# Bonferroni adjusted p values (from a dunns test)

Are these P values to the same alpha value; ie, if adj p > 0.05 then there is no significant difference? also what does it mean when p = 1 (because this has happened for some of mine yet none of the groups means are identical making this confusing as i thought that meant they were)

• If there is not much difference between two groups, then a P-value for a test comparing them might be near 1. However, P-values near 1 can occur by chance even if there is some difference between sample means, but no significant difference to indicate population means differ. Other causes of P-values near 1 include non-random data, population distributions that are not appropriate for the test you're using, and having the wrong model for the data. Apr 23 at 22:41
• Moreover, if the test is exact, the test statistic is continuous, and $H_0$ is true, then P-values are uniformly dist'd in $(0,1).$ If the signif. level is 5%, then the probability of a P-value below 0.05 is 5%. But owing to the uniform dist'n, the probability of a P-value above 0.95 is also 5%. Neither occurrence is likely; both are possible. // Altogether, your reaction to a P-val near 1 should be to consider whether you are using the correct test, the data were collected as you thought, and computations & data entry are free of errors. But you will not necessarily find anything wrong. Apr 23 at 22:49