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Statistics Explained, now in its fully revised Fourth Edition, is for students and researchers who wish to understand the statistical analyses used to analyze quantitative (numerical) research data in a wide range of academic disciplines, in particular, the behavioral, human, and social sciences.
This book explains, in a clear and informative manner, the logic of statistical analysis, in particular, the null hypothesis significance testing (NHST) method. Using this method, a range of statistical tests have been devised for different types of data. Each of these tests is explained in the book by adopting a step-by-step (“walkthrough”) approach with a specific illustrative example. Crucially, these explanations do not require the reader to have an advanced knowledge of mathematics or statistics, but only assume the basic mathematics which most readers will have learned in high school. The book also examines the criticisms of NHST and introduces the reader to Bayesian statistics. As a result, the reader will be able to critically evaluate the outcomes of statistical analysis both of their work and that of others.
Statistics Explains will be of great interest to students and researchers in the behavioral, human, and social sciences in understanding both the outcomes of their research and also the research reports in the academic journals.
Dedication.
List of figures.
Preface.
Introduction.
The Elements of Statistical Analysis.
The Importance of Scores and Populations.
Collecting Data: Measurement.
Locating Scores in a Population.
Describing the Population.
The Position of a Score in a Frequency Distribution.
Proportions, Probabilities, and Percentages.
The Importance of Samples and Sampling Distributions.
Sample Statistics.
The Sampling Distribution.
Key Points.
Null Hypothesis Significance Testing.
The Logic of Hypothesis Testing Using Statistics.
Hypothesis Testing with a Sample.
Hypothesis Testing with a Sample when the Population Standard Deviation is Not Known.
Confidence Intervals.
Hypothesis Testing with Two Samples (The Two-Sample t Test).
The Paired (Related) Samples t Test.
The Independent Samples t Test.
Entering Data into a Statistics Program: Grouping Variables.
Key Points.
Issues with Null Hypothesis Significance Testing.
Variables.
Type I and Type II Errors.
Statistical Power.
Effect Size.
Normally Distributed Populations.
Sample Skew and Kurtosis.
Tests of Normality.
Outliers.
Sample Variation.
Bootstrapping.
Analyzing a Sample.
Key Points.
The Analysis of Variance.
Beyond the Test.
Why Do Scores Vary in a Set of Data?
The Variance Ratio (The F Statistic).
One-Factor Independent Anova.
Multiple Comparisons.
The Relationship of F To T.
One-Factor Repeated Measures ANOVA.
Sphericity.
Multiple Comparisons.
Key Points.
The Interaction of Factors in the Analysis of Variance.
Main Effects and the Interaction.
The Two-Factor Independent Anova.
The Two-Factor Mixed Design Anova.
The Two-Factor Repeated Measures ANOVA.
Key Points.
Nonparametric Analysis.
Parametric and Nonparametric Tests.
Nominal Data, Categories, and Frequency Counts.
Analyzing Frequency Data: Chi-Square (x2).
Chi-Square (x2) as A Goodness of Fit Test.
Chi-Square (x2) as a Test of Independence.
The Chi-Square Distribution.
The Assumptions of the x2 Test.
Nonparametric Comparisons with Ordinal Data.
Calculating Ranks.
The Mann-Whitney U Test (for Independent Samples).
The Wilcoxon Signed-Ranks Test (For Paired Samples).
One-Factor Anova for Ranked Data.
The Kruskal-Wallis Test (For Independent Measures).
The Friedman Test (For Related Samples).
Treating Ordinal Data as Interval Data.
Key Points.
Correlation and Regression.
Correlation.
The Pearson Correlation Coefficient r.
The Spearman rs Correlation Coefficient.
Linear Regression.
The Interpretation of Correlation and Regression.
The Significance of the Regression.
Homoscedasticity.
Binary Logistic Regression.
Multiple Correlation.
Multiple Regression.
Key Points.
Modeling Relationships Between Variables.
Factor Models.
Reliability.
Factor Analysis.
Multivariate Analysis of Variance (Manova).
Discriminant Function Analysis.
Structural Equation Modeling.
Moderation and Mediation.
Moderation.
Mediation.
Latent Variables: Reflective and Formative Constructs.
Conclusion to Structural Equation Modeling.
Key Points.
An Introduction to the General Linear Model.
Models.
A Linear Model.
Modeling Data.
The Model as a Regression Equation.
Selecting a Good Model.
The Variation in the Data Explained by the Model.
The Linear Model and Correlation.
The Linear Model and the Analysis of Variance.
Comparing Samples (The Analysis of Variance Once Again).
Explaining Variations in the Data by a Model.
The General Linear Model (GLM).
The General Linear Model and Multivariate Analysis.
Key Points.
Bayesian Statistics.
Frequentist and Bayesian Approaches to Statistics.
An Illustrative Example: is That a Gorilla?
Conditional Probability and Bayes’ Theorem.
The Bayesian Dilemma.
A Bayesian Approach to Statistical Inference.
Creating Bayesian Equivalent of Null Hypothesis Significance Tests.
Comparison of Frequentist and Bayesian Tests.
The Wider Importance Of Bayesian Methods.
Key Points.
'Lies, Damned Lies, and Statistics'.
Experimenter Effects.
Demand Characteristics.
Publication Bias.
Data Manipulation.
The Replication Problem.
Bayes and Beyond.
References.
Appendix.
Glossary.
Index.
Choosing a statistical test