# Thread: Combined p-value of ANOVA tests and its post hoc tests

1. ## Combined p-value of ANOVA tests and its post hoc tests

Hi all!

I have conducted a one way ANOVA test of the impact of 3 different shoes on oxygen consumption of a runner and got a P-value of 0.12 (for each shoe condition 5 runs at same speed were conducted). So I could conclude that there is no significant influece of shoes.
But I was not sattisfied with this conclusion. Therefore I repeated the test later on with 9 runs per each shoe condition. Again, the one way anova gave a P-value of 0.10. So again, no signifficance. But if I look at the average values of oxygen consumption the relative differences between different shoe conditions stayed very similar to the ones acquiered in the first test.
So I found out, that p-values can be combined for multiple independent tests. I calculated the combined p-value using a calculator (http://igm.cumc.columbia.edu/MetaP/metap.php) and found out a combined p-value of 0,0475 (Stouffer's z method). So I can conclude, that there are signifficant differences between shoe conditions.
The question are:
• Do I need to perform post hoc tests to find out between which shoe conditions signifficant differences appear? How can I perform them-take all data of the both tests?
• Do
I need to check the normal distrubution and variances equality?
How to calculate the relative differences between different shoe conditions - on the basis of all data?

Any help will be appreciated. Thank you!

Jurij H

2. ## Re: Combined p-value of ANOVA tests and its post hoc tests

What if the post hoc t-tests of equal means are insignifficant for all boot combinations? Can I still say: "Ok, the relative difference between soft and stiff boot condition is #%, but this result is statistically insignificant"?

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