Question

If I ran an ANOVA with sample 1 having a mean of 5, sample 2 having a mean of 9 and sample 3 having a mean of 10. According to post-hoc comparisons, which means would be different with a q critical value of 3?

Answer 1

If you have the critical value of 'q' = 3, you need to compare the absolute value of differences between pair of means to this critical value. If the difference is greater than the critical value, you conclude that the difference between that pair of mean is significant and else its not significant.

Its easier to do this by forming table as shown -

Pairwise Absolute Difference	Difference Value	Critical Value	Conclusion
$|\overline{X_{1}} - \overline{X_{2}}|$	4	3	Significant
$|\overline{X_{2}} - \overline{X_{3}}|$	1	3	Not Significant
$|\overline{X_{1}} - \overline{X_{3}}|$	5	3	Significant

Thus, we can say that the mean of population 1 is significantly different from that of population 2 and 3. Whereas the population 2 and 3 have non significant difference which means they are not significantly different.

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