has to say about the tool:

Chantelle Clarke

Research Student

Now, let’s dive into the research proposal examples.

1. Research Proposal Presentation Template

This research proposal presentation template is a powerful tool for presenting your research plan to stakeholders. The slides include specific sections to help you outline your research, including the research background, questions, objectives, methodology and expected results.

The slides create a coherent narrative, highlighting the importance and significance of your research. Overall, the template has a calming and professional blue color scheme with text that enables your audience to grasp the key points.

If you need help creating your presentation slides in a fraction of the time, check out Visme's AI presentation maker . Enter your requirements using text prompts, and the AI tool will generate a complete presentation with engaging visuals, text and clear structure. You can further customize the template completely to your needs.

2. Sales Research Proposal Template

Sales research gives you a deeper understanding of their target audience. It also helps you identify gaps in the market and develop effective sales strategies that drive revenue growth. With this research proposal template, you can secure funding for your next research project.

It features a sleek and professional grayscale color palette with a classic and modern vibe. The high-quality images in the template are strategically placed to reinforce the message without overwhelming the reader. Furthermore, the template includes a vertical bar graph that effectively represents budget allocations, enabling the reader to quickly grasp the information.

Use Visme's interactive elements and animations to add a dynamic layer to your research proposals. You can animate any object and add pop-ups or link pages for a more immersive experience. Use these functionalities to highlight key findings, demonstrate trends or guide readers through your proposal, making the content engaging and interactive.

3. General Funding Research Proposal Template

This proposal template is a great tool for securing funding for any type of research project. It begins with a captivating title page that grabs attention. The beautiful design elements and vector icons enhance the aesthetic and aid visual communication.

This template revolves around how a specific user group adopts cryptocurrencies like Bitcoin and Ethereum. The goal is to assess awareness, gauge interest and understand key factors affecting cryptocurrency adoption.

The project methodology includes survey design, data collection, and market research. The expected impact is to enhance customer engagement and position the company as a customer-centric brand.

Do you need additional help crafting the perfect text for your proposal? Visme's AI writer can quickly generate content outlines, summaries and even entire sections. Just explain your requirements to the tool using a text prompt, and the tool will generate it for you.

4. Product Research Proposal Template

Creating a product that delights users begins with detailed product research. With this modern proposal template, you can secure buy-in and funding for your next research.

It starts with a background that explains why the research is important. Next, it highlights what the research is set to achieve, how the research will be conducted, how much it will cost, the timeline and the expected outcomes. With a striking color scheme combining black, yellow, and gray, the template grabs attention and maintains it until the last page.

What we love about this template is the smart use of visuals. You'll find a flowchart explaining the methodology, a bar graph for the budget, and a timeline for the project. But that’s just the tip of the iceberg regarding the visual elements you’ll find in Visme.

Visme offers data visualization tools with 30+ data widgets, such as radial gauges, population arrays, progress bars and more. These tools can help you turn complex data into engaging visuals for your research proposal or any other document.

For larger data sets, you can choose from 20+ types of charts and graphs , including bar graphs , bubble charts , Venn diagrams and more.

5. Tech Research Proposal Template

If you’re a tech researcher, we’ve got the perfect template for you. This research proposal example is about predictive analytics in e-commerce. However, you can customize it for any other type of research proposal.

It highlights the project's objectives, including the effectiveness of predictive analysis, the impact of product recommendations and supply chain optimization. The methods proposed for achieving these objectives involve A/B testing and data analysis, a comprehensive budget and a 12-month timeline for clear project planning.

The title page has a unique triptych-style layout that immediately catches the reader's attention. It has plenty of white space that enhances readability, allowing your audience to focus on the critical points.

Submitting to different funding agencies? You don’t have to manually make changes to your document. Visme's dynamic fields can help save time and eliminate repetitive data entry.

Create custom fields like project names, addresses, contact information and more. Any changes made to these fields will automatically populate throughout the document.

6. Marketing Research Proposal Template

Artificial intelligence (AI) is taking the world by storm and the marketing niche isn’t left out. With this eye-catching template, you can attract attention to your proposed marketing research project for an AI-driven platform.

The main goal of the research is to evaluate the platform's feasibility and marketing potential. To achieve this goal, the scope of work includes a comprehensive analysis of the market and competitors and pilot testing. The proposal also contains a budget overview that clearly outlines the allocation of funds, ensuring a well-planned and transparent approach.

Using Visme's Brand Design Tool , you can easily customize this template to suit your branding with just one click. Simply enter your URL into the brand wizard, and the tool will automatically extract your company logo, brand colors, and brand fonts . Once saved, you or your team members can apply the branding elements to any document. It's that simple!

