The POWER Procedure

ONESAMPLEMEANS Statement

Summary of Options
Dictionary of Options
Restrictions on Option Combinations
Option Groups for Common Analyses

ONESAMPLEMEANS <options> ;

The ONESAMPLEMEANS statement performs power and sample size analyses for t tests, equivalence tests, and confidence interval precision involving one sample.

Summary of Options

Table 71.10 summarizes the options available in the ONESAMPLEMEANS statement.

Table 71.10: ONESAMPLEMEANS Statement Options

Option	Description
Define analysis
CI=	Specifies an analysis of precision of the confidence interval for the mean
DIST=	Specifies the underlying distribution assumed for the test statistic
TEST=	Specifies the statistical analysis
Specify analysis information
ALPHA=	Specifies the significance level
LOWER=	Specifies the lower equivalence bound for the mean
NULLMEAN=	Specifies the null mean
SIDES=	Specifies the number of sides and the direction of the statistical test
UPPER=	Specifies the upper equivalence bound for the mean
Specify effect
HALFWIDTH=	Specifies the desired confidence interval half-width
MEAN=	Specifies the mean
Specify variability
CV=	Specifies the coefficient of variation
STDDEV=	Specifies the standard deviation
Specify sample size
NFRACTIONAL	Enables fractional input and output for sample sizes
NTOTAL=	Specifies the sample size
Specify power and related probabilities
POWER=	Specifies the desired power of the test
PROBTYPE=	Specifies the type of probability for the PROBWIDTH= option
PROBWIDTH=	Specifies the probability of obtaining a confidence interval half-width less than or equal to the value specified by HALFWIDTH=
Control ordering in output
OUTPUTORDER=	Controls the output order of parameters

Table 71.11 summarizes the valid result parameters for different analyses in the ONESAMPLEMEANS statement.

Table 71.11: Summary of Result Parameters in the ONESAMPLEMEANS Statement

Analyses	Solve For	Syntax
TEST=T DIST=NORMAL	Power	POWER=.
	Sample size	NTOTAL=.
	Alpha	ALPHA=.
	Mean	MEAN=.
	Standard Deviation	STDDEV=.
TEST=T DIST=LOGNORMAL	Power	POWER=.
	Sample size	NTOTAL=.
TEST=EQUIV	Power	POWER=.
	Sample size	NTOTAL=.
CI=T	Prob(width)	PROBWIDTH=.
	Sample size	NTOTAL=.

Dictionary of Options

ALPHA=number-list

specifies the level of significance of the statistical test or requests a solution for alpha with a missing value (ALPHA=.). The default is 0.05, corresponding to the usual 0.05 $\times$ 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 number-list.

CI CI=T

specifies an analysis of precision of the confidence interval for the mean. Instead of power, the relevant probability for this analysis is the probability of achieving a desired precision. Specifically, it is the probability that the half-width of the confidence interval will be at most the value specified by the HALFWIDTH= option. If neither the CI= option nor the TEST= option is used, the default is TEST=T.

CV=number-list

specifies the coefficient of variation, defined as the ratio of the standard deviation to the mean. You can use this option only with DIST=LOGNORMAL. See the section Specifying Value Lists in Analysis Statements for information about specifying the number-list.

DIST=LOGNORMAL DIST=NORMAL

specifies the underlying distribution assumed for the test statistic. NORMAL corresponds the normal distribution, and LOGNORMAL corresponds to the lognormal distribution. The default value is NORMAL.

HALFWIDTH=number-list

specifies the desired confidence interval half-width. The half-width is defined as the distance between the point estimate and a finite endpoint. This option can be used only with the CI=T analysis. See the section Specifying Value Lists in Analysis Statements for information about specifying the number-list.

LOWER=number-list

specifies the lower equivalence bound for the mean. This option can be used only with the TEST=EQUIV analysis. See the section Specifying Value Lists in Analysis Statements for information about specifying the number-list.

MEAN=number-list

specifies the mean, in the original scale, or requests a solution for the mean with a missing value (MEAN=.). The mean is arithmetic if DIST=NORMAL and geometric if DIST=LOGNORMAL. This option can be used only with the TEST=T and TEST=EQUIV analyses. See the section Specifying Value Lists in Analysis Statements for information about specifying the number-list.

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.

NTOTAL=number-list

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 number-list.

NULLMEAN=number-list NULLM=number-list

specifies the null mean, in the original scale (whether DIST=NORMAL or DIST=LOGNORMAL). The default value is 0 when DIST=NORMAL and 1 when DIST=LOGNORMAL. This option can be used only with the TEST=T analysis. See the section Specifying Value Lists in Analysis Statements for information about specifying the number-list.

OUTPUTORDER=INTERNAL OUTPUTORDER=REVERSE OUTPUTORDER=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:

The OUTPUTORDER=SYNTAX option arranges the parameters in the output in the same order in which their corresponding options are specified in the ONESAMPLEMEANS 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 ONESAMPLEMEANS statement.

