Final answer:
If we assume equal variances between groups, we use the pooled variance approach. Pooled variance is used when we need a common estimate of variance for multiple groups. However, in some tests like the F test for equality of two variances, variances are not pooled, especially when sample sizes are equal and sufficient.
Step-by-step explanation:
When we assume that the populations from which our samples come have equal variances, we use the pooled variance approach in statistical analysis. Pooled variance is an estimate of the common variance of two or more populations. In scenarios where sample sizes differ, this estimate is a weighted average of the sample variances that accounts for the sample sizes.
However, in certain statistical tests such as the test of two variances, or the F test for equality of two variances, the sample variances are not pooled when the sample sizes are equal, particularly when each is five or larger. The F test compares the ratio of two sample variances and determines if they are significantly different, under the assumption that the populations they are drawn from are normally distributed.
An application of the pooled variance approach occurs when conducting tests on the difference of two proportions. To test if the population proportions are the same, we use a pooled proportion that takes into account the total successes and total sample size from both samples.