Question

A new student in the program is interested in doing a study that seeks to understand why people receive shorter or longer prison sentences - seeks to explain the variation that exists in prison sentences. He believes that offenders might receive different sentence lengths based on the type of crime they commit. There are three types of crimes (drug offense, property offense, violent offense). He conducts an ANOVA test, but needs some guidance on background concepts related to the test. Using this example, explain the concepts of "variance," "within group variance," and "between group variance" as it relates to ANOVA in this situation using your own words.

Answer 1

There is the between-group variation and the within-group variation. The whole idea behind the analysis of variance is to compare the ratio of between-group variance to within-group variance. If the variance caused by the interaction between the samples is much larger when compared to the variance that appears within each group, then it is because the means aren't the same.

The variation due to the interaction between the samples is denoted SS(B) for the Sum of Squares Between groups.

The variance due to the differences within individual samples is denoted MS(W) for Mean Square Within groups.

The total variation (not variance) is comprised the sum of the squares of the differences of each mean with the grand mean.