## Stata 15 help for pwmean

```
[R] pwmean -- Pairwise comparisons of means

Syntax

pwmean varname, over(varlist) [options]

options                 Description
-------------------------------------------------------------------------
Main
* over(varlist)         compare means across each combination of the
levels in varlist
mcompare(method)      adjust for multiple comparisons; default is

Reporting
level(#)              confidence level; default is level(95)
cieffects             display a table of mean differences and
confidence intervals; the default
pveffects             display a table of mean differences and p-values
effects               display a table of mean differences with p-values
and confidence intervals
cimeans               display a table of means and confidence intervals
groups                display a table of means with codes that group
them with other means that are not
significantly different
sort                  sort results tables by displayed mean or
difference
display_options       control column formats, line width, and
factor-variable labeling
-------------------------------------------------------------------------
*over(varlist) is required.
See [R] pwmean postestimation for features available after estimation.

method                  Description
-------------------------------------------------------------------------
default
bonferroni              Bonferroni's method
sidak                   Sidak's method
scheffe                 Scheffe's method
tukey                   Tukey's method
snk                     Student-Newman-Keuls's method
duncan                  Duncan's method
dunnett                 Dunnett's method
-------------------------------------------------------------------------

Statistics > Summaries, tables, and tests > Summary and descriptive
statistics > Pairwise comparisons of means

Description

pwmean performs pairwise comparisons of means. It computes all pairwise
differences of the means of varname over the combination of the levels of
the variables in varlist.  The tests and confidence intervals for the
pairwise comparisons assume equal variances across groups.  pwmean also
allows for adjusting the confidence intervals and p-values to account for
multiple comparisons using Bonferroni's method, Scheffe's method, Tukey's
method, Dunnett's method, and others.

See [R] pwcompare for performing pairwise comparisons of means, estimated
marginal means, and other types of marginal linear predictions after
anova, regress, and most other estimation commands.

Options

+------+
----+ Main +-------------------------------------------------------------

over(varlist) is required and specifies that the means are computed for
each combination of the levels of the variables in varlist.

mcompare(method) specifies the method for computing p-values and
confidence intervals that account for multiple comparisons.

Most methods adjust the comparisonwise error rate, alpha_c, to
achieve a prespecified experimentwise error rate, alpha_e.

alpha_c = alpha_e

mcompare(bonferroni) adjusts the comparisonwise error rate based on
the upper limit of the Bonferroni inequality:

alpha_e <= m * alpha_c

where m is the number of comparisons within the term.

The adjusted comparisonwise error rate is

alpha_c = alpha_e/m

mcompare(sidak) adjusts the comparisonwise error rate based on the
upper limit of the probability inequality

alpha_e <= 1 - (1 - alpha_c)^m

where m is the number of comparisons within the term.

The adjusted comparisonwise error rate is

alpha_c = 1 - (1 - alpha_e)^(1/m)

This adjustment is exact when the m comparisons are independent.

mcompare(scheffe) controls the experimentwise error rate using the F
(or chi-squared) distribution with degrees of freedom equal to
k-1 where k is the number of means being compared.

mcompare(tukey) uses what is commonly referred to as Tukey's honestly
significant difference.  This method uses the Studentized range
distribution instead of the t distribution.

mcompare(snk) is a variation on mcompare(tukey) that counts only the
number of means participating in the range for a given comparison
instead of the full number of means.

mcompare(duncan) is a variation on mcompare(snk) with additional

mcompare(dunnett) uses Dunnett's method for making comparisons with a
reference category.

+-----------+
----+ Reporting +--------------------------------------------------------

level(#) specifies the confidence level, as a percentage, for confidence
intervals.  The default is level(95) or as set by set level.  The
significance level used by the groups option is 100-#, expressed as a
percentage.

cieffects specifies that a table of the pairwise comparisons of means
with their standard errors and confidence intervals be reported.
This is the default.

pveffects specifies that a table of the pairwise comparisons of means
with their standard errors, test statistics, and p-values be
reported.

effects specifies that a table of the pairwise comparisons of means with
their standard errors, test statistics, p-values, and confidence
intervals be reported.

cimeans specifies that a table of the means with their standard errors
and confidence intervals be reported.

groups specifies that a table of the means with their standard errors and
group codes be reported.  Means with the same letter in the group
code are not significantly different at the specified significance
level.

sort specifies that the reported tables be sorted by the mean or
difference that is displayed in the table.

display_options:  nofvlabel, fvwrap(#), fvwrapon(style), cformat(%fmt),
pformat(%fmt), sformat(%fmt), and nolstretch.

nofvlabel displays factor-variable level values rather than attached
value labels.  This option overrides the fvlabel setting; see [R]
set showbaselevels.

fvwrap(#) specifies how many lines to allow when long value labels
must be wrapped.  Labels requiring more than # lines are
truncated.  This option overrides the fvwrap setting; see [R] set
showbaselevels.

fvwrapon(style) specifies whether value labels that wrap will break
at word boundaries or break based on available space.

fvwrapon(word), the default, specifies that value labels break at
word boundaries.

fvwrapon(width) specifies that value labels break based on
available space.

This option overrides the fvwrapon setting; see [R] set
showbaselevels.

cformat(%fmt) specifies how to format means, standard errors, and
confidence limits in the table of pairwise comparison of means.

pformat(%fmt) specifies how to format p-values in the table of
pairwise comparison of means.

sformat(%fmt) specifies how to format test statistics in the table of
pairwise comparison of means.

nolstretch specifies that the width of the table of pairwise
comparisons not be automatically widened to accommodate longer
variable names. The default, lstretch, is to automatically widen
the table of pairwise comparisons up to the width of the Results
window.  To change the default, use set lstretch off. nolstretch
is not shown in the dialog box.

Examples

Setup
. webuse yield

Mean yield for each fertilizer
. pwmean yield, over(fertilizer) cimeans

Pairwise comparisons of mean yields for the fertilizers
. pwmean yield, over(fertilizer) effects

Pairwise comparisons of the mean yields using Tukey's adjustment for
multiple comparisons when computing p-values
. pwmean yield, over(fertilizer) pveffects mcompare(tukey)

Comparisons of the mean yield for each fertilizer to the control
. pwmean yield, over(fertilizer) effects mcompare(dunnett)

Stored results

pwmean stores the following in e():

Scalars
e(df_r)             variance degrees of freedom
e(balanced)         1 if fully balanced data, 0 otherwise

Macros
e(cmd)              pwmean
e(cmdline)          command as typed
e(title)            title in output
e(depvar)           name of variable from which the means are computed
e(over)             varlist from over()
e(properties)       b V

Matrices
e(b)                mean estimates
e(V)                variance-covariance matrix of the mean estimates
e(error)            mean estimability codes;
0 means estimable,
8 means not estimable
e(b_vs)             mean difference estimates
e(V_vs)             variance-covariance matrix of the mean difference
estimates
e(error_vs)         mean difference estimability codes;
0 means estimable,
8 means not estimable

```