Final answer:
Within group variance (SSwithin) refers to variation due to chance within groups, and estimates the population variance, while between group variance (SSbetween) captures variation among different samples, suggestive of differences in population means. The F ratio used in ANOVA tests compares these variances to determine if group means differ significantly.
Step-by-step explanation:
The difference between "within group variance" (SSwithin) and "between group variance" (SSbetween) lies in what they measure in the context of variability. SSwithin, or within group variance, is the sum of squares that represents the variation within samples due to chance or error. It estimates the population variance and is used to calculate within-group differences, effectively accounting for natural fluctuations in data. Conversely, SSbetween, or between group variance, is the sum of squares that illustrates the variation amongst different samples or treatments. This measure can reveal differences in population means among various groups in an experiment.
When performing a one-way ANOVA test, which checks for significant differences between group means, the F ratio is calculated using MSbetween (mean square between groups) and MSwithin (mean square within groups). If the null hypothesis, stating that all group variances are equal, is false, then usually MSbetween will be larger than MSwithin because it contains the population variance plus any variance produced from differences between sample means.