11. Comparing two means

In this chapter, we delve into the statistical techniques used to compare the means of two groups, particularly when the outcome variable is on an interval or ratio scale, and the predictor variable is binary. Such scenarios are prevalent in real-world applications across diverse fields like psychology, medicine, and agriculture. The primary focus is on the application of various forms of the t-test, including the one-sample, independent samples (Student and Welch), and paired-samples t-tests. These methods allow researchers to test hypotheses regarding mean differences between groups while considering key assumptions like normality and independence. Furthermore, the chapter introduces effect size metrics, particularly Cohen's d, as a measure of the magnitude of observed effects. Special attention is given to the interpretation of results, with clear guidance on reporting statistical outputs.

The chapter also explores practical methods for assessing the normality of data distributions, using tools like QQ plots and the Shapiro-Wilk test, and addresses the challenges posed by non-normal data. For such cases, nonparametric alternatives, including the Mann-Whitney U test and Wilcoxon tests, are presented. The importance of aligning statistical tests with research design is underscored, highlighting when one-sided versus two-sided tests are appropriate. Through comprehensive examples and practical insights, the chapter equips readers with a robust understanding of how to evaluate mean differences effectively and report findings in a scientifically rigorous manner.