Unpaired Two-Sample t-Tests

Social science students naturally have a lot of questions. Are college students majoring in the humanities more social than students majoring in the physical sciences? Are religious societies happier than secular societies? Do children with divorced parents have more behavioral problems than children with married parents? Are inmates who attended school in prison less likely to reoffend than inmates who do not receive education? These questions compare two groups (e.g., children of divorced parents and children of married parents) and ask which group has a higher score on a variable (e.g., number of behavioral problems). These kind of questions are extremely common in the social sciences, so it should not surprise you that there is a statistical method developed to answer them. That method is the unpaired two-sample t-test, which is a comparison of scores from two different unrelated groups. The topic of this chapter is the unpaired two-sample t-test , one of the most common statistical methods in the social sciences. Learning Goals • Explain when an unpaired two-sample t -test is an appropriate NHST procedure. • Conduct an unpaired two-sample t -test. • Calculate an effect size (i.e., Cohen's d) for an unpaired two-sample t -test. • Show how the unpaired two-sample t -test is a member of the general linear model (GLM). • Correctly find and interpret a p -value. Making Group Comparisons Answering the questions at the beginning of the chapter requires comparing two scores. When these groups are unrelated to one another, an unpaired-samples t-test is an appropriate method of analyzing data. You may remember in Chapter 9 we paired scores, the two sets of scores formed pairs across the datasets (e.g., pre-test and post-test data, or scores about a pair of siblings). This allowed us to simplify the two sets of scores into one group of difference scores and to conduct a one-sample t -test with the difference scores. However, in the social sciences our scores are often unrelated to one another. For example, a sociology student interested in the happiness levels in different societies would collect data on happiness levels from people in both religious and non-religious societies. After these data are collected, she would have two sets of scores – but there would be no logical reason to pair individuals from one group with individuals from another group because the people in the two groups had nothing to do with each other.