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Say I have data as follows: type|value where type takes values $A$, $B$ and $C$ and value is metric and numerical.

I know that testing $\mu_A<\mu_B$ can be done with a 2-sample t-test. Further I know that testing whether the means are different can be done with ANOVA.

But I want to test that $\mu_A<\mu_B<\mu_C$.

This question (which I asked) is similar and it mentions Fischer's Method where the Wikipedia page says:

Fisher's method is a way of combining the information in the p-values from different statistical tests so as to form a single overall test:

which is what I want: to combine the p-value of $\mu_A<\mu_B$ with that of $\mu_B<\mu_C$. But the sentence continues...

...this method requires that the individual test statistics (or, more immediately, their resulting p-values) should be statistically independent.

which I suppose is not the case since the $\mu_B$ data are used in both tests.

So my question: How can I test the order of three means?

Community
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Geoff
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1 Answers1

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You can use ANOVA with post hoc pairwise comparisons. Holm or Tukey correction on the p-value prevents against exceeding alpha level for the test.

Paweł Kleka
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