# Samples p-value in ANOVA

#### axeler

##### New Member
Hi,
my problem regards ANOVA: if the ANOVA test is sginificant (p-value<0.05), is there a way to calculate a p-value for each sample, in order to detect which is (are) significant different from the others?
I know there are some post hoc tests, like Tukey or Scheffé, but they all compare difference of means to detect which differences are significant, but I want to detect which sample(s) is significantly different from the others.

As an example, I have to compare these 7 samples:

Sample 1 1.14 1.14 1.28 1.36
Sample 2 1.11 1.30 1.44 1.28 1.37 1.35
Sample 3 1.67 1.60 1.41 1.58 1.65
Sample 4 1.42 1.48 1.46 1.40 1.23
Sample 5 1.53 1.70 1.43 1.56
Sample 6 1.34 1.51 1.37 1.58
Sample 7 1.19 1.37 1.32 1.14 1.43 1.40 1.38

ANOVA is significant (p-value=0.000146), and Sheffé's test says that there are significant differences between sample3/samples1,2,7 and sample5/sample1, so I think that samples 3, 1 and 5 are significant different from the others, but how I can demonstrate it?
I thought to calculate the variance between each sample and the gran mean by
(sumi(xi-xgrm)^2)/dfi where df are the degrees of freedom of sample i
and divide it by MSE, in order to obtain a sort of F-value comparing each sample with the population, and turn it to a p-value. These p-values confirm that samples 3, 5 and 1 are significant (p-values<0.05), but is this procedure correct?