The POWER Procedure 
ONESAMPLEFREQ Statement 
The ONESAMPLEFREQ statement performs power and sample size analyses for exact and approximate tests (including equivalence, noninferiority, and superiority) and confidence interval precision for a single binomial proportion.
Table 68.8 summarizes categories of options available in the ONESAMPLEFREQ statement.
Task 
Options 

Define analysis 

Specify analysis information 

Specify effect 

Specify variance estimation 

Specify sample size 

Specify power and related 

probabilities 

Control sample size rounding 

Choose computational method 

Control ordering in output 
Table 68.9 summarizes the valid result parameters for different analyses in the ONESAMPLEFREQ statement.
Analyses 
Solve For 
Syntax 

CI=WILSON 
Prob(width) 

CI=AGRESTICOULL 
Prob(width) 

CI=JEFFREYS 
Prob(width) 

CI=EXACT 
Prob(width) 

CI=WALD 
Prob(width) 

CI=WALD_CORRECT 
Prob(width) 

Power 

Power 

Sample size 

Power 

Power 

Sample size 

TEST=EQUIV_EXACT 
Power 

Power 

Power 

Sample size 

TEST=EXACT 
Power 

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. If the CI= and SIDES=1 options are used, then the value must be less than 0.5. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies an analysis of precision of a confidence interval for the sample binomial proportion.
The value of the CI= option specifies the type of confidence interval. The CI=AGRESTICOULL option is a generalization of the "Adjusted Wald / add 2 successes and 2 failures" interval of Agresti and Coull (1998) and is presented in Brown, Cai, and DasGupta (2001). It corresponds to the TABLES / BINOMIAL (AGRESTICOULL) option in PROC FREQ. The CI=JEFFREYS option specifies the equaltailed Jeffreys prior Bayesian interval, corresponding to the TABLES / BINOMIAL (JEFFREYS) option in PROC FREQ. The CI=EXACT option specifies the exact ClopperPearson confidence interval based on enumeration, corresponding to the TABLES / BINOMIAL (EXACT) option in PROC FREQ. The CI=WALD option specifies the confidence interval based on the Wald test (also commonly called the test or normalapproximation test), corresponding to the TABLES / BINOMIAL (WALD) option in PROC FREQ. The CI=WALD_CORRECT option specifies the confidence interval based on the Wald test with continuity correction, corresponding to the TABLES / BINOMIAL (CORRECT WALD) option in PROC FREQ. The CI=WILSON option (the default) specifies the confidence interval based on the score statistic, corresponding to the TABLES / BINOMIAL (WILSON) option in PROC FREQ.
Instead of power, the relevant probability for this analysis is the probability of achieving a desired precision. Specifically, it is the probability that the halfwidth of the confidence interval will be at most the value specified by the HALFWIDTH= option.
specifies the lower and upper equivalence bounds, representing the same information as the combination of the LOWER= and UPPER= options but grouping them together. The EQUIVBOUNDS= option can be used only with equivalence analyses (TEST=EQUIV_ADJZ  EQUIV_EXACT  EQUIV_Z). Values must be strictly between 0 and 1. See the section Specifying Value Lists in Analysis Statements for information about specifying the groupednumberlist.
specifies the desired confidence interval halfwidth. The halfwidth for a twosided interval is the length of the confidence interval divided by two. This option can be used only with the CI= analysis. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the lower equivalence bound for the binomial proportion. The LOWER= option can be used only with equivalence analyses (TEST=EQUIV_ADJZ  EQUIV_EXACT  EQUIV_Z). Values must be strictly between 0 and 1. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the equivalence or noninferiority or superiority margin, depending on the analysis.
The MARGIN= option can be used with onesided analyses (SIDES = 1  U  L), in which case it specifies the margin added to the null proportion value in the hypothesis test, resulting in a noninferiority or superiority test (depending on the agreement between the effect and hypothesis directions and the sign of the margin). A test with a null proportion and a margin is the same as a test with null proportion and no margin.
The MARGIN= option can also be used with equivalence analyses (TEST=EQUIV_ADJZ  EQUIV_EXACT  EQUIV_Z) when the NULLPROPORTION= option is used, in which case it specifies the lower and upper equivalence bounds as and , where is the value of the NULLPROPORTION= option and is the value of the MARGIN= option.
The MARGIN= option cannot be used in conjunction with the SIDES=2 option. (Instead, specify an equivalence analysis by using TEST=EQUIV_ADJZ or TEST=EQUIV_EXACT or TEST=EQUIV_Z). Also, the MARGIN= option cannot be used with the CI= option.
Values must be strictly between –1 and 1. In addition, the sum of NULLPROPORTION and MARGIN must be strictly between 0 and 1 for onesided analyses, and the derived lower equivalence bound (2 * NULLPROPORTION – MARGIN) must be strictly between 0 and 1 for equivalence analyses.
See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the computational method. METHOD=EXACT (the default) computes exact results by using the binomial distribution. METHOD=NORMAL computes approximate results by using the normal approximation to the binomial distribution.
enables fractional input and output for sample sizes. This option is invalid when the METHOD=EXACT option is specified. See the section Sample Size Adjustment Options for information about the ramifications of the presence (and absence) of the NFRACTIONAL option.
specifies the sample size or requests a solution for the sample size with a missing value (NTOTAL=.). See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the null proportion. A value of 0.5 corresponds to the sign test. 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:
The OUTPUTORDER=SYNTAX option arranges the parameters in the output in the same order in which their corresponding options are specified in the ONESAMPLEFREQ 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 ONESAMPLEFREQ statement.
