statistical analysis thesis pdf

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Mathematics and Statistics Theses and Dissertations

Theses/dissertations from 2024 2024.

The Effect of Fixed Time Delays on the Synchronization Phase Transition , Shaizat Bakhytzhan

On the Subelliptic and Subparabolic Infinity Laplacian in Grushin-Type Spaces , Zachary Forrest

Utilizing Machine Learning Techniques for Accurate Diagnosis of Breast Cancer and Comprehensive Statistical Analysis of Clinical Data , Myat Ei Ei Phyo

Quandle Rings, Idempotents and Cocycle Invariants of Knots , Dipali Swain

Comparative Analysis of Time Series Models on U.S. Stock and Exchange Rates: Bayesian Estimation of Time Series Error Term Model Versus Machine Learning Approaches , Young Keun Yang

Theses/Dissertations from 2023 2023

Classification of Finite Topological Quandles and Shelves via Posets , Hitakshi Lahrani

Applied Analysis for Learning Architectures , Himanshu Singh

Rational Functions of Degree Five That Permute the Projective Line Over a Finite Field , Christopher Sze

Theses/Dissertations from 2022 2022

New Developments in Statistical Optimal Designs for Physical and Computer Experiments , Damola M. Akinlana

Advances and Applications of Optimal Polynomial Approximants , Raymond Centner

Data-Driven Analytical Predictive Modeling for Pancreatic Cancer, Financial & Social Systems , Aditya Chakraborty

On Simultaneous Similarity of d-tuples of Commuting Square Matrices , Corey Connelly

Symbolic Computation of Lump Solutions to a Combined (2+1)-dimensional Nonlinear Evolution Equation , Jingwei He

Boundary behavior of analytic functions and Approximation Theory , Spyros Pasias

Stability Analysis of Delay-Driven Coupled Cantilevers Using the Lambert W-Function , Daniel Siebel-Cortopassi

A Functional Optimization Approach to Stochastic Process Sampling , Ryan Matthew Thurman

Theses/Dissertations from 2021 2021

Riemann-Hilbert Problems for Nonlocal Reverse-Time Nonlinear Second-order and Fourth-order AKNS Systems of Multiple Components and Exact Soliton Solutions , Alle Adjiri

Zeros of Harmonic Polynomials and Related Applications , Azizah Alrajhi

Combination of Time Series Analysis and Sentiment Analysis for Stock Market Forecasting , Hsiao-Chuan Chou

Uncertainty Quantification in Deep and Statistical Learning with applications in Bio-Medical Image Analysis , K. Ruwani M. Fernando

Data-Driven Analytical Modeling of Multiple Myeloma Cancer, U.S. Crop Production and Monitoring Process , Lohuwa Mamudu

Long-time Asymptotics for mKdV Type Reduced Equations of the AKNS Hierarchy in Weighted L 2 Sobolev Spaces , Fudong Wang

Online and Adjusted Human Activities Recognition with Statistical Learning , Yanjia Zhang

Theses/Dissertations from 2020 2020

Bayesian Reliability Analysis of The Power Law Process and Statistical Modeling of Computer and Network Vulnerabilities with Cybersecurity Application , Freeh N. Alenezi

Discrete Models and Algorithms for Analyzing DNA Rearrangements , Jasper Braun

Bayesian Reliability Analysis for Optical Media Using Accelerated Degradation Test Data , Kun Bu

On the p(x)-Laplace equation in Carnot groups , Robert D. Freeman

Clustering methods for gene expression data of Oxytricha trifallax , Kyle Houfek

Gradient Boosting for Survival Analysis with Applications in Oncology , Nam Phuong Nguyen

Global and Stochastic Dynamics of Diffusive Hindmarsh-Rose Equations in Neurodynamics , Chi Phan

Restricted Isometric Projections for Differentiable Manifolds and Applications , Vasile Pop

On Some Problems on Polynomial Interpolation in Several Variables , Brian Jon Tuesink

Numerical Study of Gap Distributions in Determinantal Point Process on Low Dimensional Spheres: L -Ensemble of O ( n ) Model Type for n = 2 and n = 3 , Xiankui Yang

Non-Associative Algebraic Structures in Knot Theory , Emanuele Zappala

Theses/Dissertations from 2019 2019

Field Quantization for Radiative Decay of Plasmons in Finite and Infinite Geometries , Maryam Bagherian

Probabilistic Modeling of Democracy, Corruption, Hemophilia A and Prediabetes Data , A. K. M. Raquibul Bashar

Generalized Derivations of Ternary Lie Algebras and n-BiHom-Lie Algebras , Amine Ben Abdeljelil

Fractional Random Weighted Bootstrapping for Classification on Imbalanced Data with Ensemble Decision Tree Methods , Sean Charles Carter

Hierarchical Self-Assembly and Substitution Rules , Daniel Alejandro Cruz

Statistical Learning of Biomedical Non-Stationary Signals and Quality of Life Modeling , Mahdi Goudarzi

Probabilistic and Statistical Prediction Models for Alzheimer’s Disease and Statistical Analysis of Global Warming , Maryam Ibrahim Habadi

Essays on Time Series and Machine Learning Techniques for Risk Management , Michael Kotarinos

The Systems of Post and Post Algebras: A Demonstration of an Obvious Fact , Daviel Leyva

Reconstruction of Radar Images by Using Spherical Mean and Regular Radon Transforms , Ozan Pirbudak

Analyses of Unorthodox Overlapping Gene Segments in Oxytricha Trifallax , Shannon Stich

An Optimal Medium-Strength Regularity Algorithm for 3-uniform Hypergraphs , John Theado

Power Graphs of Quasigroups , DayVon L. Walker

Theses/Dissertations from 2018 2018

Groups Generated by Automata Arising from Transformations of the Boundaries of Rooted Trees , Elsayed Ahmed

Non-equilibrium Phase Transitions in Interacting Diffusions , Wael Al-Sawai

A Hybrid Dynamic Modeling of Time-to-event Processes and Applications , Emmanuel A. Appiah

Lump Solutions and Riemann-Hilbert Approach to Soliton Equations , Sumayah A. Batwa

Developing a Model to Predict Prevalence of Compulsive Behavior in Individuals with OCD , Lindsay D. Fields

Generalizations of Quandles and their cohomologies , Matthew J. Green

Hamiltonian structures and Riemann-Hilbert problems of integrable systems , Xiang Gu

Optimal Latin Hypercube Designs for Computer Experiments Based on Multiple Objectives , Ruizhe Hou

Human Activity Recognition Based on Transfer Learning , Jinyong Pang

Signal Detection of Adverse Drug Reaction using the Adverse Event Reporting System: Literature Review and Novel Methods , Minh H. Pham

Statistical Analysis and Modeling of Cyber Security and Health Sciences , Nawa Raj Pokhrel

Machine Learning Methods for Network Intrusion Detection and Intrusion Prevention Systems , Zheni Svetoslavova Stefanova

Orthogonal Polynomials With Respect to the Measure Supported Over the Whole Complex Plane , Meng Yang

Theses/Dissertations from 2017 2017

Modeling in Finance and Insurance With Levy-It'o Driven Dynamic Processes under Semi Markov-type Switching Regimes and Time Domains , Patrick Armand Assonken Tonfack

Prevalence of Typical Images in High School Geometry Textbooks , Megan N. Cannon

On Extending Hansel's Theorem to Hypergraphs , Gregory Sutton Churchill

Contributions to Quandle Theory: A Study of f-Quandles, Extensions, and Cohomology , Indu Rasika U. Churchill

Linear Extremal Problems in the Hardy Space H p for 0 p , Robert Christopher Connelly

Statistical Analysis and Modeling of Ovarian and Breast Cancer , Muditha V. Devamitta Perera

Statistical Analysis and Modeling of Stomach Cancer Data , Chao Gao

Structural Analysis of Poloidal and Toroidal Plasmons and Fields of Multilayer Nanorings , Kumar Vijay Garapati

Dynamics of Multicultural Social Networks , Kristina B. Hilton

Cybersecurity: Stochastic Analysis and Modelling of Vulnerabilities to Determine the Network Security and Attackers Behavior , Pubudu Kalpani Kaluarachchi

Generalized D-Kaup-Newell integrable systems and their integrable couplings and Darboux transformations , Morgan Ashley McAnally

Patterns in Words Related to DNA Rearrangements , Lukas Nabergall

Time Series Online Empirical Bayesian Kernel Density Segmentation: Applications in Real Time Activity Recognition Using Smartphone Accelerometer , Shuang Na

Schreier Graphs of Thompson's Group T , Allen Pennington

Cybersecurity: Probabilistic Behavior of Vulnerability and Life Cycle , Sasith Maduranga Rajasooriya

Bayesian Artificial Neural Networks in Health and Cybersecurity , Hansapani Sarasepa Rodrigo

Real-time Classification of Biomedical Signals, Parkinson’s Analytical Model , Abolfazl Saghafi

Lump, complexiton and algebro-geometric solutions to soliton equations , Yuan Zhou

Theses/Dissertations from 2016 2016

A Statistical Analysis of Hurricanes in the Atlantic Basin and Sinkholes in Florida , Joy Marie D'andrea

Statistical Analysis of a Risk Factor in Finance and Environmental Models for Belize , Sherlene Enriquez-Savery

Putnam's Inequality and Analytic Content in the Bergman Space , Matthew Fleeman

On the Number of Colors in Quandle Knot Colorings , Jeremy William Kerr

Statistical Modeling of Carbon Dioxide and Cluster Analysis of Time Dependent Information: Lag Target Time Series Clustering, Multi-Factor Time Series Clustering, and Multi-Level Time Series Clustering , Doo Young Kim

Some Results Concerning Permutation Polynomials over Finite Fields , Stephen Lappano

Hamiltonian Formulations and Symmetry Constraints of Soliton Hierarchies of (1+1)-Dimensional Nonlinear Evolution Equations , Solomon Manukure

Modeling and Survival Analysis of Breast Cancer: A Statistical, Artificial Neural Network, and Decision Tree Approach , Venkateswara Rao Mudunuru

Generalized Phase Retrieval: Isometries in Vector Spaces , Josiah Park

Leonard Systems and their Friends , Jonathan Spiewak

Resonant Solutions to (3+1)-dimensional Bilinear Differential Equations , Yue Sun

Statistical Analysis and Modeling Health Data: A Longitudinal Study , Bhikhari Prasad Tharu

Global Attractors and Random Attractors of Reaction-Diffusion Systems , Junyi Tu

Time Dependent Kernel Density Estimation: A New Parameter Estimation Algorithm, Applications in Time Series Classification and Clustering , Xing Wang

On Spectral Properties of Single Layer Potentials , Seyed Zoalroshd

Theses/Dissertations from 2015 2015

Analysis of Rheumatoid Arthritis Data using Logistic Regression and Penalized Approach , Wei Chen

Active Tile Self-assembly and Simulations of Computational Systems , Daria Karpenko

Nearest Neighbor Foreign Exchange Rate Forecasting with Mahalanobis Distance , Vindya Kumari Pathirana

Statistical Learning with Artificial Neural Network Applied to Health and Environmental Data , Taysseer Sharaf

Radial Versus Othogonal and Minimal Projections onto Hyperplanes in l_4^3 , Richard Alan Warner

Ensemble Learning Method on Machine Maintenance Data , Xiaochuang Zhao

Theses/Dissertations from 2014 2014

Properties of Graphs Used to Model DNA Recombination , Ryan Arredondo

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The Beginner's Guide to Statistical Analysis | 5 Steps & Examples

Statistical analysis means investigating trends, patterns, and relationships using quantitative data . It is an important research tool used by scientists, governments, businesses, and other organizations.

