t-Tests

This chapter discusses three t-tests for three different situations: comparing the sample mean against the population/hypothesised mean, comparing means of two independent groups, and comparing means of dependent samples (for example, a before-after scenario). Each of these three t-tests is a one-sample t-test, independent samples t-test and paired/dependent samples t-test. Using the example of consumption expenditure from our employment dataset, we discuss the use of one-sample and independent sample t-test, whereas we make use of another dataset on salaries (before and after graduation) for the paired samples t-test. We explain both the two-tailed as well as one-tailed tests for each of these t-tests, including the formulation of hypotheses for both these scenarios. Examining homogeneity of variance, especially for the independent samples t-test, is also discussed. The data could be in tall or wide format, and we explain by converting our data (originally in tall format) to wide format, and then the procedure to undertake the independent samples t-test. The chapter also includes a discussion on the concept and procedure to estimate the effect size and the power of these tests. We also discuss handling missing values for the paired samples t-test, especially in the context of the paired samples t-test.