Explain the difference between the Between Treatments Estima

Explain the difference between the Between Treatments Estimate of Variance and the Within Treatments Estimate of Variance.

Why do we need two estimates? Wouldn\'t one estimate suffice?

Solution

Between Treatments Estimate of Variance is the amount of variation by comparing the means of different groups.

Within Treatments Estimate of Variance is the amount of variation by comparing the values inside groups.

We need two estimates because we want to compare if the variation is simply due to the groups themselves, or is it really because the means of the different groups are different from each other.

Computing for their ratio, we can determine if the means of the different groups are significantly different.

Hence, one estimate does not suffice, we need both.