7. Environmental Research Proposal Template

The environmental research proposal example focuses on carbon emissions, identifies their contributing factors, and suggests sustainable practices to address them. It uses an appropriate sample size and data collection techniques to gather and evaluate data and provide sustainable recommendations to reduce industrial carbon footprints and waste.

From a design standpoint, the green and white color combination matches the theme of nature and environmental friendliness. In addition to its aesthetic appeal, the proposal includes relevant images that support ecological advocacy, making it informative and visually aligned with its purpose.

A key feature of this template is its detailed breakdown of the project's timeline. It uses a Gantt chart to clearly present stages, milestones and deadlines.

Collaborate with your team members to customize these research proposal templates using Visme’s collaborative design features . These features allow you to leave feedback, draw annotations and even make live edits. Invite your teammates via email or a shareable link and allow them to work together on projects.

8. General Approval Research Proposal Template

This research proposal template is a total game-changer - you can use it for any research proposal and customize it however you want. It features a modern and refreshing color scheme that immediately makes it stand out, providing a contemporary look that can adapt to any project's needs.

The template's layout is thoughtfully designed with primary fields that users can easily personalize by changing text, adjusting colors, or swapping images. No matter the research topic, you can tailor the template to fit your specific needs.

Once you're done customizing your research proposal template on Visme, you can download, share and publish it in different ways. For offline usage, you may download the proposal in PDF, PNG, or JPG format. To share it online, you can use a private or public link or generate a code snippet that you can embed anywhere on the web.

Want to create other types of proposals? Here are 29 proposal templates that you can easily customize in Visme.

Q. What Are the Five Steps of Writing a Research Proposal?

Follow these steps to write a solid research proposal:

• Choose a topic within your field of study that can be explored and investigated.
• Research existing literature and studies to build a foundational understanding and prepare your research question.
• Outline your research proposal: introduction, literature review, proposed methodology, budget and timeline.
• Conduct more detailed studies to strengthen your proposition, refine your research question and justify your methodology.
• Follow your outline to write a clear and organized proposal, then review and edit for accuracy before submitting.

If you want to learn more about creating an expert research proposal , we highly recommend checking out our in-depth guide.

Q. How Long Is a Research Proposal?

Research proposals can range from 1,000 to 5,000 words. For smaller projects or when specific requirements aren't provided, aim for a concise and informative proposal that effectively outlines your research plan.

However, the ideal length depends on these factors:

• Projects with complex methodologies or multiple phases may require longer proposals to explain the scope and procedures in detail.
• Universities, academic institutions and funding agencies often have guidelines of a specific length. Always check their requirements beforehand.
• When writing a proposal, adjust the level of study based on the audience. Academic proposals may require comprehensive explanations, while business or non-profit proposals require a more streamlined approach.

Q. How Long Does It Take to Write a Research Proposal?

The time it takes to write a research proposal depends on a few factors:

• Complex research with extensive data collection or analysis will naturally take longer to plan and write about.
• If you're new to writing research proposals, expect to spend more time learning the format and best practices.
• If you've already conducted some research or a thorough literature review, the writing process might go faster.
• Funding applications often have strict deadlines that will dictate your timeline.

Set aside several weeks to a couple of months for researching, writing, and revising your proposal. Start early to avoid stress and produce your best work.

Q. What Not to Do for a Research Proposal?

There are several factors that can make a research proposal weak. Here are some of the most common errors that you should avoid while preparing your research proposal:

• Don’t choose a topic that’s too broad. Focus on a specific area you can thoroughly explore within your proposal’s limits.
• Don’t ignore the rules for formatting and submitting your proposal. Always adhere to the requirements set by your institution or funding body.
• Don’t forget to conduct a thorough literature review. It's crucial to show your grasp of existing research related to your topic.
• Don't be vague about your methods. Ensure they're clearly defined and suitable for answering your research question.
• Don't overlook errors in grammar, typos or structure. A well-proofread proposal reflects professionalism, so review it carefully before submitting it.

Craft Professional & Engaging Proposals with Visme

Writing a compelling research proposal takes effort, but with the right tools, the process becomes a breeze. Use the research proposal examples and templates in this article as a launching point to write your own proposal.

The best part? Visme provides easy-to-use tools with a vast collection of customizable templates, design elements and powerful features.

Whether you're a seasoned researcher or a student, Visme has the resources to help you create visually appealing and well-structured research proposals. In addition to research proposals, Visme helps you create many other document types, such as presentations , infographics , reports and more.

Ready to create your own research proposal? Check out Visme's proposal maker and start crafting professional and engaging proposals in minutes!

Create professional research proposals with Visme

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About the Author

Raja Antony Mandal is a Content Writer at Visme. He can quickly adapt to different writing styles, possess strong research skills, and know SEO fundamentals. Raja wants to share valuable information with his audience by telling captivating stories in his articles. He wants to travel and party a lot on the weekends, but his guitar, drum set, and volleyball court don’t let him.

