The use of a control involves the Spss > Analyze > Descriptive Stats > CrossTabs

after choosing your row and col variables, then consider what control variable to put in

the "Layers" window. 

When you get your tables (with Statistics=Chi-Sq and Tau-b and with Cells=add row %s)
you will see each row by column table is repeated for different values of the control
(layer) variable. So are the statistics.

This allows you to check whether
(1) the row-col correlations replication for different categories of the control

or

(2) the values control variable makes a difference to the row-col correlations