There are a few different reasons we explore differences in scale.
Keep in mind that the scale of a dataset is basically the spread of the data. For most datasets, we’re examining the variance.
Hypothesis tests comparing means vary depending on the assumption of equal variances. Thus testing that assumption requires methods to adequately test the homogeneity of variances. The F-test should come to mind as it is a common approach.
Some datasets do not lend themselves to using the F-test, which is applicable using real numbers. Some datasets gather information that is ordinal or interval data, thus we need another approach to test for differences in scale. [Read more…]