How to Justify Sample Size in Qualitative Research

• March 21, 2023

Article Summary : Sample sizes in qualitative research can be much lower than sample sizes in quantitative research. The key is having the right participant segmentation and study design. Data saturation is also a key principle to understand.

Qualitative research is a bit of a puzzle for new practitioners: since it is done via interviewing participants, observation, or studying people’s patterns and movements (in the case of user experience design), one can’t obviously have a huge sample size that is statistically significant. Interviewing 200+ people is not only incredibly time-consuming, it’s also quite expensive.

And, moreover, the goal of qualitative research is not to understand how much or how many. The goal is to collect themes and see patterns. It’s to uncover the “why” versus the amount.

So in this post, we’re going to explore the question every qualitative researcher asks, at one point or another: How do you justify the sample size in qualitative research?

Here are some guidelines.

Qualitative sample size guideline #1: Segmentation of participants

In qualitative research, because the goal is to understand themes and patterns of a particular subset (versus a broad population), the first step is segmentation. You may also know of this as “ persona ” development, but regardless of what you call it, the idea is to first bucket your various buyer/customer types into like-categories. For example, if you’re selling sales software, your target isn’t every single company who sells products. It’s likely much more specific: like mid-market sized VP-level sales execs who have a technology product and use a cloud-based CRM. If that’s your main buyer, that’s your segment who you would focus on in qualitative research.

Generally, most companies have multiple targets, so the trick is to think about all the various buyers/consumers and identify which underlying traits they have in common, as well as which traits differentiate them from other targets. Typically, this is where quantitative data comes into play: either through internal data analysis or surveys. Whatever your process, this is step 1 to figure out the segments you will be bucketing participants into so you can move into the qualitative phase, where you’ll ask in-depth questions, via interviews, to each segment category. At this stage, it’s time to bring in your recruiting company to find your participants.

Qualitative sample size guideline #2: Figure out the appropriate study design

After you’ve tackled your segmentation exercise and know how to divide up your participants, you’ll need to think through the qualitative methodology that is most appropriate for answering your research questions. At InterQ Research, we always design studies through the lens of contextual research. This means that you want to set up your studies to be as close to real life as possible. Is your product sale done through a group discussion or individual decision? Often, when teams decide on software or technology stacks, they’ll want to test it and talk amongst themselves. If this is the case, you would need to interview the team or a team of like-minded professionals to see how they come to a decision. In this case, focus groups would be a great methodology.

Conversely, if your product is thought through on an individual-basis, like, perhaps, a person navigating a website when purchasing a plane ticket, then you’d want to interview the individual, alone. In this case, you’d want to choose a hybrid approach, of a user experience/journey mapping exercise, along with an in-depth interview.

In qualitative research, there are numerous methodologies, and frequently, mixed-methodologies work best, in order to see the context of how people behave, as well as to understand how they think.

But I digress. Let’s get back to sample sizes in qualitative research.

Qualitative sample size guideline #3: Your sample size is completed when you reach saturation

So far we’ve covered how to first segment your audiences, and then we’ve talked about the methodology to choose, based on context. The third principle in qualitative research is to understand the theory of data saturation.

Saturation in qualitative research means that, when interviewing a distinct segment of participants, you are able to explore all of the common themes the sample set has in common. In other words, after doing, let’s say, 15 interviews about a specific topic, you start to hear the participants all say similar things. Since you have a fairly homogenous sample, these themes will start to come out after 10-20 interviews, if you’ve done your recruiting well (and sometimes as soon as 6 interviews). Once you hear the same themes, with no new information, this is data saturation.

The beauty of qualitative research is that if you:

• Segment your audiences carefully, into distinct groups, and,
• Choose the right methodology

You’ll start to hit saturation, and you will get diminishing returns with more interviews. In this manner, qualitative research can have smaller sample sizes than quantitative, since it’s thematic, versus statistical.

Let’s wrap it up: So what is the ideal sample size in qualitative research?

To bring this one home, let’s answer the question we sought out to investigate: the sample size in qualitative research.

Typically, sample sizes will range from 6-20, per segment. (So if you have 5 segments, 6 is your multiplier for the total number you’ll need, so you would have a total sample size of 30.) For very specific tasks, such as in user experience research, moderators will see the same themes after as few as 5-6 interviews. In most studies, though, researchers will reach saturation after 10-20 interviews. The variable here depends on how homogenous the sample is, as well as the type of questions being asked. Some researchers aim for a bakers dozen (13), and see if they’ve reached saturation after 13. If not, the study can be expanded to find more participants so that all the themes can be explored. But 13 is a good place to start.

Interested in running a qualitative research study? Request a proposal > 

Author Bio: Joanna Jones is the founder and CEO of InterQ Research. At InterQ, she oversees study design, manages clients, and moderators studies.

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