To draw valid conclusions, statistical analysis requires careful planning from the very start of the research process . You need to specify your hypotheses and make decisions about your research design, sample size, and sampling procedure.

After collecting data from your sample, you can organize and summarize the data using descriptive statistics . Then, you can use inferential statistics to formally test hypotheses and make estimates about the population. Finally, you can interpret and generalize your findings.

This article is a practical introduction to statistical analysis for students and researchers. We’ll walk you through the steps using two research examples. The first investigates a potential cause-and-effect relationship, while the second investigates a potential correlation between variables.

Table of contents

Step 1: write your hypotheses and plan your research design, step 2: collect data from a sample, step 3: summarize your data with descriptive statistics, step 4: test hypotheses or make estimates with inferential statistics, step 5: interpret your results, other interesting articles.

To collect valid data for statistical analysis, you first need to specify your hypotheses and plan out your research design.

Writing statistical hypotheses

The goal of research is often to investigate a relationship between variables within a population . You start with a prediction, and use statistical analysis to test that prediction.

A statistical hypothesis is a formal way of writing a prediction about a population. Every research prediction is rephrased into null and alternative hypotheses that can be tested using sample data.

While the null hypothesis always predicts no effect or no relationship between variables, the alternative hypothesis states your research prediction of an effect or relationship.

• Null hypothesis: A 5-minute meditation exercise will have no effect on math test scores in teenagers.
• Alternative hypothesis: A 5-minute meditation exercise will improve math test scores in teenagers.
• Null hypothesis: Parental income and GPA have no relationship with each other in college students.
• Alternative hypothesis: Parental income and GPA are positively correlated in college students.

Planning your research design

A research design is your overall strategy for data collection and analysis. It determines the statistical tests you can use to test your hypothesis later on.

First, decide whether your research will use a descriptive, correlational, or experimental design. Experiments directly influence variables, whereas descriptive and correlational studies only measure variables.

• In an experimental design , you can assess a cause-and-effect relationship (e.g., the effect of meditation on test scores) using statistical tests of comparison or regression.
• In a correlational design , you can explore relationships between variables (e.g., parental income and GPA) without any assumption of causality using correlation coefficients and significance tests.
• In a descriptive design , you can study the characteristics of a population or phenomenon (e.g., the prevalence of anxiety in U.S. college students) using statistical tests to draw inferences from sample data.

Your research design also concerns whether you’ll compare participants at the group level or individual level, or both.

• In a between-subjects design , you compare the group-level outcomes of participants who have been exposed to different treatments (e.g., those who performed a meditation exercise vs those who didn’t).
• In a within-subjects design , you compare repeated measures from participants who have participated in all treatments of a study (e.g., scores from before and after performing a meditation exercise).
• In a mixed (factorial) design , one variable is altered between subjects and another is altered within subjects (e.g., pretest and posttest scores from participants who either did or didn’t do a meditation exercise).
• Experimental
• Correlational

First, you’ll take baseline test scores from participants. Then, your participants will undergo a 5-minute meditation exercise. Finally, you’ll record participants’ scores from a second math test.

In this experiment, the independent variable is the 5-minute meditation exercise, and the dependent variable is the math test score from before and after the intervention. Example: Correlational research design In a correlational study, you test whether there is a relationship between parental income and GPA in graduating college students. To collect your data, you will ask participants to fill in a survey and self-report their parents’ incomes and their own GPA.

Measuring variables

When planning a research design, you should operationalize your variables and decide exactly how you will measure them.

For statistical analysis, it’s important to consider the level of measurement of your variables, which tells you what kind of data they contain:

• Categorical data represents groupings. These may be nominal (e.g., gender) or ordinal (e.g. level of language ability).
• Quantitative data represents amounts. These may be on an interval scale (e.g. test score) or a ratio scale (e.g. age).

Many variables can be measured at different levels of precision. For example, age data can be quantitative (8 years old) or categorical (young). If a variable is coded numerically (e.g., level of agreement from 1–5), it doesn’t automatically mean that it’s quantitative instead of categorical.

Identifying the measurement level is important for choosing appropriate statistics and hypothesis tests. For example, you can calculate a mean score with quantitative data, but not with categorical data.

In a research study, along with measures of your variables of interest, you’ll often collect data on relevant participant characteristics.

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In most cases, it’s too difficult or expensive to collect data from every member of the population you’re interested in studying. Instead, you’ll collect data from a sample.

Statistical analysis allows you to apply your findings beyond your own sample as long as you use appropriate sampling procedures . You should aim for a sample that is representative of the population.

Sampling for statistical analysis

There are two main approaches to selecting a sample.

• Probability sampling: every member of the population has a chance of being selected for the study through random selection.
• Non-probability sampling: some members of the population are more likely than others to be selected for the study because of criteria such as convenience or voluntary self-selection.

In theory, for highly generalizable findings, you should use a probability sampling method. Random selection reduces several types of research bias , like sampling bias , and ensures that data from your sample is actually typical of the population. Parametric tests can be used to make strong statistical inferences when data are collected using probability sampling.

But in practice, it’s rarely possible to gather the ideal sample. While non-probability samples are more likely to at risk for biases like self-selection bias , they are much easier to recruit and collect data from. Non-parametric tests are more appropriate for non-probability samples, but they result in weaker inferences about the population.

If you want to use parametric tests for non-probability samples, you have to make the case that:

• your sample is representative of the population you’re generalizing your findings to.
• your sample lacks systematic bias.

Keep in mind that external validity means that you can only generalize your conclusions to others who share the characteristics of your sample. For instance, results from Western, Educated, Industrialized, Rich and Democratic samples (e.g., college students in the US) aren’t automatically applicable to all non-WEIRD populations.

If you apply parametric tests to data from non-probability samples, be sure to elaborate on the limitations of how far your results can be generalized in your discussion section .

Create an appropriate sampling procedure

Based on the resources available for your research, decide on how you’ll recruit participants.

• Will you have resources to advertise your study widely, including outside of your university setting?
• Will you have the means to recruit a diverse sample that represents a broad population?
• Do you have time to contact and follow up with members of hard-to-reach groups?

Your participants are self-selected by their schools. Although you’re using a non-probability sample, you aim for a diverse and representative sample. Example: Sampling (correlational study) Your main population of interest is male college students in the US. Using social media advertising, you recruit senior-year male college students from a smaller subpopulation: seven universities in the Boston area.

Calculate sufficient sample size

Before recruiting participants, decide on your sample size either by looking at other studies in your field or using statistics. A sample that’s too small may be unrepresentative of the sample, while a sample that’s too large will be more costly than necessary.

There are many sample size calculators online. Different formulas are used depending on whether you have subgroups or how rigorous your study should be (e.g., in clinical research). As a rule of thumb, a minimum of 30 units or more per subgroup is necessary.

To use these calculators, you have to understand and input these key components:

• Significance level (alpha): the risk of rejecting a true null hypothesis that you are willing to take, usually set at 5%.
• Statistical power : the probability of your study detecting an effect of a certain size if there is one, usually 80% or higher.
• Expected effect size : a standardized indication of how large the expected result of your study will be, usually based on other similar studies.
• Population standard deviation: an estimate of the population parameter based on a previous study or a pilot study of your own.

Once you’ve collected all of your data, you can inspect them and calculate descriptive statistics that summarize them.

Inspect your data

There are various ways to inspect your data, including the following:

• Organizing data from each variable in frequency distribution tables .
• Displaying data from a key variable in a bar chart to view the distribution of responses.
• Visualizing the relationship between two variables using a scatter plot .

By visualizing your data in tables and graphs, you can assess whether your data follow a skewed or normal distribution and whether there are any outliers or missing data.

A normal distribution means that your data are symmetrically distributed around a center where most values lie, with the values tapering off at the tail ends.

In contrast, a skewed distribution is asymmetric and has more values on one end than the other. The shape of the distribution is important to keep in mind because only some descriptive statistics should be used with skewed distributions.

Extreme outliers can also produce misleading statistics, so you may need a systematic approach to dealing with these values.

Calculate measures of central tendency

Measures of central tendency describe where most of the values in a data set lie. Three main measures of central tendency are often reported:

• Mode : the most popular response or value in the data set.
• Median : the value in the exact middle of the data set when ordered from low to high.
• Mean : the sum of all values divided by the number of values.

However, depending on the shape of the distribution and level of measurement, only one or two of these measures may be appropriate. For example, many demographic characteristics can only be described using the mode or proportions, while a variable like reaction time may not have a mode at all.

Calculate measures of variability

Measures of variability tell you how spread out the values in a data set are. Four main measures of variability are often reported:

• Range : the highest value minus the lowest value of the data set.
• Interquartile range : the range of the middle half of the data set.
• Standard deviation : the average distance between each value in your data set and the mean.
• Variance : the square of the standard deviation.

Once again, the shape of the distribution and level of measurement should guide your choice of variability statistics. The interquartile range is the best measure for skewed distributions, while standard deviation and variance provide the best information for normal distributions.

Using your table, you should check whether the units of the descriptive statistics are comparable for pretest and posttest scores. For example, are the variance levels similar across the groups? Are there any extreme values? If there are, you may need to identify and remove extreme outliers in your data set or transform your data before performing a statistical test.

From this table, we can see that the mean score increased after the meditation exercise, and the variances of the two scores are comparable. Next, we can perform a statistical test to find out if this improvement in test scores is statistically significant in the population. Example: Descriptive statistics (correlational study) After collecting data from 653 students, you tabulate descriptive statistics for annual parental income and GPA.

It’s important to check whether you have a broad range of data points. If you don’t, your data may be skewed towards some groups more than others (e.g., high academic achievers), and only limited inferences can be made about a relationship.

A number that describes a sample is called a statistic , while a number describing a population is called a parameter . Using inferential statistics , you can make conclusions about population parameters based on sample statistics.

Researchers often use two main methods (simultaneously) to make inferences in statistics.

• Estimation: calculating population parameters based on sample statistics.
• Hypothesis testing: a formal process for testing research predictions about the population using samples.

You can make two types of estimates of population parameters from sample statistics:

• A point estimate : a value that represents your best guess of the exact parameter.
• An interval estimate : a range of values that represent your best guess of where the parameter lies.

If your aim is to infer and report population characteristics from sample data, it’s best to use both point and interval estimates in your paper.

You can consider a sample statistic a point estimate for the population parameter when you have a representative sample (e.g., in a wide public opinion poll, the proportion of a sample that supports the current government is taken as the population proportion of government supporters).

There’s always error involved in estimation, so you should also provide a confidence interval as an interval estimate to show the variability around a point estimate.

A confidence interval uses the standard error and the z score from the standard normal distribution to convey where you’d generally expect to find the population parameter most of the time.

Hypothesis testing

Using data from a sample, you can test hypotheses about relationships between variables in the population. Hypothesis testing starts with the assumption that the null hypothesis is true in the population, and you use statistical tests to assess whether the null hypothesis can be rejected or not.

Statistical tests determine where your sample data would lie on an expected distribution of sample data if the null hypothesis were true. These tests give two main outputs:

• A test statistic tells you how much your data differs from the null hypothesis of the test.
• A p value tells you the likelihood of obtaining your results if the null hypothesis is actually true in the population.

Statistical tests come in three main varieties:

• Comparison tests assess group differences in outcomes.
• Regression tests assess cause-and-effect relationships between variables.
• Correlation tests assess relationships between variables without assuming causation.

