I have one row of raw data 13, 0, 24, 26, 17 and 14. It is a larval survival rate / six treatments. Can I run chi-squared with zero inluded? I use R, and it looks like it works, but I am not sure whether it is OK. Or would it be better to do the survival rate in terms of mortality rates?
Also, is it possible to run an post hoc analysis pairwise comparison test to see individually the differences between the treatments?
Thank you in advance.
Yes. This should broadly be fine. The chi-square approximation is OK if the expected values of cells are not too low. A common guideline is 80% of the expected values greater than 5 or so. There are also simple corrections like the Egon Pearson corrected test that are supposed to work well down to expected values of 1 or so. The observed counts aren't the issue. Note however that low expected cells also indicate low statistical power (less data) for the contribution of those cells.
There are various options for post hoc type tests. This includes contrasts in a log linear model (probably overkill for this case), collapsing cells or just running the chi-square test on the parts of there cells of interest (maybe thinking about using a correction for multiple testing in some cases).
Usually for most exploratory work I'd look at the residuals. Standardised Pearson residuals and adjusted standardised residuals are both approximately z distributed and can be thought of as the contribution of the cell to the overall Chi-square statistic. I'd usually look at the adjusted standardised residuals with a correction for multiple testing.
I wrote this function to run the egon-pearson corrected test and residual tests (with a correction for multiple testing). It also shows expected cell values etc. It isn't very pretty but I find it quite convenient:
https://rpubs.com/seriousstats/epcs_test
yes you can do the test , but interpretation depends on levels of significance.
good question to start with.
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