The Independent Samples t-Test

This chapter introduces the concept of the t-statistic by first (briefly) explaining the one-sample t-test, referring students to the water giveaway example discussed in Chap. 4 , in which we compared a treated sample to an untreated population. Because the One-Sample t-Test does not have a lot of practical application, we move on to discuss how to compare a control group and a treatment group using the Independent Samples t-Test. We walk students, step-by-step, through the calculations, using equations and a small data set. We use the example of studying the effects of pulling an all-nighter on test-taking ability: the treatment group stays awake all night before taking a quiz, and the control group is allowed to sleep during the night. We discuss the null and research hypotheses, and then students learn how to begin by appropriately setting up the data and calculating the squared scores and sums of scores that they will need. Working step-by-step, we apply equations to calculate sample variances, pooled variance, standard error, and, finally, the t-statistic. Cohen’s d is taught as a measure of effect size, and hypothesis testing using the t-distribution and critical values of the t-statistic are explained. Results are presented in APA (seventh edition) format. We discuss one-tailed versus two-tailed hypothesis tests and present graphs illustrating differences between the two. We then present an additional example for extra practice and clarification, working through all of the steps in the calculations of t, Cohen’s d, and the hypothesis test, and we report results in APA format. Sidebar notes alert students to commonly made mistakes, and a biography box briefly tells about how William Sealy Gosset developed Student’s t-Test while he worked at the Guinness Beer Factory. The chapter concludes with a summary of important concepts, illustrated instructions for computing the Independent Samples t-Test using the Data Analysis Toolpak, critical thinking questions, and practice problems.