Your choice of statistical test depends on your research questions, research design, sampling method, and data characteristics.

Parametric tests

Parametric tests make powerful inferences about the population based on sample data. But to use them, some assumptions must be met, and only some types of variables can be used. If your data violate these assumptions, you can perform appropriate data transformations or use alternative non-parametric tests instead.

A regression models the extent to which changes in a predictor variable results in changes in outcome variable(s).

• A simple linear regression includes one predictor variable and one outcome variable.
• A multiple linear regression includes two or more predictor variables and one outcome variable.

Comparison tests usually compare the means of groups. These may be the means of different groups within a sample (e.g., a treatment and control group), the means of one sample group taken at different times (e.g., pretest and posttest scores), or a sample mean and a population mean.

• A t test is for exactly 1 or 2 groups when the sample is small (30 or less).
• A z test is for exactly 1 or 2 groups when the sample is large.
• An ANOVA is for 3 or more groups.

The z and t tests have subtypes based on the number and types of samples and the hypotheses:

• If you have only one sample that you want to compare to a population mean, use a one-sample test .
• If you have paired measurements (within-subjects design), use a dependent (paired) samples test .
• If you have completely separate measurements from two unmatched groups (between-subjects design), use an independent (unpaired) samples test .
• If you expect a difference between groups in a specific direction, use a one-tailed test .
• If you don’t have any expectations for the direction of a difference between groups, use a two-tailed test .

The only parametric correlation test is Pearson’s r . The correlation coefficient ( r ) tells you the strength of a linear relationship between two quantitative variables.

However, to test whether the correlation in the sample is strong enough to be important in the population, you also need to perform a significance test of the correlation coefficient, usually a t test, to obtain a p value. This test uses your sample size to calculate how much the correlation coefficient differs from zero in the population.

You use a dependent-samples, one-tailed t test to assess whether the meditation exercise significantly improved math test scores. The test gives you:

• a t value (test statistic) of 3.00
• a p value of 0.0028

Although Pearson’s r is a test statistic, it doesn’t tell you anything about how significant the correlation is in the population. You also need to test whether this sample correlation coefficient is large enough to demonstrate a correlation in the population.

A t test can also determine how significantly a correlation coefficient differs from zero based on sample size. Since you expect a positive correlation between parental income and GPA, you use a one-sample, one-tailed t test. The t test gives you:

• a t value of 3.08
• a p value of 0.001

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The final step of statistical analysis is interpreting your results.

Statistical significance

In hypothesis testing, statistical significance is the main criterion for forming conclusions. You compare your p value to a set significance level (usually 0.05) to decide whether your results are statistically significant or non-significant.

Statistically significant results are considered unlikely to have arisen solely due to chance. There is only a very low chance of such a result occurring if the null hypothesis is true in the population.

This means that you believe the meditation intervention, rather than random factors, directly caused the increase in test scores. Example: Interpret your results (correlational study) You compare your p value of 0.001 to your significance threshold of 0.05. With a p value under this threshold, you can reject the null hypothesis. This indicates a statistically significant correlation between parental income and GPA in male college students.

Note that correlation doesn’t always mean causation, because there are often many underlying factors contributing to a complex variable like GPA. Even if one variable is related to another, this may be because of a third variable influencing both of them, or indirect links between the two variables.

Effect size

A statistically significant result doesn’t necessarily mean that there are important real life applications or clinical outcomes for a finding.

In contrast, the effect size indicates the practical significance of your results. It’s important to report effect sizes along with your inferential statistics for a complete picture of your results. You should also report interval estimates of effect sizes if you’re writing an APA style paper .

With a Cohen’s d of 0.72, there’s medium to high practical significance to your finding that the meditation exercise improved test scores. Example: Effect size (correlational study) To determine the effect size of the correlation coefficient, you compare your Pearson’s r value to Cohen’s effect size criteria.

Decision errors

Type I and Type II errors are mistakes made in research conclusions. A Type I error means rejecting the null hypothesis when it’s actually true, while a Type II error means failing to reject the null hypothesis when it’s false.

You can aim to minimize the risk of these errors by selecting an optimal significance level and ensuring high power . However, there’s a trade-off between the two errors, so a fine balance is necessary.

Frequentist versus Bayesian statistics

Traditionally, frequentist statistics emphasizes null hypothesis significance testing and always starts with the assumption of a true null hypothesis.

However, Bayesian statistics has grown in popularity as an alternative approach in the last few decades. In this approach, you use previous research to continually update your hypotheses based on your expectations and observations.

Bayes factor compares the relative strength of evidence for the null versus the alternative hypothesis rather than making a conclusion about rejecting the null hypothesis or not.

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

• Student’s  t -distribution
• Normal distribution
• Null and Alternative Hypotheses
• Chi square tests
• Confidence interval

Methodology

• Cluster sampling
• Stratified sampling
• Data cleansing
• Reproducibility vs Replicability
• Peer review
• Likert scale

Research bias

• Implicit bias
• Framing effect
• Cognitive bias
• Placebo effect
• Hawthorne effect
• Hostile attribution bias
• Affect heuristic

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Home > Mathematics and Statistics > MathStat TDs > Masters Theses

Mathematics and Statistics Masters Theses

Theses from 2024 2024.

A new proper orthogonal decomposition method with second difference quotients for the wave equation , Andrew Calvin Janes

The deep bsde method , Daniel Kovach

Theses from 2023 2023

THE APPLICATION OF STATISTICAL MODELING TO IDENTIFY GENETIC ASSOCIATIONS WITH MILD TRAUMATIC BRAIN INJURY OUTCOMES , Caroline Schott

META-ANALYSIS OF MESENCHYMAL STEM CELL GENE EXPRESSION MICROARRAY DATA FROM OBESE AND NON-OBESE PATIENTS , Dakota William Shields

Theses from 2022 2022

Continuous and discrete models for optimal harvesting in fisheries , Nagham Abbas Al Qubbanchee

Several problems in nonlinear Schrödinger equations , Tim Van Hoose

Theses from 2020 2020

Decoupled finite element methods for general steady two-dimensional Boussinesq equations , Lioba Boveleth

Quantifying effects of sleep deprivation on cognitive performance , Quang Nghia Le

The application of machine learning models in the concussion diagnosis process , Sujit Subhash

Theses from 2019 2019

Less is more: Beating the market with recurrent reinforcement learning , Louis Kurt Bernhard Steinmeister

Theses from 2018 2018

Models for high dimensional spatially correlated risks and application to thunderstorm loss data in Texas , Tobias Merk

An investigation of the influence of the 2007-2009 recession on the day of the week effect for the S&P 500 and its sectors , Marcel Alwin Trick

Theses from 2017 2017

The pantograph equation in quantum calculus , Thomas Griebel

Comparing region level testing methods for differential DNA methylation analysis , Arnold Albert Harder

A review of random matrix theory with an application to biological data , Jesse Aaron Marks

Family-based association studies of autism in boys via facial-feature clusters , Luke Andrew Settles

Theses from 2016 2016

Pricing of geometric Asian options in general affine stochastic volatility models , Johannes Ruppert

On the double chain ladder for reserve estimation with bootstrap applications , Larissa Schoepf

Theses from 2015 2015

Some combinatorial applications of Sage, an open source program , Jessica Ruth Chowning

Day of the week effect in returns and volatility of the S&P 500 sector indices , Juan Liu

Application of loglinear models to claims triangle runoff data , Netanya Lee Martin

Theses from 2014 2014

Adaptive wavelet discretization of tensor products in H-Tucker format , Mazen Ali

An iterative algorithm for variational data assimilation problems , Xin Shen

Statistical analysis of sleep patterns in Drosophila melanogaster , Luyang Wang

Theses from 2013 2013

Statistical analysis of microarray data in sleep deprivation , Stephanie Marie Berhorst

Immersed finite element method for interface problems with algebraic multigrid solver , Wenqiang Feng

Theses from 2012 2012

Abel dynamic equations of the first and second kind , Sabrina Heike Streipert

Lattice residuability , Philip Theodore Thiem

Theses from 2011 2011

A time series approach to electric load modelling , Matthias Benjamin Noller

Theses from 2010 2010

Closed-form solutions to discrete-time portfolio optimization problems , Mathias Christian Goeggel

Inverse limits with upper semi-continuous set valued bonding functions: an example , Christopher David Jacobsen

Theses from 2009 2009

The analogue of the iterated logarithm for quantum difference equations , Karl Friedrich Ulrich

Theses from 2008 2008

Modeling particulate matter emissions indices at the Hartsfield-Jackson Atlanta International Airport , Lu Gan

The dynamic multiplier-accelerator model in economics , Julius Severi Heim

Dynamic equations with piecewise continuous argument , Christian Keller

Theses from 2007 2007

Ostrowski and Grüss inequalities on time scales , Thomas Matthews

The Black-Scholes equation in quantum calculus , Christian Müttel

Computerized proofs of hypergeometric identities: Methods, advances, and limitations , Paul Nathaniel Runnion

Screening for noise variables , Lisa Trautwein

Theses from 2006 2006

Distance function applications of object comparison in artificial vision systems , Christina Michelle Ayres

Sensitivity analysis on the relationship between alcohol abuse or dependence and wages , Tim Jensen

Sensitivity analysis on the relationship between alcohol abuse or dependence and annual hours worked , Stefan Koerner

Endogeneity bias and two-stage least squares: a simulation study , Xujun Wang

Theses from 2005 2005

Local compactness of the hyperspace of connected subsets , Robbie A. Beane

A sequential approach to supersaturated design , Angela Marie Jugan

Tests for gene-treatment interaction in microarray data analysis , Wanrong Yin

Theses from 2003 2003

Pricing of European options , Dirk Rohmeder

Prediction intervals for the binomial distribution with dependent trials , Florian Sebastian Rueck

Theses from 2002 2002

The use of a Marakov dependent Bernoulli process to model the relationship between employment status and drug use , Kathrin Koetting

Theses from 2000 2000

Inverse limits on [0,1] using sequences of piecewise linear unimodal bonding maps , Brian Edward Raines

Theses from 1998 1998

A two-stage step-stress accelerated life testing scheme , Phyllis E. Pound Singer

Theses from 1997 1997

Some properties of hereditarily indecomposable chainable continua , Thomas John Kacvinsky

Theses from 1996 1996

The Axiom of Choice, well-ordering property, Continuum Hypothesis, and other meta-mathematical considerations , Daniel Collins

Theses from 1994 1994

Approximate distributional results for tolerance limits and confidence limits on reliability based on the maximum likelihood estimators for the logistic distribution , Teriann Collins

Theses from 1986 1986

Investigating the output angular acceleration extrema of the planar four bar mechanism , Matthew H. Koebbe

Theses from 1984 1984

Approximating distributions in order restricted inference : the simple tree ordering , Tuan Anh Tran

Theses from 1982 1982

Goodness-of-fit for the Weibull distribution with unknown parameters and censored sampling. , Michael Edward Aho

Theses from 1979 1979

On L convergence of Fourier series. , William O. Bray

Theses from 1977 1977

Characterizations of inner product spaces. , John Lee Roy Williams

Theses from 1975 1975

A study of several substitution ciphers using mathematical models. , Wanda Louise Garner

Theses from 1974 1974

Models for molecular vibration , Allan Bruce Capps

The completions of local rings and their modules. , Christopher Scott Taber

Linear geometry , Phyllis L. Thomas

Theses from 1971 1971

Integrability of the sums of the trigonometric series 1/2 aₒ + ∞ [over] Σ [over] n=1 a n cos nΘ and ∞ [over] Σ [over] n=1 a n sin nΘ , John William Garrett

