PAIREDFREQ Statement 
The PAIREDFREQ statement performs power and sample size analyses for McNemar’s test for paired proportions.
Table 70.14 summarizes categories of options available in the PAIREDFREQ statement.
Task 
Options 

Define analysis 

Specify analysis information 

Specify effects 

Specify sample size 

Specify power 

Control sample size rounding 

Choose computational method 

Control ordering in output 
Table 70.15 summarizes the valid result parameters in the PAIREDFREQ statement.
Analyses 
Solve For 
Syntax 

Power 

Sample size 

Power 

Power 

Sample size 
specifies the level of significance of the statistical test. The default is 0.05, corresponding to the usual 0.05 100% = 5% level of significance. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the correlation between members of a pair. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the two discordant proportions, and . See the section Specifying Value Lists in Analysis Statements for information about specifying the groupednumberlist.
specifies the difference between discordant proportions. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the ratio of discordant proportions. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the underlying distribution assumed for the test statistic. EXACT_COND corresponds to the exact conditional test, based on the exact binomial distribution of the two types of discordant pairs given the total number of discordant pairs. NORMAL corresponds to the conditional test based on the normal approximation to the binomial distribution of the two types of discordant pairs given the total number of discordant pairs. The default value is EXACT_COND.
specifies the computational method. METHOD=EXACT (the default) uses the exact binomial distributions of the total number of discordant pairs and the two types of discordant pairs. METHOD=CONNOR uses an approximation from Connor (1987), and METHOD=MIETTINEN uses an approximation from Miettinen (1968). The CONNOR and MIETTINEN methods are valid only for DIST=NORMAL.
enables fractional input and output for sample sizes. See the section Sample Size Adjustment Options for information about the ramifications of the presence (and absence) of the NFRACTIONAL option. This option cannot be used with METHOD=EXACT.
specifies the total number of proportion pairs (concordant and discordant) or requests a solution for the number of pairs with a missing value (NPAIRS=.). See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the null value of the ratio of discordant proportions. The default value is 1. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the odds ratio . See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
controls how the input and default analysis parameters are ordered in the output. OUTPUTORDER=INTERNAL (the default) arranges the parameters in the output according to the following order of their corresponding options:
TOTALPROPDISC=
The OUTPUTORDER=SYNTAX option arranges the parameters in the output in the same order in which their corresponding options are specified in the PAIREDFREQ statement. The OUTPUTORDER=REVERSE option arranges the parameters in the output in the reverse of the order in which their corresponding options are specified in the PAIREDFREQ statement.
specifies the two paired proportions, and . See the section Specifying Value Lists in Analysis Statements for information about specifying the groupednumberlist.
specifies the desired power of the test or requests a solution for the power with a missing value (POWER=.). The power is expressed as a probability, a number between 0 and 1, rather than as a percentage. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the proportion difference . See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies either the reference first proportion (when used in conjunction with the PROPORTIONDIFF=, ODDSRATIO=, or RELATIVERISK= option) or the reference discordant proportion (when used in conjunction with the DISCPROPDIFF= or DISCPROPRATIO= option). See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the relative risk . See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the number of sides (or tails) and the direction of the statistical test or confidence interval. See the section Specifying Value Lists in Analysis Statements for information about specifying the keywordlist. Valid keywords and their interpretation are as follows:
onesided with alternative hypothesis in same direction as effect
twosided
upper onesided with alternative greater than null value
lower onesided with alternative less than null value
If the effect size is zero, then SIDES=1 is not permitted; instead, specify the direction of the test explicitly in this case with either SIDES=L or SIDES=U. The default value is 2.
specifies the McNemar test of paired proportions. This is the default test option.
specifies the sum of the two discordant proportions, . See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
To specify the proportions, choose one of the following parameterizations:
discordant proportions (using the DISCPROPORTIONS= option)
difference and sum of discordant proportions (using the DISCPROPDIFF= and TOTALPROPDISC=options)
difference of discordant proportions and reference discordant proportion (using the DISCPROPDIFF= and REFPROPORTION= options)
ratio of discordant proportions and reference discordant proportion (using the DISCPROPRATIO= and REFPROPORTION= options)
ratio and sum of discordant proportions (using the DISCPROPRATIO= and TOTALPROPDISC=options)
paired proportions and correlation (using the PAIREDPROPORTIONS= and CORR= options)
proportion difference, reference proportion, and correlation (using the PROPORTIONDIFF=, REFPROPORTION=, and CORR= options)
odds ratio, reference proportion, and correlation (using the ODDSRATIO=, REFPROPORTION=, and CORR= options)
relative risk, reference proportion, and correlation (using the RELATIVERISK=, REFPROPORTION=, and CORR= options)
This section summarizes the syntax for the common analyses supported in the PAIREDFREQ statement.
You can express effects in terms of the individual discordant proportions, as in the following statements. Default values for the TEST=, SIDES=, ALPHA=, and NULLDISCPROPRATIO= options specify a twosided McNemar test for no effect with a significance level of 0.05.
proc power; pairedfreq dist=exact_cond discproportions = 0.15  0.45 npairs = 80 power = .; run;
You can also express effects in terms of the difference and sum of discordant proportions:
proc power; pairedfreq dist=exact_cond discpropdiff = 0.3 totalpropdisc = 0.6 npairs = 80 power = .; run;
You can also express effects in terms of the difference of discordant proportions and the reference discordant proportion:
proc power; pairedfreq dist=exact_cond discpropdiff = 0.3 refproportion = 0.15 npairs = 80 power = .; run;
You can also express effects in terms of the ratio of discordant proportions and the denominator of the ratio:
proc power; pairedfreq dist=exact_cond discpropratio = 3 refproportion = 0.15 npairs = 80 power = .; run;
You can also express effects in terms of the ratio and sum of discordant proportions:
proc power; pairedfreq dist=exact_cond discpropratio = 3 totalpropdisc = 0.6 npairs = 80 power = .; run;
You can also express effects in terms of the paired proportions and correlation:
proc power; pairedfreq dist=exact_cond pairedproportions = 0.6  0.8 corr = 0.4 npairs = 45 power = .; run;
You can also express effects in terms of the proportion difference, reference proportion, and correlation:
proc power; pairedfreq dist=exact_cond proportiondiff = 0.2 refproportion = 0.6 corr = 0.4 npairs = 45 power = .; run;
You can also express effects in terms of the odds ratio, reference proportion, and correlation:
proc power; pairedfreq dist=exact_cond oddsratio = 2.66667 refproportion = 0.6 corr = 0.4 npairs = 45 power = .; run;
You can also express effects in terms of the relative risk, reference proportion, and correlation:
proc power; pairedfreq dist=exact_cond relativerisk = 1.33333 refproportion = 0.6 corr = 0.4 npairs = 45 power = .; run;
The following statements demonstrate a sample size computation for the normalapproximate McNemar test. The default value for the METHOD= option specifies an exact sample size computation. Default values for the TEST=, SIDES=, ALPHA=, and NULLDISCPROPRATIO= options specify a twosided McNemar test for no effect with a significance level of 0.05.
proc power; pairedfreq dist=normal method=connor discproportions = 0.15  0.45 npairs = . power = .9; run;