- Complete a one-way ANOVA hypothesis test
- Write the conclusion of a one-way ANOVA hypothesis test in context of the problem
Mean Square
When performing a formal hypothesis test for a one-way ANOVA, the mean square values are used to calculate the value of our test statistic; thus, they impact the P-value we get.
As noted in the previous table, the mean square for error and mean square for group are calculated by taking each of the sum of square values and dividing them by the degrees of freedom associated with the respective source (i.e., Group or Error).
mean square
[latex]\text{Mean Square for Error (MSError)}=\dfrac{\text{Error sum of squares}}{\text{degrees of freedom (Error)}}=\dfrac{SSE}{N-k}[/latex]
[latex]\text{Mean Square for Group (MSGroup)}=\dfrac{\text{Group sum of squares}}{\text{degrees of freedom (Group)}}=\dfrac{SSG}{k-1}[/latex]
F-statistic
The test statistic that we use to complete the appropriate hypothesis test for a one-way ANOVA is calculated with the ratio below:
[latex]\text{F-Statistic}=\dfrac{\text{MSGroup}}{\text{MSError}}=\dfrac{\text{Variation BETWEEN groups}}{\text{Variation WITHIN groups}}[/latex]