The POWER Procedure

Common Notation

Table 70.29 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 70.29 Common Notation
Symbol	Description	Associated Syntax
$\text{[math]}$	Significance level	ALPHA=
$\text{[math]}$	Total sample size	NTOTAL=, NPAIRS=
$\text{[math]}$	Sample size in $\text{[math]}$ th group	NPERGROUP=, GROUPNS=
$\text{[math]}$	Allocation weight for $\text{[math]}$ th group (standardized to sum to 1)	GROUPWEIGHTS=
$\text{[math]}$	(Arithmetic) mean	MEAN=
$\text{[math]}$	(Arithmetic) mean in $\text{[math]}$ th group	GROUPMEANS=, PAIREDMEANS=
$\text{[math]}$	(Arithmetic) mean difference, $\text{[math]}$ or $\text{[math]}$	MEANDIFF=
$\text{[math]}$	Null mean or mean difference (arithmetic)	NULL=, NULLDIFF=
$\text{[math]}$	Geometric mean	MEAN=
$\text{[math]}$	Geometric mean in $\text{[math]}$ th group	GROUPMEANS=, PAIREDMEANS=
$\text{[math]}$	Null mean or mean ratio (geometric)	NULL=, NULLRATIO=
$\text{[math]}$	Standard deviation (or common standard deviation per group)	STDDEV=
$\text{[math]}$	Standard deviation in $\text{[math]}$ th group	GROUPSTDDEVS=, PAIREDSTDDEVS=
$\text{[math]}$	Standard deviation of differences
$\text{[math]}$	Coefficient of variation, defined as the ratio of the standard deviation to the (arithmetic) mean	CV=, PAIREDCVS=
$\text{[math]}$	Correlation	CORR=
$\text{[math]}$	Treatment and reference (arithmetic) means for equivalence test	GROUPMEANS=, PAIREDMEANS=
$\text{[math]}$	Treatment and reference geometric means for equivalence test	GROUPMEANS=, PAIREDMEANS=
$\text{[math]}$	Lower equivalence bound	LOWER=
$\text{[math]}$	Upper equivalence bound	UPPER=
$\text{[math]}$	$\text{[math]}$ distribution with d.f. $\text{[math]}$ and noncentrality $\text{[math]}$
$\text{[math]}$	$\text{[math]}$ distribution with numerator d.f. $\text{[math]}$ , denominator d.f. $\text{[math]}$ , and noncentrality $\text{[math]}$
$\text{[math]}$	$\text{[math]}$ th percentile of $\text{[math]}$ distribution with d.f. $\text{[math]}$
$\text{[math]}$	$\text{[math]}$ th percentile of $\text{[math]}$ distribution with numerator d.f. $\text{[math]}$ and denominator d.f. $\text{[math]}$
$\text{[math]}$	Binomial distribution with sample size $\text{[math]}$ and proportion $\text{[math]}$

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 $\text{[math]}$ , that is convenient for representing terms in power formulas for confidence intervals and equivalence tests:

$\text{[math]}$

where $\text{[math]}$ and $\text{[math]}$ are the density and cumulative distribution function of the standard normal distribution, respectively.