Question

What do the terms between-sample variability and within-sample variability mean? Discuss in the context of a particular problem.

Answer 1

We know that the two terms between sample variability and within sample variability are very important in the analysis of variances or ANOVA tables.

The between sample variability is associated with the explained variation of the experiment while within sample variability is associated with the unexplained variation of the experiment.

As the name suggests that between sample variability represents the variability between the different samples and the within sample variability represents the variability within all samples included in the analysis.

Suppose we want to compare the average score of the students from three different schools. We have three samples of student scores from three schools. In this particular case, the between sample variability is the variability between given three samples of student scores. Also, within sample variation is associated with within all observations from three samples. Note the difference between ‘between’ and ‘within’ sample variation in detail as the ‘between’ used for find the variation between samples and ‘within’ used for finding the variation within all observations of the samples.