- F-Test/Analysis of Variance — One Way, Equal or Unequal Sample Size
- F-Test/Analysis of Variance — Two Way, Equal Sample Size
- F-Test/Analysis of Variance — Three Way, Equal Sample Size
The ANOVA or F test determines if significant differences exist among treatment means or interactions. It’s a preliminary test that indicates if further analysis of the relationship among treatment means is warranted. If the null hypothesis of no difference among treatments is accepted, the test result implies factor levels and response are unrelated, so the analysis is terminated. When the null hypothesis is rejected, the analysis is usually continued to examine the nature of the factor-level effects. Examples are:
- Tukey’s Method — tests all possible pairwise differences of means
- Scheffe’s Method — tests all possible contrasts at the same time
- Bonferroni’s Method — tests, or puts simultaneous confidence intervals around a pre-selected group of contrasts
The N-way F-Test is designed to execute within groups defined by the distinct values of the group-by variables (GBVs), the same as most of the other nonparametric tests. Two or more treatments must exist in the data within the groups defined by the distinct GBV values.
Given a column of interest (dependent variable), one or more input columns (independent variables) and optionally one or more group-by columns (all from the same input table), an F-Test is produced. The N-Way ANOVA tests whether a set of sample means are all equal (the null hypothesis). Output is a p-value which when compared to the user’s threshold, determines whether the null hypothesis should be rejected.