Inclusion theorems for boundary value problems for delay differential equations , Leon M. Hall

Theses from 1965 1965

A study of certain conservative sets for parameters in the linear statistical model , Roger Alan Chapin

Comparison of methods to select a probability model , Howard Lyndal Colburn

Latent class analysis and information retrieval , George Loyd Jensen

Linear and quadratic programming with more than one objective function , William John Lodholz

Tschebyscheff fitting with polynomials and nonlinear functions , George F. Luffel

Theses from 1964 1964

The effect of matrix condition in the solution of a system of linear algebraic equations. , Herbert R. Alcorn

Estimation and tabulation of bias coefficients for regression analysis in incompletely specified linear models. , Harry Kerry Edwards

A study of a method for selecting the best of two or more mathematical models , August J. Garver

A study of methods for estimating parameters in the model y(t) = A₁e -p₁t + A₂e -p₂t + ϵ , Gerald Nicholas Haas

A parameter perturbation procedure for obtaining a solution to systems of nonlinear equations. , James Carlton Helm

A study of stability of numerical solution for parabolic partial differential equations. , Tsang-Chi Huang

A numerical study of Van Der Pol's nonlinear differential equation for various values of the parameter E. , Charles C. Limbaugh

A study on estimating parameters restricted by linear inequalities , William Lawrence May

Minimization of Boolean functions. , Don Laroy Rogier

A method to give the best linear combination of order statistics to estimate the mean of any symmetric population , Robert M. Smith

On a numerical solution of Dirichlet type problems with singularity on the boundary. , Randall Loran Yoakum

Theses from 1963 1963

A study of methods for estimating parameters in rational polynomial models , Thomas B. Baird

Investigation of measures of ill-conditioning , Thomas D. Calton

A numerical approach to a Sturm-Liouville type problem with variable coefficients and its application to heat transfer and temperature prediction in the lower atmosphere. , Troyce Don Jones

A study of methods for determining confidence intervals for the mean of a normal distribution with unknown varience by comparison of average lengths , Karl Richard Kneile

Stability properties of various predictor corrector methods for solving ordinary differential equations numerically. , Charles Edward. Leslie

Mathematical techniques in the solution of boundary value problems. , Vincent Paul Pusateri

A modified algorithm for Henrici's solution of y' ' = f (x,y) , Frank Garnett Walters

Theses from 1962 1962

An investigation of Lehmer's method for finding the roots of polynomial equations using the Royal-McBee LGP-30 , James W. Joiner

Theses from 1931 1931

The spinning top , Aaron Jefferson Miles

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Department of statistics: dissertations, theses, and student work.

Measuring Jury Perception of Explainable Machine Learning and Demonstrative Evidence , Rachel Rogers

Examining the Effect of Word Embeddings and Preprocessing Methods on Fake News Detection , Jessica Hauschild

Exploring Experimental Design and Multivariate Analysis Techniques for Evaluating Community Structure of Bacteria in Microbiome Data , Kelsey Karnik

Human Perception of Exponentially Increasing Data Displayed on a Log Scale Evaluated Through Experimental Graphics Tasks , Emily Robinson

Factors Influencing Student Outcomes in a Large, Online Simulation-Based Introductory Statistics Course , Ella M. Burnham

Comparing Machine Learning Techniques with State-of-the-Art Parametric Prediction Models for Predicting Soybean Traits , Susweta Ray

Using Stability to Select a Shrinkage Method , Dean Dustin

Statistical Methodology to Establish a Benchmark for Evaluating Antimicrobial Resistance Genes through Real Time PCR assay , Enakshy Dutta

Group Testing Identification: Objective Functions, Implementation, and Multiplex Assays , Brianna D. Hitt

Community Impact on the Home Advantage within NCAA Men's Basketball , Erin O'Donnell

Optimal Design for a Causal Structure , Zaher Kmail

Role of Misclassification Estimates in Estimating Disease Prevalence and a Non-Linear Approach to Study Synchrony Using Heart Rate Variability in Chickens , Dola Pathak

A Characterization of a Value Added Model and a New Multi-Stage Model For Estimating Teacher Effects Within Small School Systems , Julie M. Garai

Methods to Account for Breed Composition in a Bayesian GWAS Method which Utilizes Haplotype Clusters , Danielle F. Wilson-Wells

Beta-Binomial Kriging: A New Approach to Modeling Spatially Correlated Proportions , Aimee Schwab

Simulations of a New Response-Adaptive Biased Coin Design , Aleksandra Stein

MODELING THE DYNAMIC PROCESSES OF CHALLENGE AND RECOVERY (STRESS AND STRAIN) OVER TIME , Fan Yang

A New Approach to Modeling Multivariate Time Series on Multiple Temporal Scales , Tucker Zeleny

A Reduced Bias Method of Estimating Variance Components in Generalized Linear Mixed Models , Elizabeth A. Claassen

NEW STATISTICAL METHODS FOR ANALYSIS OF HISTORICAL DATA FROM WILDLIFE POPULATIONS , Trevor Hefley

Informative Retesting for Hierarchical Group Testing , Michael S. Black

A Test for Detecting Changes in Closed Networks Based on the Number of Communications Between Nodes , Christopher S. Wichman

GROUP TESTING REGRESSION MODELS , Boan Zhang

A Comparison of Spatial Prediction Techniques Using Both Hard and Soft Data , Megan L. Liedtke Tesar

STUDYING THE HANDLING OF HEAT STRESSED CATTLE USING THE ADDITIVE BI-LOGISTIC MODEL TO FIT BODY TEMPERATURE , Fan Yang

Estimating Teacher Effects Using Value-Added Models , Jennifer L. Green

SEQUENCE COMPARISON AND STOCHASTIC MODEL BASED ON MULTI-ORDER MARKOV MODELS , Xiang Fang

DETECTING DIFFERENTIALLY EXPRESSED GENES WHILE CONTROLLING THE FALSE DISCOVERY RATE FOR MICROARRAY DATA , SHUO JIAO

Spatial Clustering Using the Likelihood Function , April Kerby

FULLY EXPONENTIAL LAPLACE APPROXIMATION EM ALGORITHM FOR NONLINEAR MIXED EFFECTS MODELS , Meijian Zhou

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Introduction to Research Statistical Analysis: An Overview of the Basics

Christian vandever.

1 HCA Healthcare Graduate Medical Education

Description

This article covers many statistical ideas essential to research statistical analysis. Sample size is explained through the concepts of statistical significance level and power. Variable types and definitions are included to clarify necessities for how the analysis will be interpreted. Categorical and quantitative variable types are defined, as well as response and predictor variables. Statistical tests described include t-tests, ANOVA and chi-square tests. Multiple regression is also explored for both logistic and linear regression. Finally, the most common statistics produced by these methods are explored.

Introduction

Statistical analysis is necessary for any research project seeking to make quantitative conclusions. The following is a primer for research-based statistical analysis. It is intended to be a high-level overview of appropriate statistical testing, while not diving too deep into any specific methodology. Some of the information is more applicable to retrospective projects, where analysis is performed on data that has already been collected, but most of it will be suitable to any type of research. This primer will help the reader understand research results in coordination with a statistician, not to perform the actual analysis. Analysis is commonly performed using statistical programming software such as R, SAS or SPSS. These allow for analysis to be replicated while minimizing the risk for an error. Resources are listed later for those working on analysis without a statistician.

After coming up with a hypothesis for a study, including any variables to be used, one of the first steps is to think about the patient population to apply the question. Results are only relevant to the population that the underlying data represents. Since it is impractical to include everyone with a certain condition, a subset of the population of interest should be taken. This subset should be large enough to have power, which means there is enough data to deliver significant results and accurately reflect the study’s population.

The first statistics of interest are related to significance level and power, alpha and beta. Alpha (α) is the significance level and probability of a type I error, the rejection of the null hypothesis when it is true. The null hypothesis is generally that there is no difference between the groups compared. A type I error is also known as a false positive. An example would be an analysis that finds one medication statistically better than another, when in reality there is no difference in efficacy between the two. Beta (β) is the probability of a type II error, the failure to reject the null hypothesis when it is actually false. A type II error is also known as a false negative. This occurs when the analysis finds there is no difference in two medications when in reality one works better than the other. Power is defined as 1-β and should be calculated prior to running any sort of statistical testing. Ideally, alpha should be as small as possible while power should be as large as possible. Power generally increases with a larger sample size, but so does cost and the effect of any bias in the study design. Additionally, as the sample size gets bigger, the chance for a statistically significant result goes up even though these results can be small differences that do not matter practically. Power calculators include the magnitude of the effect in order to combat the potential for exaggeration and only give significant results that have an actual impact. The calculators take inputs like the mean, effect size and desired power, and output the required minimum sample size for analysis. Effect size is calculated using statistical information on the variables of interest. If that information is not available, most tests have commonly used values for small, medium or large effect sizes.

When the desired patient population is decided, the next step is to define the variables previously chosen to be included. Variables come in different types that determine which statistical methods are appropriate and useful. One way variables can be split is into categorical and quantitative variables. ( Table 1 ) Categorical variables place patients into groups, such as gender, race and smoking status. Quantitative variables measure or count some quantity of interest. Common quantitative variables in research include age and weight. An important note is that there can often be a choice for whether to treat a variable as quantitative or categorical. For example, in a study looking at body mass index (BMI), BMI could be defined as a quantitative variable or as a categorical variable, with each patient’s BMI listed as a category (underweight, normal, overweight, and obese) rather than the discrete value. The decision whether a variable is quantitative or categorical will affect what conclusions can be made when interpreting results from statistical tests. Keep in mind that since quantitative variables are treated on a continuous scale it would be inappropriate to transform a variable like which medication was given into a quantitative variable with values 1, 2 and 3.

Categorical vs. Quantitative Variables

Both of these types of variables can also be split into response and predictor variables. ( Table 2 ) Predictor variables are explanatory, or independent, variables that help explain changes in a response variable. Conversely, response variables are outcome, or dependent, variables whose changes can be partially explained by the predictor variables.

Response vs. Predictor Variables

Choosing the correct statistical test depends on the types of variables defined and the question being answered. The appropriate test is determined by the variables being compared. Some common statistical tests include t-tests, ANOVA and chi-square tests.

T-tests compare whether there are differences in a quantitative variable between two values of a categorical variable. For example, a t-test could be useful to compare the length of stay for knee replacement surgery patients between those that took apixaban and those that took rivaroxaban. A t-test could examine whether there is a statistically significant difference in the length of stay between the two groups. The t-test will output a p-value, a number between zero and one, which represents the probability that the two groups could be as different as they are in the data, if they were actually the same. A value closer to zero suggests that the difference, in this case for length of stay, is more statistically significant than a number closer to one. Prior to collecting the data, set a significance level, the previously defined alpha. Alpha is typically set at 0.05, but is commonly reduced in order to limit the chance of a type I error, or false positive. Going back to the example above, if alpha is set at 0.05 and the analysis gives a p-value of 0.039, then a statistically significant difference in length of stay is observed between apixaban and rivaroxaban patients. If the analysis gives a p-value of 0.91, then there was no statistical evidence of a difference in length of stay between the two medications. Other statistical summaries or methods examine how big of a difference that might be. These other summaries are known as post-hoc analysis since they are performed after the original test to provide additional context to the results.

