# The POWER Procedure

#### Analyses in the LOGISTIC Statement

##### Likelihood Ratio Chi-Square Test for One Predictor (TEST=LRCHI)

The power-computing formula is based on Shieh and O’Brien (1998); Shieh (2000); Self, Mauritsen, and Ohara (1992), and Hsieh (1989).

Define the following notation for a logistic regression analysis:

The logistic regression model is

The hypothesis test of the first predictor variable is

Assuming independence among all predictor variables, is defined as follows:

where is calculated according to the following algorithm:

This algorithm causes the elements of the transposed vector to vary fastest to slowest from right to left as m increases, as shown in the following table of values:

The values are determined in a completely analogous manner.

The discretization is handled as follows (unless the distribution is ordinal, or binomial with sample size parameter at least as large as requested number of bins): for , generate quantiles at evenly spaced probability values such that each such quantile is at the midpoint of a bin with probability . In other words,

The primary noncentrality for the power computation is

where

where

The power is

The factor is the adjustment for correlation between the predictor that is being tested and other predictors, from Hsieh (1989).

Alternative input parameterizations are handled by the following transformations: