1. ## Quick Chi-Square Question

Hi all,

I'm familiar with chi-square and have used it for a while at work. Just wondering something...

When calculating the Chi-Square for each cell of a Crosstab, is each cell's Chi-Square meaningful individually, or is it only useful when summed with all other cells?

Would I need to use a different df for a critical value if it is? Can I say, for instance, that one or two cells are statistically significant while others are not?

2. ## Re: Quick Chi-Square Question

Each cell doesn't have a chi square, but they do have a difference between expected and observed values. These are meaningful because they tell you where the departure from expected values are located.

3. ## Re: Quick Chi-Square Question

Hi!
As far as I know, to put in a nutshell, the chi-square statistics provide you with the overall picture of the "amount" of difference that exists between observed and expected frequencies.
The second step, is to evaluate how much this difference is significant. The latter is, quite obviuously, provided by the p value.

You are correct in wondering how pinpoint cells with significant amount of difference. For this very reason, you should inspect the table of standardized residuals that should be provided along with chi-square test's results.
From that table, you can see in what cell the observed frequency is significantly different from the expected one (greater or smaller). Generally, standardized residuals greater than 1.96 (in terms of absolute value) indicate that the frequency in that specific cell is significantly different from the expected frequency at alpha=0.05.

Hope this help,
Best Regards
Gm

4. ## Re: Quick Chi-Square Question

Thanks, GM. That was the response I was looking for. Not sure why but I had not been using the Standardized residuals function... SMRT!

5. ## Re: Quick Chi-Square Question

This is the queston I have, and I just found this thread. Surely chi-squared works on single counts, no? X2 is the sum of squared Zs where Zi = (observed-expected)/sqrt(expected) - is there a minimum number of Zs allowed?

Example: observed=120, expected=100 so Z=(120-100)/sqrt(100) = 2 so X2 = 2^2 = 4, and then P-value (df=1) < 0.05. Is this correct?

One thing I don't understand is that sample size doesn't come into the equation. Is there no difference between 120/150 vs. 100/150 and 120/5000 vs. 100/5000 ?

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