Analysis of variance, or ANOVA, tests can observe mean differences in a quantitative variable between values of a categorical variable, typically with three or more values to distinguish from a t-test. ANOVA could add patients given dabigatran to the previous population and evaluate whether the length of stay was significantly different across the three medications. If the p-value is lower than the designated significance level then the hypothesis that length of stay was the same across the three medications is rejected. Summaries and post-hoc tests also could be performed to look at the differences between length of stay and which individual medications may have observed statistically significant differences in length of stay from the other medications. A chi-square test examines the association between two categorical variables. An example would be to consider whether the rate of having a post-operative bleed is the same across patients provided with apixaban, rivaroxaban and dabigatran. A chi-square test can compute a p-value determining whether the bleeding rates were significantly different or not. Post-hoc tests could then give the bleeding rate for each medication, as well as a breakdown as to which specific medications may have a significantly different bleeding rate from each other.

A slightly more advanced way of examining a question can come through multiple regression. Regression allows more predictor variables to be analyzed and can act as a control when looking at associations between variables. Common control variables are age, sex and any comorbidities likely to affect the outcome variable that are not closely related to the other explanatory variables. Control variables can be especially important in reducing the effect of bias in a retrospective population. Since retrospective data was not built with the research question in mind, it is important to eliminate threats to the validity of the analysis. Testing that controls for confounding variables, such as regression, is often more valuable with retrospective data because it can ease these concerns. The two main types of regression are linear and logistic. Linear regression is used to predict differences in a quantitative, continuous response variable, such as length of stay. Logistic regression predicts differences in a dichotomous, categorical response variable, such as 90-day readmission. So whether the outcome variable is categorical or quantitative, regression can be appropriate. An example for each of these types could be found in two similar cases. For both examples define the predictor variables as age, gender and anticoagulant usage. In the first, use the predictor variables in a linear regression to evaluate their individual effects on length of stay, a quantitative variable. For the second, use the same predictor variables in a logistic regression to evaluate their individual effects on whether the patient had a 90-day readmission, a dichotomous categorical variable. Analysis can compute a p-value for each included predictor variable to determine whether they are significantly associated. The statistical tests in this article generate an associated test statistic which determines the probability the results could be acquired given that there is no association between the compared variables. These results often come with coefficients which can give the degree of the association and the degree to which one variable changes with another. Most tests, including all listed in this article, also have confidence intervals, which give a range for the correlation with a specified level of confidence. Even if these tests do not give statistically significant results, the results are still important. Not reporting statistically insignificant findings creates a bias in research. Ideas can be repeated enough times that eventually statistically significant results are reached, even though there is no true significance. In some cases with very large sample sizes, p-values will almost always be significant. In this case the effect size is critical as even the smallest, meaningless differences can be found to be statistically significant.

These variables and tests are just some things to keep in mind before, during and after the analysis process in order to make sure that the statistical reports are supporting the questions being answered. The patient population, types of variables and statistical tests are all important things to consider in the process of statistical analysis. Any results are only as useful as the process used to obtain them. This primer can be used as a reference to help ensure appropriate statistical analysis.

Funding Statement

This research was supported (in whole or in part) by HCA Healthcare and/or an HCA Healthcare affiliated entity.

Conflicts of Interest

The author declares he has no conflicts of interest.

Christian Vandever is an employee of HCA Healthcare Graduate Medical Education, an organization affiliated with the journal’s publisher.

This research was supported (in whole or in part) by HCA Healthcare and/or an HCA Healthcare affiliated entity. The views expressed in this publication represent those of the author(s) and do not necessarily represent the official views of HCA Healthcare or any of its affiliated entities.

Statistical Methods in Theses: Guidelines and Explanations

Signed August 2018 Naseem Al-Aidroos, PhD, Christopher Fiacconi, PhD Deborah Powell, PhD, Harvey Marmurek, PhD, Ian Newby-Clark, PhD, Jeffrey Spence, PhD, David Stanley, PhD, Lana Trick, PhD

Version:  2.00

This document is an organizational aid, and workbook, for students. We encourage students to take this document to meetings with their advisor and committee. This guide should enhance a committee’s ability to assess key areas of a student’s work. 

In recent years a number of well-known and apparently well-established findings have  failed to replicate , resulting in what is commonly referred to as the replication crisis. The APA Publication Manual 6 th Edition notes that “The essence of the scientific method involves observations that can be repeated and verified by others.” (p. 12). However, a systematic investigation of the replicability of psychology findings published in  Science  revealed that over half of psychology findings do not replicate (see a related commentary in  Nature ). Even more disturbing, a  Bayesian reanalysis of the reproducibility project  showed that 64% of studies had sample sizes so small that strong evidence for or against the null or alternative hypotheses did not exist. Indeed, Morey and Lakens (2016) concluded that most of psychology is statistically unfalsifiable due to small sample sizes and correspondingly low power (see  article ). Our discipline’s reputation is suffering. News of the replication crisis has reached the popular press (e.g.,  The Atlantic ,   The Economist ,   Slate , Last Week Tonight ).

An increasing number of psychologists have responded by promoting new research standards that involve open science and the elimination of  Questionable Research Practices . The open science perspective is made manifest in the  Transparency and Openness Promotion (TOP) guidelines  for journal publications. These guidelines were adopted some time ago by the  Association for Psychological Science . More recently, the guidelines were adopted by American Psychological Association journals ( see details ) and journals published by Elsevier ( see details ). It appears likely that, in the very near future, most journals in psychology will be using an open science approach. We strongly advise readers to take a moment to inspect the  TOP Guidelines Summary Table . 

A key aspect of open science and the TOP guidelines is the sharing of data associated with published research (with respect to medical research, see point #35 in the  World Medical Association Declaration of Helsinki ). This practice is viewed widely as highly important. Indeed, open science is recommended by  all G7 science ministers . All Tri-Agency grants must include a data-management plan that includes plans for sharing: “ research data resulting from agency funding should normally be preserved in a publicly accessible, secure and curated repository or other platform for discovery and reuse by others.”  Moreover, a 2017 editorial published in the  New England Journal of Medicine announced that the  International Committee of Medical Journal Editors believes there is  “an ethical obligation to responsibly share data.”  As of this writing,  60% of highly ranked psychology journals require or encourage data sharing .

The increasing importance of demonstrating that findings are replicable is reflected in calls to make replication a requirement for the promotion of faculty (see details in  Nature ) and experts in open science are now refereeing applications for tenure and promotion (see details at the  Center for Open Science  and  this article ). Most dramatically, in one instance, a paper resulting from a dissertation was retracted due to misleading findings attributable to Questionable Research Practices. Subsequent to the retraction, the Ohio State University’s Board of Trustees unanimously revoked the PhD of the graduate student who wrote the dissertation ( see details ). Thus, the academic environment is changing and it is important to work toward using new best practices in lieu of older practices—many of which are synonymous with Questionable Research Practices. Doing so should help you avoid later career regrets and subsequent  public mea culpas . One way to achieve your research objectives in this new academic environment is  to incorporate replications into your research . Replications are becoming more common and there are even websites dedicated to helping students conduct replications (e.g.,  Psychology Science Accelerator ) and indexing the success of replications (e.g., Curate Science ). You might even consider conducting a replication for your thesis (subject to committee approval).

As early-career researchers, it is important to be aware of the changing academic environment. Senior principal investigators may be  reluctant to engage in open science  (see this student perspective in a  blog post  and  podcast ) and research on resistance to data sharing indicates that one of the barriers to sharing data is that researchers do not feel that they have knowledge of  how to share data online . This document is an educational aid and resource to provide students with introductory knowledge of how to participate in open science and online data sharing to start their education on these subjects. 

Guidelines and Explanations

In light of the changes in psychology, faculty members who teach statistics/methods have reviewed the literature and generated this guide for graduate students. The guide is intended to enhance the quality of student theses by facilitating their engagement in open and transparent research practices and by helping them avoid Questionable Research Practices, many of which are now deemed unethical and covered in the ethics section of textbooks.

This document is an informational tool.

How to Start

In order to follow best practices, some first steps need to be followed. Here is a list of things to do:

• Get an Open Science account. Registration at  osf.io  is easy!
• If conducting confirmatory hypothesis testing for your thesis, pre-register your hypotheses (see Section 1-Hypothesizing). The Open Science Foundation website has helpful  tutorials  and  guides  to get you going.
• Also, pre-register your data analysis plan. Pre-registration typically includes how and when you will stop collecting data, how you will deal with violations of statistical assumptions and points of influence (“outliers”), the specific measures you will use, and the analyses you will use to test each hypothesis, possibly including the analysis script. Again, there is a lot of help available for this. 

Exploratory and Confirmatory Research Are Both of Value, But Do Not Confuse the Two

We note that this document largely concerns confirmatory research (i.e., testing hypotheses). We by no means intend to devalue exploratory research. Indeed, it is one of the primary ways that hypotheses are generated for (possible) confirmation. Instead, we emphasize that it is important that you clearly indicate what of your research is exploratory and what is confirmatory. Be clear in your writing and in your preregistration plan. You should explicitly indicate which of your analyses are exploratory and which are confirmatory. Please note also that if you are engaged in exploratory research, then Null Hypothesis Significance Testing (NHST) should probably be avoided (see rationale in  Gigerenzer  (2004) and  Wagenmakers et al., (2012) ). 

This document is structured around the stages of thesis work:  hypothesizing, design, data collection, analyses, and reporting – consistent with the headings used by Wicherts et al. (2016). We also list the Questionable Research Practices associated with each stage and provide suggestions for avoiding them. We strongly advise going through all of these sections during thesis/dissertation proposal meetings because a priori decisions need to be made prior to data collection (including analysis decisions). 

To help to ensure that the student has informed the committee about key decisions at each stage, there are check boxes at the end of each section.

How to Use This Document in a Proposal Meeting

• Print off a copy of this document and take it to the proposal meeting.
• During the meeting, use the document to seek assistance from faculty to address potential problems.
• Revisit responses to issues raised by this document (especially the Analysis and Reporting Stages) when you are seeking approval to proceed to defense.

Consultation and Help Line

Note that the Center for Open Science now has a help line (for individual researchers and labs) you can call for help with open science issues. They also have training workshops. Please see their  website  for details.

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A Handbook of Statistical Analyses using SPSS

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These notes are a basic guide to statistics using SPSS and are primarily written for undergraduate students, as well as for graduates and scholars with limited statistical knowledge. Explanations of basic statistical concepts are provided, along with an introduction to confidence intervals and a brief description of each statistical test. However, the notes focus on applied statistics. In other words, emphasis is placed on understanding which statistical test should be used for different types of data and different types of problems under examination. Both descriptive and inferential statistics are covered and a step-by-step description of how to run the most widely used univariate and multivariate tests is provided.

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Neuromarketing and big data analysis of banking firms’ website interfaces and performance.

1. Introduction

2. literature background, 2.1. banking firms, digital marketing, and user engagement, 2.2. metrics and kpis of friendly website user interface (ui), 2.3. neuromarketing and big data analysis implications on website interface and performance, 2.4. hypotheses development, 3. materials and methods, 3.1. methodological concept.

