#### Contrasts

For a testable hypothesis , the Wald F statistic is computed as

where is a contrast vector or matrix that you specify, is the vector of regression parameters, is the estimated regression coefficients, 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 by 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 a given set of linear contrasts, in which case the contrasts are not testable.

If the DF=NONE option in the MODEL statement is specified, then the procedure performs a chi-square significance test.