I'm a new member to the list. My background is in neuropsychology rather
than statistics so please excuse this naive question. I did a simple ANOVA
comparing a mean score across five groups. The ANOVA was barely
significanct (0.04) but in post hoc tests using Bonferroni, Scheffe and
Sida none of the group mean differences were near significant (the largest
group mean difference had a p of 0.14).
Any explanation is appreciated.
An F-test comparing 5 groups is implicitly defining a 95% confidence
region, in 4-dimensional "hyperspace", for 4 mean differences between the 4
non-reference groups and the reference group. Jim's "barely significant"
P-value implies that this confidence region does not contain the vector of
4 zero mean differences, which would be the true population mean
differences if all 5 groups had the same mean. However, the post-hoc tests
seem to imply that the confidence region for the 4 mean differences might
contain zero values for any of the 4 mean differences individually.
Therefore, although it seems that at least one difference is non-zero, Jim
has insufficient data to incriminate one of these differences as being "the
culprit".