• The research started with the collection of data on website customers and digital marketing activities from banking firm websites. A website’s user behavioral data (pages per visit, bounce rate, time on site, etc.) were sourced from the website platform Semrush [ 61 ], which enables the extraction of big data from corporate webpages.
• The next step involved statistical analysis using methods such as descriptive statistics, correlation, and linear regression. By analyzing the coefficients obtained, researchers can determine the impact of banking firms’ website customer data on their digital marketing and interface performance metrics, including purchase conversion, display ads, organic traffic, and bounce rate.
• After statistical analysis, a hybrid model (HM) incorporating agent-based models (ABMs) and System Dynamics (SD) was used for the simulation. The software AnyLogic (version 8.9.1) [ 62 ] was employed to create a hybrid model that simulates the relationships between the study’s dependent and independent variables over 360 days. This model aims to represent the dynamic interaction between banking firms’ website interface metrics and key metrics of their digital marketing strategies.
• The final stage included a neuromarketing approach to gain deeper insights from 26 participants who viewed the websites of the selected banking firms. They were instructed to search and observe, in 20 s, the selected banking firm websites and their provided financial products and services. Eye-tracking and heatmap analysis were conducted using the SeeSo Web Analysis platform (Eyedid SDK) [ 63 ]. This method seeks to extract additional information about the onsite activity and engagement of the participants from the qualitative methodological concept.

3.2. Fuzzy Cognitive Mapping (FCM) Framework

3.3. research sample, 4.1. statistical analysis, 4.2. simulation model, 4.3. neuromarketing applications, 5. discussion, 6. conclusions, 6.1. theoretical, practical, and managerial implications, 6.2. future work and limitations, author contributions, data availability statement, conflicts of interest.

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Giannakopoulos, N.T.; Sakas, D.P.; Migkos, S.P. Neuromarketing and Big Data Analysis of Banking Firms’ Website Interfaces and Performance. Electronics 2024 , 13 , 3256. https://doi.org/10.3390/electronics13163256

Giannakopoulos NT, Sakas DP, Migkos SP. Neuromarketing and Big Data Analysis of Banking Firms’ Website Interfaces and Performance. Electronics . 2024; 13(16):3256. https://doi.org/10.3390/electronics13163256

Giannakopoulos, Nikolaos T., Damianos P. Sakas, and Stavros P. Migkos. 2024. "Neuromarketing and Big Data Analysis of Banking Firms’ Website Interfaces and Performance" Electronics 13, no. 16: 3256. https://doi.org/10.3390/electronics13163256

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Rotavirus infections are a significant cause of severe diarrhea and related illness and death in children under five worldwide. Despite the global introduction of vaccinations for rotavirus over a decade ago, rotavirus infections still result in high deaths annually, mainly in low-income countries, including Ethiopia, and need special attention. This system review and meta-analysis aimed to comprehensively explore the positive proportion of rotavirus at pre- and post-vaccine introduction periods and genotype distribution in children under five with diarrhea in Ethiopia.

The review followed the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) 2020 guidelines. Database sources included PubMed, Scopus, EMBASE, and Epistemonikos, focusing on studies published before November 30, 2023. The search targeted rotavirus infection and genotype distribution in Ethiopia before and after the introduction of the Rota vaccine. Data was managed using EndNote 2020 software and stored in an Excel 2010 sheet. A random-effects model determined the pooled estimate of the rotavirus infection rate at 95% confidence intervals. The Q-and I² statistics were used to assess the study heterogeneity, and a funnel plot (Egger test) was used to determine the possibility of publication bias.

The analysis included data from nine studies conducted in different regions of Ethiopia. The overall prevalence of rotavirus infection was significant, with a prevalence rate of approximately 22.63% (1362/6039). The most common genotypes identified before the Rota vacation introduction were G1, G2, G3, G12, P [4], P [6], P [8], P [9], and P [10]. Meanwhile, G3 and P [8] genotypes were particularly prevalent after the Rota vaccine introduction. These findings highlight the importance of implementing preventive measures, such as vaccination, to reduce the burden of rotavirus infection in this population. The identified genotypes provide valuable insights for vaccine development and targeted interventions.

This study contributes to the evidence base for public health interventions and strategies to reduce the impact of rotavirus infection in children under five in Ethiopia. Despite the rollout of the Rota vaccination in Ethiopia, rotavirus heterogeneity is still high, and thus, enhancing vaccination and immunization is essential.

Peer Review reports

Introduction

Rotavirus infection detrimentally affects the childhood population, mostly in low-income counties, through the induction of severe diarrhea, leading to hospitalizations and fatalities [ 1 , 2 ]. It constitutes a significant contributor to childhood morbidity and mortality on a global scale and still annually results in > 500,000 deaths globally and > 200,000 deaths in low-income countries [ 3 ]. The frequency of diarrhea diminishes with age [ 4 , 5 ]. Several risk factors are associated with rotavirus infection, including the availability of contaminated water supplies, malnutrition, and the coexistence of individuals afflicted with gastroenteritis within the household [ 5 ]. Nevertheless, breastfeeding has been identified as a safe option against rotavirus-induced gastroenteritis. Children afflicted with rotavirus infection exhibit diminished levels of micronutrients such as ferritin and vitamin B12, rendering them more susceptible to allergic ailments [ 6 ]. Vaccination against rotavirus plays a pivotal role in preempting the onset of infection and its subsequent complications. Consequently, public health initiatives aimed at endorsing potable water consumption, adhering to effective personal hygiene practices, advocating for exclusive breastfeeding, and administering vaccinations are highly recommended to mitigate the impact of rotavirus infection within developing countries [ 7 ].

In Ethiopia, where infectious diseases pose a significant public health challenge, rotavirus infection has been a notable contributor to childhood illness and death [ 8 ]. Understanding the historical context of rotavirus infection in Ethiopia involves considering its impact on child health, healthcare infrastructure, and the burden it places on families and communities. Numerous studies in Ethiopia showed no seasonal variation in diarrhea associated with enterotoxigenic enterobacteria, rotavirus, and the two parasites Giardia lamblia and Entamoeba histolytica . The study isolated that rotavirus was present in 27.8% of the patients and 6.85% of the two parasites. The study also found that Rotavirus in 27.8% of the patients with diarrhea, most prevalent in the 7–12-month age group, and enterotoxigenic enterobacteria during the second year of life, while parasites continuously increased with age [ 9 ].

Rotaviruses are non-enveloped double-stranded RNA viruses with a complex genome of 11 segments of dsRNA and are classified into 32 G genotypes and 47 P genotypes. In Ethiopia, the distribution of rotavirus genotypes in children under five is diverse, with several dominant genotypes identified. The most common genotypes include G1, G2, G3, G12, P [4], P [6], P [8], P [9], and P [10]. The most prevalent combinations are G12P [8], G3P [6], G1P [8], and G3P [8]. These genotypes comprise a significant proportion of rotavirus strains in Ethiopia. The prevalence of rotavirus infection among children under five in Ethiopia is approximately 23%. The G3 genotype is prevalent, accounting for 27.1% of cases, followed by the P [8] genotype at 49%. The G8 genotype, which is more commonly found in cattle, has also been reported in Ethiopia, although at a lower frequency [ 10 ].

Without age restriction, the rotavirus vaccine was introduced in Ethiopia on November 13, 2013, according to the WHO/SAGE recommendation [ 11 ]. In Ethiopia, fully vaccinated children aged between 15 and 23 months took one dose of Bacille Calmette Guerin (BCG), three doses of PCV (pneumococcal conjugate vaccine), three doses of pentavalent, three doses of OPV, two doses of Rota, and two doses of measles vaccine by card plus mother history [ 12 ]. According to a study in Ethiopia, since no indication of the virus was isolated in children who had received the rotavirus vaccine, it suggests the vaccine shows a protective benefit [ 13 ].

The importance of examining rotavirus in Ethiopia resides in its implications for public health and the potential for well-informed interventions. The infection caused by the rotavirus disproportionately affects children in settings with limited resources, resulting in heightened costs for healthcare, economic burdens, and reduced productivity. Experts and policymakers can identify more susceptible populations, formulate targeted interventions, and enhance healthcare strategies by delving into the prevalence, impact, and risk factors associated with Rotavirus in Ethiopia. Furthermore, comprehending the distribution of genotypes can contribute to the development and effectiveness of vaccines.

Hence, this study aimed to comprehensively explore the positive proportion of rotavirus at pre- and post-vaccine introduction periods and genotype distribution in children under five years old with diarrhea in Ethiopia.

Materials and methods

Study protocol.

The review was performed using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) 2020 guidelines [ 14 ]. Following the STROBE checklist and additional STROME-ID items, units were used to conduct systematic reviews to evaluate the reported quality of records [ 15 ]. This systematic review and meta-analysis proposal was registered at the PROSPERO International Prospective Register of Systematic Reviews on November 24, 2023, as PROSPERO 2023 ID: = CRD42023481674.

Searching strategies and information sources

We utilized the data from PubMed, Scopus, EMBASE, Epistemonikos database, and additional sources such as Google Scholar and Addis Ababa University Electronic Thesis and Dissertation for all published and unpublished articles before November 30, 2023. The search data from databases was done based on keywords, medical subject headings (MeSH) terms, and other terms such as epidemiology, risk factors, genotype distribution, and vaccination status of rotavirus infection in the pre-vaccine and post-vaccine introduction in Ethiopia, which are available in Annex S1 Supplementary Document ( Annex file 1 ). The articles were searched and downloaded from databases on November 24–30, 2023, with language restricted to English.

However, for the search string of PubMed, Epistemonikos, EMBASE and Scopus, we used the terms; " rotavirus infection ‘’, “pre-vaccine,” " post-vaccine,‘’ “epidemiology,” " risk factors,” " genotypes,” vaccination status,” [MeSH], “Ethiopia” with the combination of Boolean logic (“AND,” OR”) based upon the given databases ( Annex file 2 ).

Study selection

Inclusion criteria.

The studies deal with the human population socio-demographics in Ethiopia under five years old (0–59 months) and original research, including cross-sectional, cohort, case-control, and randomized controlled trials (RCTs). Studies reporting epidemiological data on rotavirus infection in under-five children, including incidence and prevalence, and data on risk factors associated with rotavirus infection, specifically in the under-five age group, genotype distribution of rotavirus strains in under-five children, vaccination status of under-five children, and studies published in English or with an English translation available were included.

Exclusion criteria

Studies focusing exclusively on populations above five, review articles, editorials, commentaries, letters, and conference abstracts without full-text availability, and studies with a high risk of bias or poor methodological quality were excluded. In addition, articles conducted after November 30, 2023, excluded studies without relevant epidemiological data on rotavirus infection, risk factors, genotypes, or vaccination status in the under-five age group.

Quality assessment

The quality of the records was assessed according to the Joanna Briggs Institute’s (JBI) 2017 checklist. The included records were critically appraised using the predetermined criteria or checklist. In addition, each article was appraised using the Joanna Bridges Institute (JBI) assessment tool for observational studies, particularly the analytical cross-sectional studies design. The study with a minimum of 5 scores was considered acceptable methodological quality and included in the review [ 16 ].

On the other hand, STROME-ID (Strengthening the Reporting of Molecular Epidemiology for Infectious Diseases) was also used to investigate the quality of each selected record. This statement is an extension of the 22-item STROBE statement with 20 additional elements aiming to promote transparency, clarity, and comparability of scientific reporting, specifically in Molecular Epidemiology for Infectious Diseases studies [ 15 ].

Data extraction

Three reviewers (WT, BT, and DE) screened the titles and abstracts and independently evaluated the titles and abstracts of potentially eligible records. The full texts of selected records were assessed against inclusion criteria, and three reviewers extracted data separately using the prepared data extraction tool (Table  1 ). The extracted data included the first author’s name and publication year, study area, population/sample, sample size, laboratory diagnostic methods, and total rotavirus-isolated genotypes. The extracted data was transferred to an Excel sheet. The results were then cross-checked, with a “checked” value of “1” for discrepancies. Any discrepancies that occurred between reviewers were discussed and resolved through consensus.

