What is the assumption about variances for the standard two-sample t-test?

What is the assumption about variances for the standard two-sample t-test?

• A. Variances are homogeneous (equal)
• B. Variances must be different
• C. Variances must be zero
• D. Variances must be proportional

Answer: (A)

The standard two-sample t-test assumes that the two populations have the same variance. This idea, often called homogeneity of variances, lets us pool the variability from both samples into a single estimate of the common variance. That pooled variance is then used to compute the standard error of the difference between the means, which in turn determines the t-statistic and the degrees of freedom (n1 + n2 − 2). If the variances are actually different (heteroscedastic), the pooled estimate can be biased and the test can be unreliable, which is why a version that uses separate variances (Welch’s t-test) is recommended in that case. The notions that variances must be zero or must be proportional aren’t correct, and variances being different is not an assumption of the standard test.

The standard two-sample t-test assumes that the two populations have the same variance. This idea, often called homogeneity of variances, lets us pool the variability from both samples into a single estimate of the common variance. That pooled variance is then used to compute the standard error of the difference between the means, which in turn determines the t-statistic and the degrees of freedom (n1 + n2 − 2). If the variances are actually different (heteroscedastic), the pooled estimate can be biased and the test can be unreliable, which is why a version that uses separate variances (Welch’s t-test) is recommended in that case. The notions that variances must be zero or must be proportional aren’t correct, and variances being different is not an assumption of the standard test.