Significance level of kwallis2 test in Stata I have a question concerning the use of the kwallis2 test in Stata. If looking at the multiple comparison output, I receive a probability and (NS) or (S).
What does the probability there mean and to what does the program compare this value to reach the outcome significant or not? I suppose that the standard 5% significance level is used. But I also see some adjusted p-value for significance... I am a little confused about the output given by this test. 
Another question: How can the significance level be changed? 
I hope (and am thankful) for good explanations! 
 A: The single p-values from the multiple comparisons are compared to the critical value computed by the kwallis2 command and reported as "Adjusted p-value for significance". If for some reasons you don't like that critical value and, for example, you want to use an $\alpha=0.01$, then you can compare the single p-values for the different pairwise comparisons with your $\alpha$ and forget about the (S) and (NS) output.
Looking at the code behind kwallis2, in the case of multiple comparisons between groups (i.e. all the possible pairwise comparisons), the critical value $\alpha'$ is calculated as $\alpha/(k∗(k−1))$, where $\alpha=0.05$ by default (but can be modified using set level before running kwallis2) and $k$ is the number of groups. If you choose a control group and compare all the other groups versus that one, then $\alpha'=\alpha/(2∗(k−1))$
For example:
. sysuse auto, clear
(1978 Automobile Data)

. set level 90 // (i.e. alpha = 0.1)

. kwallis2 length, by(rep78) control(1)

One-way analysis of variance by ranks (Kruskal-Wallis Test)
[omitted output]
(Adjusted p-value for significance is 0.012500)
[omitted output]

. di 0.1/(2*4)
.0125

