Computing the N-1 chi-square with SPSS

[Bruce Weaver]

In 2007, Ian Campbell published a nice simulation study in Statistics in Medicine demonstrating that the N-1 chi-square performs better than Pearson's chi-square (with or without Yates' correction) or the Fisher-Irwin test (aka Fisher's exact test) for 2x2 tables with low expected counts.  (The only exceptions are that the Fisher-Irwin test should be used if the row and column totals are truly fixed in advance, which is quite a rare situation with real data, or if any expected counts are < 1.)  See Campbell's website for more details.

My webpage on assumptions for chi-square tests used to have links to two SPSS syntax files I wrote for computing the N-1 chi-square.  But my colleague Sacha Dubois (aka Hawkeye) recently pointed out that for some data he was analyzing, the N-1 chi-square was equivalent to the Linear-by-Linear Association chi-square computed by the CROSSTABS procedure.  That prompted me to look at the algorithms, and it turned out Sacha was right:  For 2x2 tables, the Linear-by-Linear Association chi-square from CROSSTABS is equivalent to the N-1 chi-square--see this document for details.  

So when you want to report the N-1 chi-square for a 2x2 table, use the Linear-by-Linear Association result from CROSSTABS, but call it the N-1 chi-square.  This is much easier than using my now obsolete syntax files.

Cheers,
Bruce