# SIMSTAT: Analysis of variance

This is a rather over-rated technique and there is almost always something better you can do to exploit the special features of your data, if you know how. Consult program FTEST for more details about the F distribution. The best way to do 1-way ANOVA is to practise first with the library test file anova1.tfl. Observe how you can do all the usual variance stabilising transformations on request, and note how you can suppress selected columns interactively. You can explore 2-way ANOVA with row and column design by using the test files anova2.tf1 and anova2.tf2, while 3-way Latin Square design can be appreciated by analysing anova3.tf1. For more complex designs with blocks and treatments with possibly unequal numbers of replicates, it is obvious that each observation must be classifed according to the group number and subgroup number. To see how this is done you should analyse anova4.tf1. The anova5.tf? test files allow you to practise with factorial designs, with or without blocking. Repeated measurements ANOVA can also be performed if the values along each row i have been obtained for subject i and you are only interested in differences between treatment effects in columns j, not the differences between subjects i. A viewing option is also provided so that you can browse the ANOVA test files in order to understand the data formats required.
With some ANOVA analyses the program can perform the related nonparametric test if required, e.g. Kruskal-Wallis test for 1-way ANOVA or the Friedman test for 2-way ANOVA, since these just exploit ranking and do not rely on the assumption that the columns are normally distributed.
After any 1-way parameteric ANOVA where the null hypothesis is rejected, the Tukey post-ANOVA Q test can be done to identify columns that are significantly different. This ranks the means from largest to smallest, but omits intermediate tests between any ranked pairs of columns that have been found to differ significantly. The p values from this test take into account the results of this procedure and are therefore corrected for multiple testing. Note that harmonic means are used for pairs with unequal sample sizes, but the test really depends on similar sample sizes, so you will be warned where extreme differences occur.

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