- Write a null and alternative hypothesis for a one-way ANOVA hypothesis test
- Discuss the error sum of squares and group sum of squares
Sum of Squares
The test statistic and P-value are calculated by considering the ratio of variation within each of the groups to the variation between each of the groups. That is, when the variation between each of the groups is significantly greater than the variation within each of the groups, we will reject the null hypothesis and conclude that at least two of the means are different. However, when there is a significant amount of variation within groups, relative to the variation between groups, we will have less evidence of a difference and may fail to reject the null hypothesis.
sum of squares
The statistic measuring the variation within the groups is the error sum of squares. This is calculated by summing the variation within each of the groups. The variation within each of the groups is visualized in the boxplot by the size of the box and in the dotplot as the spread of the dots within each group.
A statistic measuring the variation between the groups is the group sum of squares. This is calculated by summing the variation between each of the group means and the grand mean (i.e., the mean of all the data values).