Question

In your own words, describe the difference between Among Group Variation and Within Group Variation. Discuss how you would evaluate the variation and other methods to ensure that the data is appropriate to use for the test. Illustrate using a specific example.

Answer 1

Among Group Variation :

It refers to the variation which exists due to the difference among individual groups. It is also known as Within-group variation, error group, or error variance. It is considered as the variation among the samples which can be described as the sum of squares between groups.

Each group values can be different, and these differences are not caused by the presence of the independent variable. Every sample which is considered is not dependent in any manner, and there is no relationship and interaction between the two samples.

In this case, the sum of the degree of freedom of each sample is equal to the degrees of freedom. ANOVA is one of the ways to figure out whether a given survey or experiment is statistically significant or not. It tells us whether to reject the null hypothesis or to accept the null hypothesis.

Under ANOVA within-group variation is denoted as SS(W) output. It also means Sum of Squares within groups or SSW: Sum of squares Within. With the help of ANOVA model, the variance among the various group means can be evaluated and compared between the average variance within the group can be made.

Moreover, a mean difference within the group is distinct in the distribution when variances among the group are same.

The inequality of the means of the samples can be determined by analyzing the interaction among the variances between the different samples. If the variance is significantly greater, then there exists equality in the mean values.

Within-Group Variation

Within-group variation, called error group or error variation, is a terminology used in ANOVA tests. It refers to changes caused by differences within individual groups (or levels).To explain it in plain words, not all the values within each group for e.g., means, are the same. These are variations not caused by the independent variable.

Each sample is looked at on its own. In other words, no interactions between samples are considered. For example, let’s say you had four groups, representing drugs A B C D, with each group composed of 20 people in each group and you’re measuring people’s cholesterol levels. For within-group variation, you’ll look at variances in cholesterol levels for people in group A, without considering groups B,C, and D. Then you would look at cholesterol levels for people in group B, without considering groups A,C, and D. And so on.

ANOVA table output

Within-group variation is reported in ANOVA output as SS(W) or which means Sum of Squares Within groups or SSW: Sum of Squares Within. It is intrinsically linked to between group variation (Sum of Squares between), variance difference caused by how groups interact with each other. This is because the whole point of ANOVA is to compare the ratio of within group variance and between group variance. In fact, the core of the ANOVA test — the F statistic — is calculated by dividing the between group variance by the within group variance.

If the variance caused by interactions between different samples is much greater than the variance found inside values in a single group, that indicates the means aren’t equal.

Degrees of freedom for Within-group variaton equals the sum of the individual degrees of freedom for each sample in the test.