# The POWER Procedure

#### Common Notation

Table 77.29 displays notation for some of the more common parameters across analyses. The Associated Syntax column shows examples of relevant analysis statement options, where applicable.

Table 77.29: Common Notation

Symbol

Description

Associated Syntax

Significance level

ALPHA=

N

Total sample size

NTOTAL=, NPAIRS=

Sample size in ith group

NPERGROUP=, GROUPNS=

Allocation weight for ith group (standardized to sum to 1)

GROUPWEIGHTS=

(Arithmetic) mean

MEAN=

(Arithmetic) mean in ith group

GROUPMEANS=, PAIREDMEANS=

(Arithmetic) mean difference, or

MEANDIFF=

Null mean or mean difference (arithmetic)

NULL=, NULLDIFF=

Geometric mean

MEAN=

Geometric mean in ith group

GROUPMEANS=, PAIREDMEANS=

Null mean or mean ratio (geometric)

NULL=, NULLRATIO=

Standard deviation (or common standard deviation per group)

STDDEV=

Standard deviation in ith group

GROUPSTDDEVS=, PAIREDSTDDEVS=

Standard deviation of differences

CV

Coefficient of variation, defined as the ratio of the standard deviation to the (arithmetic) mean on the original data scale

CV=, PAIREDCVS=

Correlation

CORR=

Treatment and reference (arithmetic) means for equivalence test

GROUPMEANS=, PAIREDMEANS=

Treatment and reference geometric means for equivalence test

GROUPMEANS=, PAIREDMEANS=

Lower equivalence bound

LOWER=

Upper equivalence bound

UPPER=

t distribution with df and noncentrality

F distribution with numerator df , denominator df , and noncentrality

pth percentile of t distribution with df

pth percentile of F distribution with numerator df and denominator df

Binomial distribution with sample size N and proportion p

A "lower one-sided" test is associated with SIDES=L (or SIDES=1 with the effect smaller than the null value), and an "upper one-sided" test is associated with SIDES=U (or SIDES=1 with the effect larger than the null value).

Owen (1965) defines a function, known as Owen’s Q, that is convenient for representing terms in power formulas for confidence intervals and equivalence tests:

where and are the density and cumulative distribution function of the standard normal distribution, respectively.