Abstract
When comparing two independent groups, psychology researchers commonly use Student’s t-tests. Assumptions of normality and homogeneity of variance underlie this test. More often than not, when these conditions are not met, Student’s t-test can be severely biased and lead to invalid statistical inferences. Moreover, we argue that the assumption of equal variances will seldom hold in psychological research, and choosing between Student’s t-test and Welch’s t-test based on the outcomes of a test of the equality of variances often fails to provide an appropriate answer. We show that the Welch’s t-test provides a better control of Type 1 error rates when the assumption of homogeneity of variance is not met, and it loses little robustness compared to Student’s t-test when the assumptions are met. We argue that Welch’s t-test should be used as a default strategy.
Highlights
When comparing two independent groups, psychology researchers commonly use Student’s t-tests
If variances are not equal across groups and the sample sizes differ across independent groups, Student’s t-test can be severely biased and lead to invalid statistical inferences (Erceg-Hurn & Mirosevich, 2008)
When the larger variance is associated with the larger sample size, there is a decrease in the nominal Type 1 error rate (Nimon, 2012; Overall, Atlas, & Gibson, 1995)
Summary
Why Psychologists Should by Default Use Welch’s t-test Instead of Student’s t-test. When comparing two independent groups, psychology researchers commonly use Student’s t-tests. There are different types of t-tests, such as Student’s t-test, Welch’s t-test, Yuen’s t-test, and a bootstrapped t-test These variations differ in the underlying assumptions about whether data is normally distributed and whether variances in both groups are equal (see, e.g., Rasch, Kubinger, & Moder, 2011; Yuen, 1974). If variances are not equal across groups and the sample sizes differ across independent groups, Student’s t-test can be severely biased and lead to invalid statistical inferences (Erceg-Hurn & Mirosevich, 2008).. We will first discuss why we need a default test and why a two-step procedure where researchers decide whether or not to use Welch’s t-test based on a check of the assumption of normality and equal variances is undesirable. Testing the equality of variances before deciding which t-test is performed is problematic for several reasons, which will be explained after having described some of the most widely used tests of equality of variances
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