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.