Chi-square-Tests: adjusted residuals vs. standardized residuals

[Laura Bartz]

Dear Statalisters,

I performed a Chi-square test (see code below), which was not significant with my data. Here, I used the titanic-example-data.

tab class survived, cell expected V chi2

Still, I wanted to investigate the direction of the effects (Cramers V) I calculted. I used the tabchi-command and got the adjusted residuals.

tabchi class survived, a

My textbook says that I should rather use standardized residuals, which are calculated differently and seem to be reported automatically by SPSS, but not by Stata.
So my questions are:
1. Which resudial should I use and why is one superior to the other?
2. If I wanted to calculate standardized residuals, how can that be done in Stata without doing it by hand?

Thank you!

[Nick Cox]

tabchi is a community-contributed command -- in this case from tab_chi (SSC) -- as you are asked to explain.

What is your definition of "standardized"? it's a term that is less, hmm, standardized than you might hope or expect. The simplest standardization I know would be (observed - expected) / root of expected and this is often called the Pearson residual, not that Pearson ever used it as far a I know.

I can't comment on your unnamed textbook or on what SPSS chooses to show. If the choice is between following anonymous textbook authors or the author of tabchi, that's also hard for me to comment on.

If you get very different signals from different flavours of residuals (apart from raw residuals, observed - expected) then it's a probably a warning.

[Laura Bartz]

Dear Nick,
thank you for your reply!
My definition of "standardized residual" is the one you mentioned: (observed - expected) / root of expected). The author of my textbook "Deskriptive Statistik und explorative Datenanalyse" (Cleff, 2008) calls the Pearson residual standardized residual without mentioning the other term.
As far as I compared the adjusted and the standardized residuals, they pointed in the same direction.
Can I interpret the adjusted residuals like the standardized ones (positive value = empirical frequency of observed value is above average compared to expected frequency and the other way around (Cleff, 2008))

[Nick Cox]

Different flavours of residuals retain their sign so long as the divisor is positive. So yes is the answer to the last question.

As I said in #2 terminology here isn't uniform. The term "Pearson residual" is common in generalized linear model literature; it doesn't surprise me if people use other terms. Otherwise it's hard for me to remember my small choices when I wrote tabchi.

[Laura Bartz]

Okay, thanks a lot!