PAIREDFREQ Statement

Summary of Options

Table 19 summarizes the options available in the PAIREDFREQ statement.

Table 19: PAIREDFREQ Statement Options

Option	Description
Define Analysis
DIST=	Specifies the underlying distribution assumed for the test statistic
TEST=	Specifies the statistical analysis
Specify Analysis Information
ALPHA=	Specifies the significance level
NULLDISCPROPRATIO=	Specifies the null value of the ratio of discordant proportions
SIDES=	Specifies the number of sides and the direction of the statistical test or confidence interval
Specify Effects
CORR=	Specifies the correlation between members of a pair
DISCPROPDIFF=	Specifies the discordant proportion difference
DISCPROPORTIONS=	Specifies the two discordant proportions, and
DISCPROPRATIO=	Specifies the ratio
ODDSRATIO=	Specifies the odds ratio
PAIREDPROPORTIONS=	Specifies the two paired proportions, and
PROPORTIONDIFF=	Specifies the proportion difference
REFPROPORTION=	Specifies either the reference first proportion or the reference discordant proportion
RELATIVERISK=	Specifies the relative risk
TOTALPROPDISC=	Specifies the discordant proportion sum,
Specify Sample Size
NFRACTIONAL	Enables fractional input and output for sample sizes
NPAIRS=	Specifies the total number of proportion pairs
Specify Power
POWER=	Specifies the desired power of the test
Choose Computational Method
METHOD=	Specifies the computational method
Control Ordering in Output
OUTPUTORDER=	Controls the output order of parameters

Table 20 summarizes the valid result parameters in the PAIREDFREQ statement.

Table 20: Summary of Result Parameters in the PAIREDFREQ Statement

Analyses	Solve For	Syntax
TEST=MCNEMAR METHOD=CONNOR	Power	POWER=.
	Sample size	NPAIRS=.
TEST=MCNEMAR METHOD=EXACT	Power	POWER=.
TEST=MCNEMAR METHOD=MIETTINEN	Power	POWER=.
	Sample size	NPAIRS=.

Dictionary of Options

ALPHA=number-list

specifies the level of significance of the statistical test. The default is 0.05, which corresponds to the usual 0.05 100% = 5% level of significance. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

CORR=number-list

specifies the correlation between members of a pair. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

DISCPROPORTIONS=grouped-number-list DISCPS=grouped-number-list

specifies the two discordant proportions, and . For information about specifying the grouped-number-list, see the section Specifying Value Lists in Analysis Statements.

DISCPROPDIFF=number-list DISCPDIFF=number-list

specifies the difference between discordant proportions. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

DISCPROPRATIO=number-list DISCPRATIO=number-list

specifies the ratio of discordant proportions. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

DIST=EXACT_COND | NORMAL

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.

METHOD=CONNOR | EXACT | MIETTINEN

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.

NFRACTIONAL NFRAC

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.

NPAIRS=number-list

specifies the total number of proportion pairs (concordant and discordant) or requests a solution for the number of pairs by specifying a missing value (NPAIRS=.). For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

NULLDISCPROPRATIO=number-list NULLDISCPRATIO=number-list NULLRATIO=number-list NULLR=number-list

specifies the null value of the ratio of discordant proportions. The default value is 1. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

ODDSRATIO=number-list OR=number-list

specifies the odds ratio . For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

OUTPUTORDER=INTERNAL | REVERSE | SYNTAX

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:

SIDES=
NULLDISCPROPRATIO=
ALPHA=
PAIREDPROPORTIONS=
PROPORTIONDIFF=
ODDSRATIO=
RELATIVERISK=
CORR=
DISCPROPORTIONS=
DISCPROPDIFF=
TOTALPROPDISC=
REFPROPORTION=
DISCPROPRATIO=
NPAIRS=
POWER=

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.

PAIREDPROPORTIONS=grouped-number-list PPROPORTIONS=grouped-number-list PAIREDPS=grouped-number-list PPS=grouped-number-list

specifies the two paired proportions, and . For information about specifying the grouped-number-list, see the section Specifying Value Lists in Analysis Statements.

POWER=number-list

specifies the desired power of the test or requests a solution for the power by specifying a missing value (POWER=.). The power is expressed as a probability, a number between 0 and 1, rather than as a percentage. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

PROPORTIONDIFF=number-list PDIFF=number-list

specifies the proportion difference . For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

REFPROPORTION=number-list REFP=number-list

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). For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

RELATIVERISK=number-list RR=number-list

specifies the relative risk . For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

SIDES=keyword-list

specifies the number of sides (or tails) and the direction of the statistical test or confidence interval. For information about specifying the keyword-list, see the section Specifying Value Lists in Analysis Statements. You can specify the following keywords:

1: specifies a one-sided test, with the alternative hypothesis in the same direction as the effect.
2: specifies a two-sided test.
U: specifies an upper one-sided test, with the alternative hypothesis indicating an effect greater than the null value.
L: specifies a lower one-sided test, with the alternative hypothesis indicating an effect less than the 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. By default, SIDES=2.

TEST=MCNEMAR

specifies the McNemar test of paired proportions. This is the default test option.

TOTALPROPDISC=number-list TOTALPDISC=number-list PDISC=number-list

specifies the sum of the two discordant proportions, . For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.

Restrictions on Option Combinations

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)

Option Groups for Common Analyses

This section summarizes the syntax for the common analyses that are supported in the PAIREDFREQ statement.

McNemar Exact Conditional Test

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 two-sided 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;

McNemar Normal Approximation Test

The following statements demonstrate a sample size computation for the normal-approximate 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 two-sided 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;

The POWER Procedure