Question

Which of the following is a statistical assumption to violations of which the independent means t-test is USUALLY robust?

1) normality of the dependent variable
2) homogeneity of variance
3) independence of observations
4) equality of sample sizes

Answer 1

The independent means t-test is usually robust to violations of normality of the dependent variable. It is not as robust to violations of homogeneity of variance, independence of observations, nor to unequal sample sizes.

Step-by-step explanation:

Of the given options concerning the independent means t-test, it is generally known that the t-test is robust to violations of the normality assumption, especially as the sample size becomes large. Therefore, the correct answer is that the independent means t-test is usually robust to violations of normality of the dependent variable (1). However, it is not as robust to violations of homogeneity of variance (2), independence of observations (3), or equality of sample sizes (4). Violations of these assumptions can significantly affect the validity of the t-test.

It is noteworthy that while the t-test can tolerate departures from normality, especially with larger sample sizes, the assumptions of independence of observations and homogeneity of variances are critical. When these assumptions are violated, alternative statistical methods should be considered. In case of unequal sample sizes, the t-test can be performed, but more caution is needed in interpreting the results.