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 is computed as


where is the contrast vector or matrix you specify, is the vector of regression parameters, , is the estimated covariance matrix of , rank() is the rank of , and is a matrix such that

  • has the same number of columns as

  • has full row rank

  • the rank of equals the rank of the matrix

  • all rows of are estimable functions

  • the Wald F statistic computed using the matrix is equivalent to the Wald F statistic computed by using the matrix with any row deleted that is a linear combination of previous rows

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