Respuesta :
When testing the difference between two independent population means, the sample variances are pooled to estimate the population variance when the population variances are assumed equal but unknown
What is pooled variance?
The pooled variance is an estimate of the common variance. It is a weighted average of the sample variances for each group, where the larger groups are weighted more heavily than smaller groups.
The pooled variance is a better estimate of the (unknown) common group variance than either of the individual group variances. If each group has the same number of observations, then the pooled variance is a simple average. If the group sizes are different, then the pooled variance is a weighted average, where larger groups receive more weight than smaller groups.
Under the assumption of equal population variances, the pooled sample variance provides a higher precision estimate of variance than the individual sample variances. This higher precision can lead to increased statistical power when used in statistical tests that compare the populations, such as the t-test
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