Which statement is an assumption of the two-sample t-test regarding population distributions?

Which statement is an assumption of the two-sample t-test regarding population distributions?

• A. Samples drawn from normally distributed populations
• B. Samples drawn from skewed populations
• C. The dependent variable is ordinal
• D. The sample sizes must be identical

Answer: (A)

The main idea is that the standard two-sample t-test relies on the populations from which the two samples are drawn being normally distributed. This normality assumption ensures the sampling distribution of the difference between the two sample means follows a t distribution (when variances are estimated), which underpins the accuracy of the test, especially with small samples. In practice, if you have larger sample sizes, the Central Limit Theorem makes the test more robust to deviations from normality, so normality isn’t as strictly required as a rule. The dependent variable should be a continuous measure, not ordinal, and you don’t need equal sample sizes—the test can handle unequal group sizes. Skewed distributions violate the assumption for small samples, which can affect the test’s validity, though alternatives like nonparametric tests or Welch’s t-test can be used in such cases.

The main idea is that the standard two-sample t-test relies on the populations from which the two samples are drawn being normally distributed. This normality assumption ensures the sampling distribution of the difference between the two sample means follows a t distribution (when variances are estimated), which underpins the accuracy of the test, especially with small samples. In practice, if you have larger sample sizes, the Central Limit Theorem makes the test more robust to deviations from normality, so normality isn’t as strictly required as a rule. The dependent variable should be a continuous measure, not ordinal, and you don’t need equal sample sizes—the test can handle unequal group sizes. Skewed distributions violate the assumption for small samples, which can affect the test’s validity, though alternatives like nonparametric tests or Welch’s t-test can be used in such cases.