Pearson's Chi Square vs. Z contrast (r-alerting-CV & r-contrast-CV)

Hi one and all,

I have a relatively small set of data, from 15 participants. I have run them through P's Chi Square and now, for the sake of construct validity, I want to run them through Z contrast, as generally explained in "Quantifying Construct Validity: Two Simple Measures" by Westen and Rosenthal.
But I am not sure how to proceed and calculate the Z contrast, it eludes me.
I would highly appreciate it if you could clarify it to me.

I look forward to hearing from you.