Issue on page /05.03-anova.html

[rnrd1919]

In "15.5. Multiple comparisons and post hoc tests" the table is flawed:

The principle of transitivity dictates that if A is equal to B, and B is equal to C, then A must also be equal to C. The table incorrectly allows for possibilities where, for example, μ_placebo = μ_anxifree and μ_anxifree = μ_joyzepam, but μ_placebo ≠ μ_joyzepam, which is a logical contradiction.

The Correct Possibilities

When comparing the means of three groups (let's call them A, B, and C), there are only five logically distinct possibilities regarding their equality, not eight.

All groups are equal: This is the complete null hypothesis.

    A = B = C

Two groups are equal, and the third is different: There are three ways this can happen.

    A = B ≠ C

    A = C ≠ B

    B = C ≠ A

All three groups are different: No two group means are equal.

    A ≠ B ≠ C

So, instead of the eight rows in the original table, the true "states of the world" are these five patterns of mean differences.