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.

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.

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

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

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