POWER=number-list

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. This option can be used only with the TEST=T and TEST=EQUIV analyses. See the section Specifying Value Lists in Analysis Statements for information about specifying the number-list.

PROBTYPE=keyword-list

specifies the type of probability for the PROBWIDTH= option. A value of CONDITIONAL (the default) indicates the conditional probability that the confidence interval half-width is at most the value specified by the HALFWIDTH= option, given that the true mean is captured by the confidence interval. A value of UNCONDITIONAL indicates the unconditional probability that the confidence interval half-width is at most the value specified by the HALFWIDTH= option. You can use the alias GIVENVALIDITY for CONDITIONAL. The PROBTYPE= option can be used only with the CI=T analysis. See the section Specifying Value Lists in Analysis Statements for information about specifying the keyword-list.

CONDITIONAL: width probability conditional on interval containing the mean
UNCONDITIONAL: unconditional width probability

PROBWIDTH=number-list

specifies the desired probability of obtaining a confidence interval half-width less than or equal to the value specified by the HALFWIDTH= option. A missing value (PROBWIDTH=.) requests a solution for this probability. The type of probability is controlled with the PROBTYPE= option. Values are expressed as probabilities (for example, 0.9) rather than percentages. This option can be used only with the CI=T analysis. See the section Specifying Value Lists in Analysis Statements for information about specifying the number-list.

SIDES=keyword-list

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 keyword-list. Valid keywords and their interpretation for the TEST= analyses are as follows:

1: one-sided with alternative hypothesis in same direction as effect
2: two-sided
U: upper one-sided with alternative greater than null value
L: lower one-sided with alternative less than null value

For confidence intervals, SIDES=U refers to an interval between the lower confidence limit and infinity, and SIDES=L refers to an interval between minus infinity and the upper confidence limit. For both of these cases and SIDES=1, the confidence interval computations are equivalent. The SIDES= option can be used only with the TEST=T and CI=T analyses. The default value is 2.

STDDEV=number-list STD=number-list

specifies the standard deviation, or requests a solution for the standard deviation with a missing value (STDDEV=.). You can use this option only with DIST=NORMAL. See the section Specifying Value Lists in Analysis Statements for information about specifying the number-list.

TEST TEST=EQUIV TEST=T

specifies the statistical analysis. TEST=EQUIV specifies an equivalence test of the mean by using a two one-sided tests (TOST) analysis (Schuirmann, 1987). TEST or TEST=T (the default) specifies a t test on the mean. If neither the TEST= option nor the CI= option is used, the default is TEST=T.

UPPER=number-list

specifies the upper equivalence bound for the mean, in the original scale (whether DIST=NORMAL or DIST=LOGNORMAL). This option can be used only with the TEST=EQUIV analysis. See the section Specifying Value Lists in Analysis Statements for information about specifying the number-list.

Restrictions on Option Combinations

To define the analysis, choose one of the following parameterizations:

a statistical test (by using the TEST= option)
confidence interval precision (by using the CI= option)

Option Groups for Common Analyses

This section summarizes the syntax for the common analyses supported in the ONESAMPLEMEANS statement.

One-Sample t Test

The following statements demonstrate a power computation for the one-sample t test. Default values for the DIST=, SIDES=, NULLMEAN=, and ALPHA= options specify a two-sided test for zero mean with a normal distribution and a significance level of 0.05.

proc power;
   onesamplemeans test=t
      mean = 7
      stddev = 3
      ntotal = 50
      power = .;
run;

One-Sample t Test with Lognormal Data

The following statements demonstrate a sample size computation for the one-sample t test for lognormal data. Default values for the SIDES=, NULLMEAN=, and ALPHA= options specify a two-sided test for unit mean with a significance level of 0.05.

proc power;
   onesamplemeans test=t dist=lognormal
      mean = 7
      cv = 0.8
      ntotal = .
      power = 0.9;
run;

Equivalence Test for Mean of Normal Data

The following statements demonstrate a power computation for the TOST equivalence test for a normal mean. Default values for the DIST= and ALPHA= options specify a normal distribution and a significance level of 0.05.

proc power;
   onesamplemeans test=equiv
      lower = 2
      upper = 7
      mean = 4
      stddev = 3
      ntotal = 100
      power = .;
run;

Equivalence Test for Mean of Lognormal Data

The following statements demonstrate a sample size computation for the TOST equivalence test for a lognormal mean. The default of ALPHA=0.05 specifies a significance level of 0.05.

proc power;
   onesamplemeans test=equiv dist=lognormal
      lower = 1
      upper = 5
      mean = 3
      cv = 0.6
      ntotal = .
      power = 0.85;
run;

Confidence Interval for Mean

By default CI=T analyzes the conditional probability of obtaining the desired precision, given that the interval contains the true mean, as in the following statements. The defaults of SIDES=2 and ALPHA=0.05 specify a two-sided interval with a confidence level of 0.95.

proc power;
   onesamplemeans ci = t
      halfwidth = 14
      stddev = 8
      ntotal = 50
      probwidth = .;
run;