Statistical analysis

The extracted data from the records was stored on the Excel version 2010 sheet. Descriptive statistics and bar graphs were prepared from extracted data in Excel 2010 and Jamovi 2.3.5. Comprehensive Meta-Analysis Version V3.ext software was installed, and a shortcut labeled on the personal computer with the Windows start menu was created. Next, the specific columns containing the study names, sample size, and outcome variables were transferred to the Comprehensive Meta-Analysis column for analysis.

A random-effect model determined the pooled rotavirus infection test to assess the possibility of publication bias by using Compressive Meta-analysis V3.exe software to analyze the data.

Operational definition

Epidemiology.

Diagnosis of the prevalence and distribution of Rotavirus infection in pre- and post-vaccine introduction periods. It includes analyzing trends, affected age groups, and regional variations to provide a thorough understanding of the disease burden.

Risk factors

Isolating the socio-economic characteristics, environmental, and topographic factors that contribute to the vulnerability of specific populations to Rotavirus infection. This analysis can guide targeted public health interventions to reduce risk and improve overall child health.

Genotype distribution

Examining the genetic diversity of Rotavirus strains circulating in Ethiopia before and after vaccine introduction. Understanding genotype distribution is crucial for monitoring strain evolution, assessing vaccine efficacy, and adapting vaccination strategies if necessary.

Vaccination status

Evaluating the impact and effectiveness of Rotavirus vaccination programs in Ethiopia. It involves assessing coverage rates, identifying challenges in vaccine distribution and administration, and determining the overall success in reducing the burden of Rotavirus-related morbidity and mortality among children.

By addressing these essential aspects, the literature aims to contribute valuable evidence that can inform evidence-based policies, improve healthcare practices, and ultimately reduce the impact of Rotavirus infection on child health in Ethiopia.

Selection process and characterization of the included studies

A systematic review and meta-analysis were conducted to estimate the incidence of rotavirus infection in Ethiopia pre- and post-vaccine introduction. A total of 479 research articles were accessed from PubMed, EMBASE, Scopus, and Epistemonikos. After excluding 52 articles due to duplication, 427 records remained. Among these, 233 were excluded for lacking laboratory diagnosis for rotavirus, and 46 were excluded for being review or systematic review articles, with 233 records considered irrelevant. After screening abstracts, titles, and full texts, 148 articles met the inclusion criteria for the systematic review and meta-analysis. Subsequently, these 148 articles were thoroughly evaluated, including only nine records in the final systematic review and meta-analysis (Fig.  1 ).

The introduction of rotavirus vaccines in Ethiopia in 2013 significantly reduced the incidence of rotavirus infections, a leading cause of severe diarrhea in children. A stratified data analysis from various study years reveals a substantial reduction in the positivity proportion of rotavirus cases after the vaccine’s introduction. Before the vaccine’s introduction, the positivity proportion was relatively high, with values ranging from 0.181 to 0.277. However, after the vaccine was introduced, there was a notable decline in the positivity proportion, particularly in 2018, where it dropped to as low as 0.044. This significant reduction indicates that the rotavirus vaccination program has profoundly impacted reducing the burden of rotavirus infections among children in Ethiopia, underscoring the need for continued monitoring and evaluation of the vaccination program.

The stratified analysis of rotavirus infections in Ethiopia provides valuable insights into the effectiveness of the rotavirus vaccine introduced in 2013. Before the vaccine rollout, data from various years of study indicated a concerning prevalence of rotavirus infections among children. For instance, in 1981, the positivity proportion was 0.277; in 2013, it was 0.210. These figures highlight the significant burden of rotavirus before vaccination efforts.

Following the vaccine’s introduction, the data shows a marked decline in the positivity proportion of rotavirus infections. In 2018, the positivity proportion dropped to 0.197 in one study and decreased to 0.044 in another, indicating a substantial reduction in the number of positive cases relative to the sample size (Tables  1 and Fig.  2 ). This decline suggests that the rotavirus vaccination program has effectively reduced the incidence of severe rotavirus infections among children, contributing to improved health outcomes.

However, it is essential to note that the data has fluctuations. There were instances of the positivity proportion in the post-vaccine years not following the expected trend. For example, in 2014, the positivity proportion was recorded at 0.345, higher than some pre-vaccine years. This variability may be attributed to changes in surveillance practices, the emergence of different rotavirus strains, or variations in vaccination coverage. These fluctuations remind us of the challenges and uncertainties we must navigate in public health.

The data extracted for the systematic review and meta-analysis studies provide valuable insights into the prevalence and characteristics of rotavirus infection with diarrhea in children under five in Ethiopia. As summarized in Table  1 , the majority of the research articles were from Addis Ababa (6/10); cross-sectional studies by design (7/10), studies conducted before the introduction of the rotavirus vaccine in Ethiopia (6/10), and most studies (8/10) used the EIA/ELISA method for the determination of rotavirus infection and only two used RT-PCR.

A study by Abebe A et al. conducted in 2013 in Addis Ababa examined the positive proportion of rotavirus before the vaccine introduction. This pre-vaccine sentinel surveillance study included a larger sample size of 1841, and the positive proportion of rotavirus was 388 cases (21%) in 2013. The lab method used in this study was EIA. The genotype distribution of rotavirus was identified as G1p (20%), G12p (17%), and G3p (15%) (Table  1 ; Fig.  3 ).

Another study by Abebe A. et al., also published in 2018, focused on the post-vaccine period in Addis Ababa. This sentinel surveillance study included a sample size of 815, and the positive proportion of rotavirus was 161 cases. The genotype distribution in this study revealed G9P (19%) in 2014 and G3P and G2P (19% each) in 2015, which is a fluctuating trend in Rotavirus infections across different regions and years (Table  1 ).

The data is categorized by location: Addis Ababa, Awassa, Gondar and Bahir Dar, Jimma, and Wegera. Addis Ababa shows the highest number of cases, with peaks in 1981 (267 cases), 2013 (388 cases), and 2018 (349 cases). Awassa reported 44 cases in 2013. Gondar and Bahir Dar have significant cases in 2018 (113 cases). Jimma shows lower numbers, with 41 cases in 2004. Wegera presents minimal cases, with a notable report of 10 cases (Fig.  4 ).

The majority of studies used cross-sectional designs. Stintzing G. et al. conducted a survey in 1981 in Addis Ababa, which contained a sample size of 962. The number of rotavirus infections reported in this study was 267, and the lab method used was Immunoelectron microscopy (IEO). Getahun et al. conducted a survey in 2014 in Addis Ababa, with a sample size of 246, and found 85 Rotavirus infection cases. The lab method used in this study was EIA. Additional cross-sectional studies were conducted by Abebe et al. in 1995 and Bizuneh T et al. in 2004, both in Addis Ababa. Abebe et al.‘s study included a sample size of 358, with a frequency of 65 rotavirus infection cases. The lab method used was ELISA. Bizuneh T et al.‘s study included a smaller sample size of 154, with 41 rotavirus infection cases. The lab method used in this study was also ELISA.

Two more cross-sectional studies were conducted after the vaccine introduction. Feleke H et al. conducted a study in 2018 in Wegera woreda, Amhara region, with a sample size of 225, and reported a frequency of 10 rotavirus infection cases. The lab method used was ELISA. Similarly, Gelaw A et al. conducted a study in 2018 in the Amara region with a sample size of 450 and reported a frequency of 113 rotavirus infection cases. The lab method used in this study was reverse transcription polymerase chain reaction (RT-PCR), and the identified serotype distribution included G3P [8], G2P [4], G9P [8], 12P [8], and G3P [6].

Lastly, Yassin et al. conducted a cross-sectional study in Awassa in 2013, with a sample size of 200, and reported a frequency of 44 rotavirus infection cases. The lab method used in this study was RT-PCR, and the genotype distribution included G3P [6] (48%), G1P [8] (27%), and G2P [4] (7%).

This literature review examines the impact of rotavirus vaccination on the distribution of rotavirus genotypes in Ethiopia. The study findings indicate a notable shift in rotavirus genotype distribution in Ethiopia after introducing the vaccine in 2013. Pre-vaccine periods showed the prevalence of genotypes like G1p, G12p, G3p, and G2p, whereas post-vaccination samples displayed a shift to G9P, G3P, G2P, and G12P, with G3P [8] being the most common. This shift highlights the impact of vaccination on altering the predominant rotavirus genotypes.

The data we present here is a scientific observation and a call to action. It underscores the significant effect of vaccination on rotavirus infection patterns. The transition from pre-vaccine to post-vaccination periods demonstrates changes in the circulating genotypes, indicating the vaccine’s effectiveness in influencing rotavirus genotype distribution in Ethiopia. These findings directly affect public health officials and researchers’ efforts to combat the rotavirus.

The studies employed a rigorous methodology, utilizing various laboratory methods such as EIA, ELISA, and RT-PCR to identify rotavirus genotypes. This diverse approach in methods provides a comprehensive understanding of rotavirus epidemiology and genotype distribution in different regions of Ethiopia over time, ensuring the reliability and validity of our findings.

By analyzing data from 1981 to 2018, the study captures temporal trends in rotavirus genotype distribution, showcasing the evolution of prevalent genotypes before and after the vaccine’s introduction. This longitudinal perspective offers valuable insights into Ethiopia’s changing landscape of rotavirus infections.

Overall, the studies above provide essential data on the positive proportion of rotavirus, vaccination status, lab methods used, and genotype distribution in children under five years of age with diarrhea in various regions of Ethiopia. The findings contribute to our understanding of the epidemiology and characteristics of rotavirus infection in this population, which can inform public health interventions and strategies for prevention and control.

A summary review addressed a crucial understanding of the impact of rotavirus infection, assessing disease trends, and evaluating the effectiveness of interventions like vaccines in reducing the incidence of rotavirus-related illnesses in Ethiopia.

Meta-analysis

The systematic review and meta-analysis aimed to investigate the frequency, risk factors, genotype distribution by vaccination status, and age distribution of rotavirus infection with diarrhea in Ethiopia’s children under five. The analysis included data from 9 studies, and both fixed and random effects models were used to estimate the effect size (Fig.  5 ).

In the fixed effects model, the overall effect size for Rotavirus infection in children under five with diarrhea was estimated to be 0.231 (95% CI: 0.221–0.242). This indicates a moderate prevalence of Rotavirus infection in this population. The null hypothesis test showed a significant association between Rotavirus infection and diarrhea in children under five (Z-value: -38.70, p-value: 2.18E-13).

Heterogeneity analysis revealed high heterogeneity among the included studies (Q-value: 79.35, df: 9, p-value: 8.16E-02, I-squared: 88.66%). This suggests that the variation in effect sizes across the studies is not solely due to chance. The estimated tau-squared value (0.286) indicates substantial heterogeneity beyond what would be expected by chance alone.

Given the high heterogeneity observed among the included studies in the analysis of Rotavirus infection in children under five, a fixed-effects model may not be appropriate. Fixed-effects models assume that the actual effect size is the same across all studies, which may need to be more accurate due to the substantial variation in effect sizes observed. In the presence of high heterogeneity, a random-effects model may be more suitable as it accounts for both within-study and between-study variability, providing a more robust estimate of the overall effect size. A random-effects model would better accommodate the observed heterogeneity and provide a more accurate representation of the actual underlying effect size across studies.

In the random effects model, the estimated effect size for rotavirus infection in children under five with diarrhea was slightly lower at 0.221 (95% CI: 0.189–0.257). Although the random effects model did not provide a p-value for the null hypothesis test, it can be inferred that there is still a significant association between rotavirus infection and diarrhea in this population (Fig.  5 ).

