What is pooled variance used for?

What is pooled variance used for?

• A. Pooled variance: used when you calculate standard error of the variance for independent T-test
• B. Equal variances assumption
• C. Standard error of the mean
• D. Sample variance

Answer: (A)

Pooled variance is used when two independent samples are believed to come from populations with the same variance. By combining the two sample variances into one estimate, you obtain a single, more stable estimate of the common variance: Sp^2 = [ (n1−1)s1^2 + (n2−1)s2^2 ] / (n1 + n2 − 2). This pooled estimate is then used to compute the standard error of the difference between the two means: SE_diff = sqrt( Sp^2 * (1/n1 + 1/n2) ). The t statistic for an independent two-sample test relies on this SE, so pooling helps test whether the group means differ when the equal-variances assumption holds. If variances aren’t equal, pooling isn’t appropriate and a method like Welch’s t-test should be used. This concept isn’t about the standard error of a single mean (which uses s^2/n) or about the raw sample variance itself, but about estimating the common variance to compare two means.

Pooled variance is used when two independent samples are believed to come from populations with the same variance. By combining the two sample variances into one estimate, you obtain a single, more stable estimate of the common variance: Sp^2 = [ (n1−1)s1^2 + (n2−1)s2^2 ] / (n1 + n2 − 2). This pooled estimate is then used to compute the standard error of the difference between the two means: SE_diff = sqrt( Sp^2 * (1/n1 + 1/n2) ). The t statistic for an independent two-sample test relies on this SE, so pooling helps test whether the group means differ when the equal-variances assumption holds. If variances aren’t equal, pooling isn’t appropriate and a method like Welch’s t-test should be used. This concept isn’t about the standard error of a single mean (which uses s^2/n) or about the raw sample variance itself, but about estimating the common variance to compare two means.