#### Common Notation

Table 71.29 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 71.29: 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

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.