What does only one significant standardised residual mean in 2x3 Chi Squared tables?

#1
Hi everyone. I'm writing up a report for my advisor, which compares count data for three conditions, across two different groups. I therefore have a 2x3 contingency table I've analysed with Chi Squared, and am using standardised residuals as a post-hoc test. However, my advisor and are interpreting our results differently.

In previous analyses, we've found that there's normally one high and one low residual (e.g. 2.4, -2.8), indicating that obviously, the first is higher than the latter. However, for the most recent analysis, we just have one that is significant - condition 1 has a significant residual indicating it's lower than the expected values, whereas the other two conditions are not over 2 and are therefore non-significant.

My interpretation of this is that I can only really say (based on this analysis) that the outcome measure for condition 1 was significantly lower than would be the case if there were no association between the variables. However, my advisor is suggesting that if the outcome measure is lower for condition 1, I should also be able to say that conditions 2 and 3 are significantly higher than condition 1. This feels like it's going beyond what the analysis are able to say.

Is anyone able to help with this at all? Thanks in advance!
 

gianmarco

TS Contributor
#2
Re: What does only one significant standardised residual mean in 2x3 Chi Squared tabl

However, my advisor is suggesting that if the outcome measure is lower for condition 1, I should also be able to say that conditions 2 and 3 are significantly higher than condition 1. This feels like it's going beyond what the analysis are able to say.
Is anyone able to help with this at all? Thanks in advance!
I would agree with you. In my opinion, one should just stick with the 'purpose' of the residuals, that is gauging how much the observed frequencies differ from the expected ones under the hypothesis of independence.
If just one cell has aalarge stnd residual, that means (as you know) that that particular cell significantly deviates from the expected frequency, and that that particular cell is actually contributing to the rejection of the Null Hyphotesis. In this situation, since the other cells have frequencies that do not significantly differ from the expected ones, they are more or less similar to the expected frequencies. I do not believe that the 'significance' of that one cell can be indirectly extended (by contrast or by comparison) to the other (non significant) cells. I hope the latter point (expressed in bad English) will prove understandable :)

That said, I would add a couple of things:
-as for stnd residual, remember that +-1.96 is the threshold for a significance at alpha 0.05. I stress this since it is not clear to me from your post what the other residuals of your table look like. So, bear in mind the 1.96 threshold when seeking to locate significant residuals. By the way, I put togheter an R function to do a couple of nice things related to chi-square test in R (http://cainarchaeology.weebly.com/r...on-based-chi-square-test-of-independence.html).

-I know that contraddicting a supervisor\advisor is not easy. I would strongly base my point(s) on literature, hoping that (s)he would not get upset.

Hope this helps
Gm
 

hlsmith

Less is more. Stay pure. Stay poor.
#3
Re: What does only one significant standardised residual mean in 2x3 Chi Squared tabl

Too many words...


Well if you think the two groups have distributions for the 3 categories, 1 can be significant meaning is much bigger or smaller than expected. Well that traditionally means that the difference in expectation then have to be some where. It must be near evenly distributed into the other groups, which means they themselves did not change enough to make their expectancies significant.


Ex.


males females and insurance status (group 1,2,3):


25% 15%
25% 15%
50% 70%


compared to:
25% 25%
25% 5%
50% 70%


Fex1. just 3rd group differs, ex2. 2nd and 3rd diff. I think this is the gist of your question. Sorry post sloppy, I am too tired to try harder :)