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 desired probability of obtaining a confidence interval halfwidth less than or equal to the value specified by the HALFWIDTH= option. A missing value (PROBWIDTH=.) requests a solution for this probability. Values are expressed as probabilities (for example, 0.9) rather than percentages. This option can be used only with the CI= analysis. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies the binomial proportion—that is, the expected proportion of successes in the hypothetical binomial trial. 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. See the section Specifying Value Lists in Analysis Statements for information about specifying the keywordlist. Valid keywords 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 statistical analysis. TEST=ADJZ specifies a normalapproximate z test with continuity adjustment. TEST=EQUIV_ADJZ specifies a normalapproximate twosided equivalence test based on the statistic with continuity adjustment and a TOST (two onesided tests) procedure. TEST=EQUIV_EXACT specifies the exact binomial twosided equivalence test based on a TOST (two onesided tests) procedure. TEST=EQUIV_Z specifies a normalapproximate twosided equivalence test based on the statistic without any continuity adjustment, which is the same as the chisquare statistic, and a TOST (two onesided tests) procedure. TEST or TEST=EXACT (the default) specifies the exact binomial test. TEST=Z specifies a normalapproximate z test without any continuity adjustment, which is the same as the chisquare test when SIDES=2.
specifies the upper equivalence bound for the binomial proportion. The UPPER= option can be used only with equivalence analyses (TEST=EQUIV_ADJZ  EQUIV_EXACT  EQUIV_Z). Values must be strictly between 0 and 1. See the section Specifying Value Lists in Analysis Statements for information about specifying the numberlist.
specifies how the variance is computed in the test statistic for the TEST=Z, TEST=ADJZ, TEST=EQUIV_Z, and TEST=EQUIV_ADJZ analyses. See the section Specifying Value Lists in Analysis Statements for information about specifying the keywordlist. Valid keywords are as follows:
(the default) estimates the variance by using the null proportion(s) (specified by some combination of the NULLPROPORTION=, MARGIN=, LOWER=, and UPPER= options). For TEST=Z and TEST=ADJZ, the null proportion is the value of the NULLPROPORTION= option plus the value of the MARGIN= option (if it is used). For TEST=EQUIV_Z and TEST=EQUIV_ADJZ, there are two null proportions, corresponding to the lower and upper equivalence bounds, one for each test in the TOST (two onesided tests) procedure.
estimates the variance by using the observed sample proportion.
This option is ignored if the analysis is one other than TEST=Z, TEST=ADJZ, TEST=EQUIV_Z, or TEST=EQUIV_ADJZ.
This section summarizes the syntax for the common analyses supported in the ONESAMPLEFREQ statement.
The following statements demonstrate a power computation for the exact test of a binomial proportion. Defaults for the SIDES= and ALPHA= options specify a twosided test with a 0.05 significance level.
proc power; onesamplefreq test=exact nullproportion = 0.2 proportion = 0.3 ntotal = 100 power = .; run;
The following statements demonstrate a sample size computation for the z test of a binomial proportion. Defaults for the SIDES=, ALPHA=, and VAREST= options specify a twosided test with a 0.05 significance level that uses the null variance estimate.
proc power; onesamplefreq test=z method=normal nullproportion = 0.8 proportion = 0.85 sides = u ntotal = . power = .9; run;
The following statements demonstrate a sample size computation for the z test of a binomial proportion with a continuity adjustment. Defaults for the SIDES=, ALPHA=, and VAREST= options specify a twosided test with a 0.05 significance level that uses the null variance estimate.
proc power; onesamplefreq test=adjz method=normal nullproportion = 0.15 proportion = 0.1 sides = l ntotal = . power = .9; run;
You can specify equivalence bounds by using the EQUIVBOUNDS= option, as in the following statements:
proc power; onesamplefreq test=equiv_exact proportion = 0.35 equivbounds = (0.2 0.4) ntotal = 50 power = .; run;
You can also specify the combination of NULLPROPORTION= and MARGIN= options:
proc power; onesamplefreq test=equiv_exact proportion = 0.35 nullproportion = 0.3 margin = 0.1 ntotal = 50 power = .; run;
Finally, you can specify the combination of LOWER= and UPPER= options:
proc power; onesamplefreq test=equiv_exact proportion = 0.35 lower = 0.2 upper = 0.4 ntotal = 50 power = .; run;
Note that the three preceding analyses are identical.
A noninferiority test corresponds to an upper onesided test with a negativevalued margin, as demonstrated in the following statements:
proc power; onesamplefreq test=exact sides = U proportion = 0.15 nullproportion = 0.1 margin = 0.02 ntotal = 130 power = .; run;
A superiority test corresponds to an upper onesided test with a positivevalued margin, as demonstrated in the following statements:
proc power; onesamplefreq test=exact sides = U proportion = 0.15 nullproportion = 0.1 margin = 0.02 ntotal = 130 power = .; run;
The following statements performs a confidence interval precision analysis for the Wilson scorebased confidence interval for a binomial proportion. The default value of the ALPHA= option specifies a confidence level of 0.95.
proc power; onesamplefreq ci=wilson halfwidth = 0.1 proportion = 0.3 ntotal = 70 probwidth = .; run;
To specify the equivalence bounds for TEST=EQUIV_ADJZ, TEST=EQUIV_EXACT, and TEST=EQUIV_Z, use any of these three option sets:
lower and upper equivalence bounds, using the EQUIVBOUNDS= option
lower and upper equivalence bounds, using the LOWER= and UPPER= options
null proportion (NULLPROPORTION=) and margin (MARGIN=)
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