In a two-sample t-test, Welch's t-test is used when

In a two-sample t-test, Welch's t-test is used when

• A. Variances are equal.
• B. Sample sizes are equal.
• C. Variances are unequal.
• D. Data are non-normal.

Answer: (C)

Welch's t-test is used when the two groups have different variances. If the variances are unequal, pooling a common variance and using that standard error can misrepresent the true uncertainty in the difference of means, especially when one group is more variable or has a different sample size. Welch's approach avoids pooling and uses the separate variances in the standard error, along with the Welch–Satterthwaite adjustment to the degrees of freedom. This provides more accurate p-values under heterogeneity of variances. If variances are actually equal, the pooled-variance t-test is more powerful, so Welch's method is particularly favored when you suspect or detect unequal variances.

Welch's t-test is used when the two groups have different variances. If the variances are unequal, pooling a common variance and using that standard error can misrepresent the true uncertainty in the difference of means, especially when one group is more variable or has a different sample size. Welch's approach avoids pooling and uses the separate variances in the standard error, along with the Welch–Satterthwaite adjustment to the degrees of freedom. This provides more accurate p-values under heterogeneity of variances. If variances are actually equal, the pooled-variance t-test is more powerful, so Welch's method is particularly favored when you suspect or detect unequal variances.