Wednesday, November 08, 2006

Chi-Square Null Hypotheses

I just got a colorful idea (to say the least) for how to illustrate the null hypothesis of a chi-square test. In the SPSS example we've been using, the principle behind Ho is that one group's (e.g., male) distribution into the different characteristics (marital statuses) will be equal to the other group's (female) distribution. The pie charts below serve as an illustration:

Again, the null hypothesis is that the male pie (and all its wedge sizes) will equal the female pie (and all its wedge sizes). A significant overall chi-square test tells us, of course, to reject Ho, which is to say, reject the notion of identical male and female pies.

A significant overall chi-square test can derive from any one category (wedge) or more being discrepant across males and females. That's where the standardized residuals for the cells can potentially be informative.