The findings suggest that rotavirus infection is a common cause of diarrhea in children under five in Ethiopia. The prevalence of rotavirus infection is moderate, indicating a need for preventive measures such as vaccination. The high heterogeneity observed among the studies highlights the need for further investigation into the factors contributing to the variation in effect sizes.

The results also indicate that the effect size estimates may vary depending on the model used. While the fixed effects model assumes a standard effect size across all studies, the random effects model accounts for both within-study and between-study variability. Therefore, the random effects model may provide a more conservative estimate of the actual effect size.

Overall, this systematic review and meta-analysis provide valuable insights into the epidemiology of rotavirus infection in children under five with diarrhea in Ethiopia. The findings emphasize the importance of implementing effective vaccination strategies and identifying specific risk factors associated with rotavirus infection in this population. Further research is needed to understand the sources of heterogeneity better and to inform targeted interventions for preventing and controlling rotavirus infection in Ethiopia.

Publication bias

The meta-analysis incorporated data from 9 studies categorized in 10 as pre-vaccine and post-vaccine studies, yielding a z-value of -36.19785 and a corresponding 2-tailed p-value of 0.00000. The Classic Fail-safe N for this meta-analysis is 3401, which means that 3401 additional ‘null’ studies would need to be located and included for the combined 2-tailed p-value to exceed 0.050. This indicates that for every observed study, there would need to be 340.1 missing studies for the effect to be nullified, suggesting the results are highly robust.

Egger’s Test of the Intercept was also performed to assess publication bias. The intercept (B0) was found to be -1.61283, with a 95% confidence interval ranging from − 7.10118 to 3.87552. The t-value was 0.67765 with 8 degrees of freedom. The 1-tailed p-value was 0.25855, and the 2-tailed p-value was 0.51711. These p-values are not statistically significant, indicating no significant evidence of publication bias according to Egger’s test.

Furthermore, Duval and Tweedie’s Trim and Fill method was applied. Under the fixed effect model, the combined studies’ point estimate and 95% confidence interval were 0.23134 (0.22070, 0.24233). Using Trim and Fill, these values remained unchanged. Similarly, under the random effects model, the point estimate and 95% confidence interval were 0.22147 (0.18947, 0.25717), and these values also remained unchanged after applying Trim and Fill. This consistency suggests there is no significant publication bias affecting the results.

The funnel plot, which displays the standard error by logit event rate, is likely to show a symmetrical distribution given the results from Egger’s Test and the Trim and Fill method (Fig.  6 ).

Overall, the meta-analysis demonstrates a robust effect with minimal evidence of publication bias. The high fail-safe N indicates the results are reliable and not easily nullified by potential missing studies.

Rotavirus infection poses a significant public health concern in low-income countries with poor socio-economic situations and a lack of appropriate sanitation, hygiene, and vaccination coverage. This systemic review and meta-analysis estimated the prevalence of rotavirus infection among children under five with diarrhea in Ethiopia at 22.6%, highlighting the need for preventive measures such as vaccination. The obtained review data included cases from hospitalized children, community-based studies, and outpatient departments. However, data on mild cases (community-based study and outpatient department) are fewer, which suggests that the findings may only partially represent the broader spectrum of rotavirus infection severity in the population. This limitation may be considered when interpreting the results and their implications for public health strategies (Table  1 ; Fig.  3 ).

Hospitalized children from 2013 onwards were not exclusively vaccinated cohorts; the data includes pre- and post-vaccine cases. The data primarily focuses on rotavirus infection cases, sample sizes, vaccination statuses (pre- and post-vaccine), and genotype distributions without specific details on vaccination cohorts beyond 2013. The identified genotypes, including G1, G2, G3, G12, P [4], P [6], P [8], P [9], and P [10], provide insights into the circulating strains of Rotavirus in Ethiopia. Some surveillance studies also observed similar study results [ 17 , 18 ].

Analysis of genotype variations in Rotavirus infections pre- and post-vaccination in Ethiopia

Pre-vaccination period.

Before introducing the rotavirus vaccine on June 13, 2013, the predominant genotypes identified in various studies were G1, G12, G3, and G2. For instance, in Addis Ababa, sentinel surveillance data from 2013 showed the prevalence of G1P (20%), G12P (17%), and G3P (15%). In Awassa, the genotypes G3P[6] (48%), G1P[8] (27%), and G2P[4] (7%) were common.

Post-vaccination Period

The most striking observation was the significant shift in genotype distribution following the introduction of the vaccine. The previously dominant genotypes G1, G12, G3, and G2 were replaced by G9P, G3P, G2P, and G12P. For instance, in Addis Ababa, the post-vaccination data from 2014 to 2015 revealed a dramatic change in the prevalence of genotypes. 2014 G9P emerged as the most common (19%), but in 2015, G3P and G2P (19% each) took the lead. Similarly, in Gondar and Bahir Dar, the genotypes G3P [8], G2P [4], G9P [8], G12P [8], and G3P [6] were prevalent in 2018.

Year-by-year genotype distribution :

2011–2013 (Pre-Vaccine) : In Addis Ababa, G12P was prevalent in 2011 (36%) and 2012 (27%), while G2P was dominant in 2013 (35%).

2014–2015 (Post-Vaccine) : The post-vaccination period in Addis Ababa saw a dynamic change in genotype prevalence. 2014, G9P was the most common (19%), but in 2015, G3P and G2P emerged as equally prevalent (19% each), marking a significant shift in just a year.

2018 (Post-Vaccine) : In Gondar and Bahir Dar, the genotypes G3P[8], G2P[4], G9P[8], G12P[8], and G3P[6] were identified.

In summary, the introduction of the rotavirus vaccine in Ethiopia has had a profound impact on the genotype distribution of rotavirus infections. The pre-vaccination period was characterized by the dominance of genotypes G1, G12, G3, and G2, while the post-vaccination period witnessed a shift towards genotypes G9P, G3P, G2P, and G12P, with G3P[8] being notably common. This shift underscores the significant role of vaccination in shaping the epidemiology of rotavirus genotypes in the region (Fig.  3 ).

This systematic review and meta-analysis provide essential insights into the prevalence, genotype distribution, and risk factors of rotavirus infection in children under five in Ethiopia. The identified genotypes, including G1, G2, G3, G12, P [4], P [6], P [8], P [9], and P [10], highlight the diversity of rotavirus strains circulating in Ethiopia. Other studies in different regions have also reported these genotypes, emphasizing their global significance [ 17 , 19 ].

The G3 genotype was particularly prevalent, accounting for 27.1% of cases, followed by the P [8] genotype at 49%. These findings are consistent with previous studies that have reported the predominance of G3 and P [8] genotypes in rotavirus infections [ 20 , 21 ].

The prevalence of specific genotypes can have implications for vaccine development and effectiveness. For instance, the G12P [8] combination, identified as one of the most common genotypes in this study, has been associated with reduced vaccine effectiveness in some settings [ 22 ]. Therefore, monitoring the prevalence and distribution of genotypes is crucial for informing vaccine strategies and ensuring their optimal impact.

This systematic review and meta-analysis provide valuable insights into the prevalence, genotype distribution, and risk factors of rotavirus infection in children under five in Ethiopia. The findings underscore the importance of vaccination and ongoing surveillance to reduce this population’s rotavirus-related morbidity and mortality burden [ 23 , 24 ].

However, it is important to note that this study has some limitations. The high heterogeneity observed among the included studies suggests potential variations in study design, population characteristics, and diagnostic methods. Additionally, the limited number of studies available for inclusion may only partially represent part of the population of Ethiopia.

This systematic review and meta-analysis provide valuable insights into the prevalence, genotype distribution, and risk factors of rotavirus infection in children under five in Ethiopia. The findings underscore the importance of vaccination and ongoing surveillance to reduce this population’s rotavirus-related morbidity and mortality burden.

Limitations

Among the limitations observed in this review is that there needs to be more sufficient data showing genotypes responsible for mechanisms of rotavirus infection in the included studies. In addition, these studies were limited to a few places, which didn’t reveal the actual figure for the distribution of rotavirus infection in Ethiopia. The studies’ limitations include focusing on specific regions like Addis Ababa and Awassa in Ethiopia, potentially limiting the findings’ generalizability. Another limitation is the reliance on different laboratory methods, such as EIA, ELISA, and RT-PCR, across studies, which may introduce variability in the results. Additionally, the sample sizes varied between studies, which could impact the statistical power and precision of the results. A larger sample size generally leads to more robust and statistically significant results, providing greater confidence in the study’s conclusions regarding rotavirus infection and vaccine efficacy.

Conclusion and recommendations

In conclusion, the systematic review and meta-analysis of rotavirus infection in children under five in Ethiopia revealed a moderate prevalence of rotavirus infection in this population. Overall, the stratified analysis demonstrates that the introduction of rotavirus vaccines in Ethiopia has significantly reduced the positivity proportion of rotavirus infections, particularly in the years following the vaccine’s implementation. However, this success should not lead to complacency. Continued monitoring and evaluation of the vaccination program are important to ensure its ongoing effectiveness and address any emerging challenges in controlling rotavirus infections in the future. This is a collective responsibility that we all share in the public health community, and it is crucial that we all actively participate in maintaining the success of the vaccination program. The genotype distribution was diverse, with G1, G2, G3, G12, P [4], P [6], P [8], P [9], and P [10] being the most common genotypes identified. The pooled prevalence of rotavirus infection was approximately 23%, with the G3 and P [8] genotypes being particularly prevalent. The findings underscore the importance of implementing preventive measures, such as vaccination, to reduce the burden of rotavirus infection in children under five years of age in Ethiopia. The identified genotypes provide valuable insights for vaccine development and targeted interventions. Water supply contamination, inadequate sanitation, and poor water quality can contribute to the spreading of rotavirus infection. Contaminated water sources can harbor the virus, leading to potential infections when children are consumed or used for hygiene. Proper water treatment and sanitation practices are essential to prevent rotavirus transmission and other waterborne diseases. Further studies are needed to address additional risk factors associated with rotavirus infection, better understand the observed heterogeneity among the included studies, and understand the burden of rotavirus infection, especially among children under five. Overall, this study contributes to the evidence base for public health interventions and strategies to reduce the impact of rotavirus infection in Ethiopia.

PRISMA 2020 flow diagram for updated systematic reviews, which included searches of database registers

The positivity proportion of rotavirus cases at pre-vaccine and post-vaccine studies periods in Ethiopia

Genotype distribution by Rotavirus cases in the community, hospitalized and outpatient children during pre- and post-vaccine periods

Illustrates the number of Rotavirus infection cases in different study areas during specific publication years from 1981 to 2018

Rotavirus Infection in Pre- and Post-Vaccine Introduction in Ethiopia

Forest plot

Data availability

The datasets used and analyzed in the study are available from the corresponding author on reasonable request.

Abbreviations

Enzyme Immunoassay

Enzyme-Linked Immunosorbent Assay

Immunoelectro-osmophoresis

Joanna Briggs Institute

Real-time Polymerase reaction

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Tosisa, W., Regassa, B.T., Eshetu, D. et al. Rotavirus infections and their genotype distribution pre- and post-vaccine introduction in Ethiopia: a systemic review and meta-analysis. BMC Infect Dis 24 , 836 (2024). https://doi.org/10.1186/s12879-024-09754-7

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Received : 20 February 2024

Accepted : 13 August 2024

Published : 16 August 2024

DOI : https://doi.org/10.1186/s12879-024-09754-7

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