All factors in a fully nested ANOVA model are random. Consequently, a factor that is statistically significant indicates that it contributes to the amount of variation in the response.
Source | DF | SS | MS | F | P |
---|---|---|---|---|---|
Plant | 3 | 731.5156 | 243.8385 | 5.854 | 0.011 |
Operator | 12 | 499.8125 | 41.6510 | 1.303 | 0.248 |
Shift | 48 | 1534.9167 | 31.9774 | 2.578 | 0.000 |
Batch | 128 | 1588.0000 | 12.4062 | ||
Total | 191 | 4354.2448 |
In these results, the ANOVA table indicates that plant and shift are statistically significant at the 0.05 level. The operator effect is not statistically significant at the 0.05 level. The effects in the model use all of the degrees of freedom, so no degrees of freedom remain to test the statistical significance of the different batches.
Examine the variance components to determine how much of the variation in the study can be attributed to each random term. Higher values indicate that the term contributes more variability to the response.
Source | Var Comp. | % of Total | StDev |
---|---|---|---|
Plant | 4.212 | 17.59 | 2.052 |
Operator | 0.806 | 3.37 | 0.898 |
Shift | 6.524 | 27.24 | 2.554 |
Batch | 12.406 | 51.80 | 3.522 |
Total | 23.948 | 4.894 |
In these results, the variance component estimates indicate that the variability attributable to batches, shifts, and plants was 52%, 27%, and 18%, respectively, of the total variability.