1. 1-factor analysis of variance (1-anova)
use to compare the means of 3 or more groups
in a pair-wise manner that differ by 1 factor
detects if there is a difference between the means
does not identify which pair(s) is / are different
motivation
use of multiple pair-wise comparisons using
multiple t-tests increases the error, while 1-anova
does not have such an issue.

2. Basis:
use F-test to compare 2 estimates of the variance
MS(Tr): based on the SEM
MSE: find the average of the SD2 from
each group
where
and
if the means are the same, then MS(Tr) would be
a valid estimate of the variance, SD2; otherwise,
the F-test should show that the 2 estimates of
the variance are different.

3. MS(Tr): estimate of SD2 based on the SEM. To
simplify the analysis, assume all groups have the
same sample size; if invalid assumption, then
analysis is more complicated.
recall,
where
SEM = standard deviation of the means; thus
where
k = # groups
n = # samples in a group
= mean of the ith group
.. = mean of all samples

4. MSE: estimate of SD2 by averaging the SD2 of
each group. To simplify the analysis, assume all
groups have the same sample size; if invalid
assumption, then analysis is more complicated.
where
k = # groups
SDi2 = variance of the ith group
n = # samples in a group
= mean of the ith group
= jth data in the ith group

5. Tukey test
use only if preceding 1-anova detects
a difference among the means
multiple (pair-wise) comparison test,
which identifies the pair(s) of different
means