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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