Multinomial chi square with small expected values

I'm studying extinction in Austronesian languages, and am trying to find out if a subset of 384 languages is randomly selected with respect to extinction risk from a population of 1249 languages. "Extinction risk" can take 10 different values. But the first two expected values are very small (both 0.40) and make up most of the chi-square:

   Observed | 10   | 6    |  6   | 22    | 113   |  64    | 70    | 20    | 5     | 19
Expected | 0.40 | 0.40 | 5.63 | 10.86 | 59.54 | 129.54 | 90.11 | 25.74 | 12.07 | 13.68
Chi square  | 229.0| 77.9 | 0.0  | 11.4  | 48.0  |  33.1  |  4.5  |  1.3  |  4.1  |  2.1
contribution
----------- | --------------------------------------------------------------------------
Chi square:  411.44

Critical value (alpha = 0.01): 21.67 with 9 degrees of freedom


I've heard that it is best if the expected values stay above 5 (and that one might consider Yates's correction if they aren't). What correction would you suggest?

1 Answer

First, can you show your code? Something is wrong. You should be running a two way chi-square with 10 levels of extinction and 2 groups, so getting 9 degrees of freedom, not 344.

However, instead of chi-square at all, since "level of extinction" is presumably ordinal, I would run an ordinal logistic regression with "level of extinction" as the dependent variable and "group" as an independent variable. You might also want additional independent variables. (Group would be whether the language is part of the 384 or not)

• You're right, I fixed the degrees of freedom. I'll look into ordinal logistic regression. May 25, 2014 at 13:44