The model selection determines whether the shelf life depends on batch and whether the effect of time depends on the batch. Minitab considers the following three models in sequence:
- Time + Batch + Batch*Time (unequal slopes and intercepts for batches)
- Time + Batch (equal slopes and unequal intercepts for batches)
- Time (equal slopes and intercepts for batches)
If the Batch*Time interaction is significant, the analysis fits the first model. If the interaction is not significant but the Batch term is significant in the second model, the analysis fits the second model. Otherwise, the analysis fits the third model.
The test statistic is:
The model selection uses an F-distribution to test the factors. The parameters of the F distribution are:
- Numerator degrees of freedom = degrees of freedom for the term
- Denominator degrees of freedom = degrees of freedom for error
The p-value is the proportion of the F-distribution that is greater than the test statistic:
|MS||the mean square|
|MSE||the mean square for error|
|F(x)||the cumulative distribution function of the given F-distribution evaluated at x|
1. Chow, S. (2007). Statistical Design and Analysis of Stability Studies.
2. U.S. Department of Health and Human Services, Food and Drug Administration, (2004). Guidance for Industry, Q1E Evaluation of Stability Data.