I have a sample with 181 observations. I measured two nominal variables for each observation and now want to calculate the association between the two variables. The problem is that one variable has 15 possible values, the other one 16. So when I tried to compute Cramér's V, R complained that "Chi-squared approximation may be incorrect", which the Internet tells me comes from many cells in the contingency table having too few observations in them.
Is there any way to correct for this?
The two ways I can think of won't work:
- Increase the sample. I don't have access to more observable items. With lots of effort, I may get 20 more or so, but nowhere near enough for 5 values per table cell.
- Combine variable similar variable values into categories. My variables are truly nominal, with no real similarity between the values. I can't think of any combination which will make sense.
Is there some possible treatment of the data which will reduce the error of calculating chi squared? Is there an association measure other than Cramér's V which is better suited to small sample sizes (or large variable domains)? Is there anything else I can do?
If I cannot correct, what are the implications for my analysis?
If there is nothing I can do to correct this, what will happen if I do the analysis anyway? Will the results be considered so bad as to be unusable? Will I be able to use the results, but keep in mind that they may be a bit off? If they are a bit off, how are they off? Is the resulting Cramér's V likely to be too high, or too low, or is there no way to tell?