How to do Chi square with contingency tables?

Hello,

I have 2 questions regarding doing chi square test in matlab.

1) I have a traditional 2x2 contingency table with rows = disease, no disease; columns = experimental condition, control condition.

How do I run a chi square on this? I read the crosstab function but didn't quite understand it.

2) I have nx2 contingency tables where columns are still experimental vs control condition. The rows are now a list of ethnicities. I would like to know if ethnicity distribution differed between the 2 conditions. How would I go about this?

Many thanks!

Answer 1

[Neuropragmatist]

Crosstabs expects the raw data as vectors, if you only have counts you will need to expand your data into vectors, for instance X would equal 1 for disease and 2 for no disease and Y would equal 1 for experimental condition and 2 for control condition.

If you just have the counts or don't want the hassle of expanding your data to vectors you could look at using a Fisher's exact test instead:

https://uk.mathworks.com/help/stats/fishertest.html

x = table([1;2],[3;4],'VariableNames',{'Experimental','Control'},'RowNames',{'Disease','NoDisease'})

[h,p,stats] = fishertest(x)

I tend to use Fischer's test instead because it is more relaible with small sample sizes.

Alternatively you could look at some files on the file exchange like this one:

https://uk.mathworks.com/matlabcentral/fileexchange/18705-chi-square-test-contingency-tables

Or if I just want a one off calculation I will often use online contingency table calculators instead (not Matlab?! the shock, the horror!):

https://www.graphpad.com/quickcalcs/contingency1/

Hope this helps.

[Danning Zhang]

Oh Thank you! And what about when I have a 3x2 table, will that work too?

[Neuropragmatist]

The Fischer's test only works on 2x2 tables as far as I know, but you can still use crosstabs for larger tables and it can calculate a chi-square statistic and p-value for you.

If you only have the cross-tabulation (i.e. a table or spreasheet with counts instead of actual data vectors) you will need to convert it back into data vectors for crosstabs to work; you can see this post here for further info on that route:

https://uk.mathworks.com/matlabcentral/answers/96572-how-can-i-perform-a-chi-square-test-to-determine-how-statistically-different-two-proportions-are-in

[Danning Zhang]

Oh I see, thank you!!