{smcl}
{* version 1.1.0}{...}
{cmd:help pwmc}
{hline}
{title:Title}
{p 5}
{cmd:pwmc} {hline 2} Pairwise multiple comparisons
(unequal variances)
{title:Syntax}
{p 5}
Syntax for pwmc
{p 8}
{cmd:pwmc} {varname} {ifin} {cmd:,} {opt over(varname)}
[{it:options}]
{p 5}
Immediate command
{p 8 12}
{cmd:pwmci} {it:stats{hi:1}} {it:stats{hi:2}} {it:stats{hi:3}}
[ {it:... stats{hi:k}} ] [ {cmd:,} {it:options} ]
{p 5} where {it:stats} is
{p 8}
[ {cmd:(} ] {it:#obs} {it:#mean} {it:#sd} [ {cmd: )} ]
{title:Description}
{pstd}
{cmd:pwmc} performs pairwise comparisons of means. It computes
pairwise differences of the means of {varname} over the levels
of {opt over(varname)}. Confidence intervals are derived using
procedures allowing for unequal variances across groups.
{pstd}
{cmd:pwmc} implements Dunnett's {cmd:C}, {cmd:GH} and {cmd:T2}
procedures, as proposed by Dunnett (1980), Games and Howell (1976)
and Tamhane (1979).
{pstd}
{cmd:pwmci} is the immediate form of {cmd:pwmc}. See {help immed}.
{title:Options}
{phang}
{opt over(varname)} is required and specifies that means are
computed for each level of {it:varname}.
{phang}
{opt proc:edure(proc)} specifies the procedure to be used to derive
confidence intervals. {it:proc} may be any combination of {cmd:C},
{cmd:GH} and {cmd:T2} and case does not matter. Default is to report
confidence intervals using each of the procedures.
{phang}
{opt l:evel(#)} specifies the confidence level, as a percentage, for
confindence intervals. The default is {cmd:level({hi:{ccl level}})}.
See {helpb set level}.
{phang}
{opt pv:alues} displays adjusted p-values. The Games and Howell
adjusted p-value is given by
{p 16}
p_adj = 1 - q_(k, nuhat, abs(t)*sqrt(2))
{p 8 8}
where q is the
{help tukeyprob():cumulative Studentized range distribution} with k
means and nuhat degrees of freedem, using Satterthwaite’s (1946)
approximate formula.
{p 8}
The adjusted p-value for Tamhane's T2 is
{p 16}
p_adj = 1 - (1 - p)^(k*(k - 1)/2)
{p 8 8}
where p is the p-value from a t-test based on Satterthwaite’s (1946)
approximate formula for the degrees of freedom.
{p 8} There is no adjusted p-value for Dunnet's C.
{phang}
{opt varl:abel} displays variable labels instead of variable names.
{phang}
{opt vall:abel} displays value labels instead of numeric codes.
{phang}
{cmd:cformat(}{it:{help %fmt}}{cmd:)} specifies how to format means,
standard errors, and confidence limits.
{phang}
{cmd:pformat(}{it:{help %fmt}}{cmd:)} specifies how to format
adjusted p-values.
{phang}
{cmd:sformat(}{it:{help %fmt}}{cmd:)} specifies how to format
test statistics.
{phang}
{opt notab:le} does report the results, but only stores them in
{cmd:r()}.
{title:Example}
{phang2}{cmd:. pwmc wage , over(race)}{p_end}
{phang2}
{cmd:. pwmci (1637 8.08 5.96) (583 6.84 5.08) (26 8.55 5.21)}
{p_end}
{title:Saved results}
{pstd}
{cmd:pwmc} saves the following in {cmd:r()}:
{pstd}
Scalars{p_end}
{synoptset 15 tabbed}{...}
{synopt:{cmd:r(k)}}number of levels of {opt over(varname)}{p_end}
{synopt:{cmd:r(ks)}}number of differences{p_end}
{synopt:{cmd:r(level)}}confidence level{p_end}
{pstd}
Macros{p_end}
{synoptset 15 tabbed}{...}
{synopt:{cmd:r(cmd)}}{cmd:pwmc}{p_end}
{synopt:{cmd:r(depvar)}}{it:varname} from which means are
computed{p_end}
{synopt:{cmd:r(over)}}{it:varname} in {opt over(varname)}{p_end}
{pstd}
Matrices{p_end}
{synoptset 15 tabbed}{...}
{synopt:{cmd:r(diff)}}differences of means{p_end}
{synopt:{cmd:r(Var)}}variances of differences{p_end}
{synopt:{cmd:r(nuhat)}}degrees of freedom{p_end}
{synopt:{cmd:r(ci)}}confidence intervals{p_end}
{synopt:{cmd:r(t)}}test statistics{p_end}
{synopt:{cmd:r(p_adj)}}adjusted p-values{p_end}
{synopt:{cmd:r(A)}}critical values (cf. Dunnett, 1980){p_end}
{title:References}
{pstd}
Dunnett, Charles W. (1980). Pairwise Multiple Comparisons in the
Unequal Variance Case,
{it:Journal of the American Statistical Association}, 75(372), 796-800.
{pstd}
Games, Paul A., Howell, John F. (1976). Pairwise Multiple Comparison
Procedures with Unequal N's and/or Variances: A Monte Carlo study,
{it:Journal of Educational Statistics}, 1(2), 113-125.
{pstd}
Tamhane, Ajit C. (1979). A Comparison of Procedures for Multiple
Comparisons of Means with Unequal Variances,
{it:Journal of the American Statistical Association}, 74(366), 471-480.
{title:Acknowledgments}
{pstd}
Matthew K. Lau's 'DTK' package for R was helpful developing {cmd:pwmc}.
{title:Author}
{pstd}Daniel Klein, University of Kassel, klein.daniel.81@gmail.com
{title:Also see}
{psee}
Online: {helpb pwmean}, {helpb pwcompare}, {helpb oneway}
{p_end}
{psee}
if installed: {help dunnett}, {help prcomp}
{p_end}