Example of Balanced ANOVA

Interpret the results

Minitab displays a list of factors, with their type (fixed or random), number of levels, and values. The Analysis of Variance table displays p-values for all of the terms in the model. The low p-values for setting and all of the interaction effects indicate that these terms are significant at the 0.05 level.

Setting is a fixed factor and this main effect is significant. This result indicates that the mean coating thickness is not equal for all machine settings.

Time*Setting is an interaction effect that involves two fixed factors. This interaction effect is significant which indicates that the relationship between each factor and the response depends on the level of the other factor. In this case, you should not interpret the main effects without considering the interaction effect.

The means table shows how the mean thickness varies by each level of time (morning and evening), each machine setting, and by each combination of time and machine setting. Setting is statistically significant and the means differ between the machine settings. However, because the Time*Setting interaction term is also statistically significant, do not interpret the main effects without considering the interaction effects. For example, the table for the interaction term shows that with a setting of 44, time 2 is associated with a thicker coating. However, with a setting of 52, time 1 is associated with a thicker coating.

Operator is a random factor and all interactions that include a random factor are considered to be random. If a random factor is significant, you can conclude that the factor contributes to the amount of variation in the response. Operator is not significant at the 0.05 level, but the interaction effects that include operator are significant. These interaction effects indicate that the amount of variation that operator contributes to the response depends on the value of both time and machine setting.