Suppose that we have random samples of \({Y_{1,1}},...,{Y_{n_1,1}},...,{Y_{1,10}},...,{Y_{n_{10},10}}\) from ten groups with total \(N = n_1 + ...+n_{10} = 127\) observations. From the data, we find SSB=21.6, SSW=107.8.
- Calculate the F-test statistic for ANOVA
- Find the p-value for the ANOVA F-test
1) 2.6048
The group numbers g=10, so the degrees of freedom are g-1=9 and N-g=127-10=117.
Hence, MSB=21.6/9=2.4 and MSW=107.8/117=0.921
So that F=MSB/MSW=2.6048
2) 0.0089
The p-value is found by R command:
1-pf(21.6/9/(107.8/117),df1=9,df2=117)
Find the degrees of freedom, and take the ratio MSB/MSW
Use R to find the p-value from the F-distribution.