To test if MSA is significantly different from MSE, we compare them using another probability distribution, the F-distribution, to decide on the significance. The basic idea is that both MSA and MSE will be estimators of s 2 if H o is true. Hence if H 0 is true, the F-ratio will be close to 1. The p-value is the a, probability, at which the difference would be significant. Thus, the smaller the p-value is the more significant the differences.
Several graphs can also aid with the analyses.
Specifically for each group find the mean and graph it where nj is the group size. To determine if the data exhibits a normal distribution, either a stem and leaf or normal plot of the residuals will approximate a normal distribution. Note that dots in subscripts imply sums or averages over dotted variable.