The Wald test is used in logistic regression to test if explanatory variables should be included in a statistical model. For each explanatory variable, the Wald test determines if the associated parameter is significantly different from zero. If the Wald test is significant, the variable contributes to the model and should be included. An alternative is the likelihood ratio test, which some argue is better for small sample sizes or large parameters. The Wald statistic is equivalent to the t-statistic for a single explanatory variable model.

1. 774 H. Kyngas and M. Rissanen
È
INFORMATION POINT: The Wald test is a way of testing the signi®cance of particular explanatory
variables in a statistical model. In logistic regression we have a binary
Wald test outcome variable and one or more explanatory variables. For each
explanatory variable in the model there will be an associated parameter.
The Wald test, described by Polit (1996) and Agresti (1990), is one of a
number of ways of testing whether the parameters associated with a group of
explanatory variables are zero.
If for a particular explanatory variable, or group of explanatory variables,
the Wald test is signi®cant, then we would conclude that the parameters
associated with these variables are not zero, so that the variables should be
included in the model. If the Wald test is not signi®cant then these
explanatory variables can be omitted from the model. When considering a
single explanatory variable, Altman (1991) uses a t-test to check whether the
parameter is signi®cant. For a single parameter the Wald statistic is just the
square of the t-statistic and so will give exactly equivalent results.
An alternative and widely used approach to testing the signi®cance of a
number of explanatory variables is to use the likelihood ratio test. This is
appropriate for a variety of types of statistical models. Agresti (1990) argues
that the likelihood ratio test is better, particularly if the sample size is small or
the parameters are large.
Further reading
Agresti A. (1990) Categorical Data Analysis. John Wiley and Sons, New York.
Altman D.G. (1991) Practical Statistics for Medical Research. Chapman & Hall,
London.
Polit D. (1996) Data Analysis and Statistics for Nursing Research. Appleton & Lange,
Stamford, Connecticut.
NICOLA CRICHTON
Ó 2001 Blackwell Science Ltd, Journal of Clinical Nursing, 10, 767±774