Standard Error Formula for Tukey's HSD using pwcompare or pwmean

[Saul Gabriel]

Greetings,

The standard error I have seen used for this statistic is (MSE/n*)^.5, where MSE is from the ANOVA and n* is group size when all groups are of equal size. It does not appear that Stata uses this formula when using the pwcompare of pwmean commands.
I would like to know what formula Stata is using in these computations, and share this with my students.

Thanks,

[Marcos Almeida]

There is some information in the Stata Manual that may be helpful to you:

Tukey’s HSD adjustment
Tukey’s adjustment is also referred to as Tukey’s honestly significant difference (HSD) and is
used when mcompare(tukey) is specified. It is often applied to all pairwise comparisons of means.
Tukey’s HSD is commonly used as a post hoc test although this is not a requirement.
To adjust for multiple comparisons, Tukey’s method compares the absolute value of the t statistic
from the individual comparison with a critical value based on a Studentized range distribution with
parameter equal to the number of levels in the term. When applied to pairwise comparisons of means,
q =
meanmax 􀀀 meanmin
s
follows a Studentized range distribution with parameter k and degrees of freedom. Here meanmax
and meanmin are the largest and smallest marginal means, and s is an estimate of the standard error
of the means.
Now for the comparison of the smallest and largest means, we can say that the probability of not
making a type I error is
Pr

meanmax 􀀀 meanmin
s
qk;

= 1 􀀀
Then the following inequality holds for all pairs of means simultaneously:
Pr

jmeani 􀀀 meanj j
s
qk;

1 􀀀
Based on this procedure, Tukey’s HSD computes the p-value for each of the individual comparisons
using the Studentized range distribution. However, because the equality holds only for the difference
in the largest and smallest means, this procedure produces conservative tests for the remaining
comparisons. Winer, Brown, and Michels (1991, 172–182) discuss this in further detail.

sorry for the lack of format for the formulae, but you can find them by tpyping - help pwcompare -.

[daniel klein]

This is documented in the Methods and formulas section. Note that none of the available methods actually changes the estimated standard errors; it is the p-values and confidence intervals (the critical values) that are adjusted for multiple comparisons.

Best
Daniel

[Saul Gabriel]

.

Thanks. The formula I was looking for was (MSE*(1/ni+1/nj))^.5. This formula is used in Stata and SPSS.