The SURVEYFREQ Procedure
Wald Log-Linear Chi-Square Test
If you specify the WLLCHISQ option in the TABLES statement, PROC SURVEYFREQ computes a Wald test for independence based on the log odds ratios. See the section Wald Chi-Square Test for more information about Wald tests.
For a two-way table of 
rows and 
columns, the Wald log-linear test is based on the 
array of elements 
,
 |
where 
is the estimated total for table cell 
. The null hypothesis of independence between the row and column variables can be expressed as 
for all 
and 
. This null hypothesis can be stated equivalently in terms of cell proportions.
The generalized Wald log-linear chi-square statistic is computed as
 |
where 
is the 
array of the , and 
estimates the variance of ,
 |
where 
is the covariance matrix of the estimates , which is computed as described in the section Covariance of Totals. 
is a diagonal matrix with the estimated totals on the diagonal, and 
is the by 
linear contrast matrix.
Under the null hypothesis of independence, the statistic 
approximately follows a chi-square distribution with degrees of freedom for large samples.
PROC SURVEYFREQ computes the Wald log-linear 
statistic as
 |
Under the null hypothesis of independence, 
approximately follows an distribution with numerator degrees of freedom. PROC SURVEYFREQ computes the denominator degrees of freedom as described in the section Degrees of Freedom. Alternatively, you can specify the denominator degrees of freedom with the DF= option in the TABLES statement.
For tables larger than 
, PROC SURVEYFREQ also computes the adjusted Wald log-linear statistic as
 |
where 
, and 
is the denominator degrees of freedom computed as described in the section Degrees of Freedom. Alternatively, you can specify the value of with the DF= option in the TABLES statement. Note that for tables, 
, so the adjusted Wald statistic equals the (unadjusted) Wald statistic, with the same numerator and denominator degrees of freedom.
Under the null hypothesis, 
approximately follows an distribution with 
numerator degrees of freedom and 
denominator degrees of freedom.