help pwmc

Title

pwmc -- Pairwise multiple comparisons
(unequal variances)

Syntax

Syntax for pwmc

pwmc varname [if] [in] , over(varname)
[options]

Immediate command

pwmci stats1 stats2 stats3
[ ... statsk ] [ , options ]

where stats is

[ ( ] #obs #mean #sd [ ) ]

Description

pwmc performs pairwise comparisons of means. It computes
pairwise differences of the means of varname over the levels
of over(varname). Confidence intervals are derived using
procedures allowing for unequal variances across groups.

pwmc implements Dunnett's C, GH and T2
procedures, as proposed by Dunnett (1980), Games and Howell (1976)
and Tamhane (1979).

pwmci is the immediate form of pwmc. See immed.

Options

over(varname) is required and specifies that means are
computed for each level of varname.

procedure(proc) specifies the procedure to be used to derive
confidence intervals. proc may be any combination of C,
GH and T2 and case does not matter. Default is to report
confidence intervals using each of the procedures.

level(#) specifies the confidence level, as a percentage, for
confindence intervals. The default is level().
See set level.

pvalues displays adjusted p-values. The Games and Howell
adjusted p-value is given by

p_adj = 1 - q_(k, nuhat, abs(t)*sqrt(2))

where q is the
cumulative Studentized range distribution with k
means and nuhat degrees of freedem, using Satterthwaite’s (1946)
approximate formula.

The adjusted p-value for Tamhane's T2 is

p_adj = 1 - (1 - p)^(k*(k - 1)/2)

where p is the p-value from a t-test based on Satterthwaite’s (1946)
approximate formula for the degrees of freedom.

There is no adjusted p-value for Dunnet's C.

varlabel displays variable labels instead of variable names.

vallabel displays value labels instead of numeric codes.

cformat(%fmt) specifies how to format means,
standard errors, and confidence limits.

pformat(%fmt) specifies how to format
adjusted p-values.

sformat(%fmt) specifies how to format
test statistics.

notable does report the results, but only stores them in
r().

Example

. pwmc wage , over(race)

. pwmci (1637 8.08 5.96) (583 6.84 5.08) (26 8.55 5.21)

Saved results

pwmc saves the following in r():

Scalars

r(k) number of levels of over(varname)

r(ks) number of differences

r(level) confidence level

Macros

r(cmd) pwmc

r(depvar) varname from which means are
computed

r(over) varname in over(varname)

Matrices

r(diff) differences of means

r(Var) variances of differences

r(nuhat) degrees of freedom

r(ci) confidence intervals

r(t) test statistics

r(p_adj) adjusted p-values

r(A) critical values (cf. Dunnett, 1980)

References

Dunnett, Charles W. (1980). Pairwise Multiple Comparisons in the
Unequal Variance Case,
Journal of the American Statistical Association, 75(372), 796-800.

Games, Paul A., Howell, John F. (1976). Pairwise Multiple Comparison
Procedures with Unequal N's and/or Variances: A Monte Carlo study,
Journal of Educational Statistics, 1(2), 113-125.

Tamhane, Ajit C. (1979). A Comparison of Procedures for Multiple
Comparisons of Means with Unequal Variances,
Journal of the American Statistical Association, 74(366), 471-480.

Acknowledgments

Matthew K. Lau's 'DTK' package for R was helpful developing pwmc.

Author

Daniel Klein, University of Kassel, klein.daniel.81@gmail.com

Also see

Online: pwmean, pwcompare, oneway

if installed: dunnett, prcomp