The SURVEYREG Procedure

Contrasts

You can use the CONTRAST statement to perform custom hypothesis tests. If the hypothesis is testable in the univariate case, the Wald F statistic for $\text{[math]}$ is computed as

$\text{[math]}$

where $\text{[math]}$ is the contrast vector or matrix you specify, $\text{[math]}$ is the vector of regression parameters, $\text{[math]}$ , $\text{[math]}$ is the estimated covariance matrix of $\text{[math]}$ , rank( $\text{[math]}$ ) is the rank of $\text{[math]}$ , and $\text{[math]}$ is a matrix such that

$\text{[math]}$ has the same number of columns as $\text{[math]}$
$\text{[math]}$ has full row rank
the rank of $\text{[math]}$ equals the rank of the $\text{[math]}$ matrix
all rows of $\text{[math]}$ are estimable functions
the Wald F statistic computed using the $\text{[math]}$ matrix is equivalent to the Wald F statistic computed by using the $\text{[math]}$ matrix with any row deleted that is a linear combination of previous rows

If $\text{[math]}$ is a full-rank matrix and all rows of $\text{[math]}$ are estimable functions, then $\text{[math]}$ is the same as $\text{[math]}$ . It is possible that $\text{[math]}$ matrix cannot be constructed for contrasts in a CONTRAST statement, in which case the contrasts are not testable.