Bonferroni correction gives weird results in R

Question

I have this dataset:

Treatment	data
T1	0
T1	0
T1	0
T10	0
T10	0
T10	0
T11	0.2
T11	0.2
T11	0.2
T12	0
T12	0
T12	0
T2	0.7
T2	0.6
T2	0.6
T3	0.8
T3	0.7
T3	0.8
T4	0.3
T4	0.3
T4	0.4
T5	0
T5	0
T5	0
T6	0.7
T6	0.7
T6	0.5
T7	0
T7	0
T7	0
T8	0.8
T8	0.7
T8	0.8
T9	0
T9	0
T9	0

After Scheirer–Ray–Hare test with significant results, I did Dunn test with Bonferroni correction for multiple comparisons. Code: Test = dunnTest(Data ~ Treatment, data=dataset, method="bh"). Here are some results:

Comparison	Z	P.unadj	P.adj
...	...	...	...
T1 - T3	-2.92771374	0.003414643	0.01878053
T10 - T3	-2.92771374	0.003414643	0.02048786
T11 - T3	-1.61958633	0.105321169	0.21722491
T12 - T3	-2.92771374	0.003414643	0.02253664
T2 - T3	-0.66444567	0.506405109	0.74272749
...	...	...	...
T1 - T9	0.00000000	1.000000000	1.000000000
T10 - T9	0.00000000	1.000000000	1.000000000
T11 - T9	1.30812742	0.190830096	0.38166019
T12 - T9	0.00000000	1.000000000	1.000000000
T2 - T9	2.26326807	0.023619169	0.08204554
T3 - T9	2.92771374	0.003414643	0.11268321

As you can see, P after adjustment gives very weird results. For example, T1-T3 is 0.01878053 (significant), but T3-T9 is 0.11268321 (nonsignificant) even though T1 and T9 had exactly the same data (all zero), and P before adjustment are exactly the same as well.

Am I doing it wrong somewehere?

Answer 1

According to the package docs I presume you are using (dunn.test) the method 'bh' is the 'Benjamini-Hochberg adjustment' not the bonferroni correction. This might explain why you get different adjusted values for tests with the same p values, as this method orders the tests and then adjusts values based on the ordering. I'm not sure exactly how this method deals with duplicate p values, but it may be the case that T1-T3 is arbitrarily assigned earlier in the ordering than T3-T9 and so they get different adjusted p values.