I used bisulfite conversion-->region-specific PCR-->cloning method to determine methylation of a gene at a specific region between two treatment groups. I had 8 individuals in one treatment group, and I sequenced several colonies from one individual. Now I am struggling if I should use Chi-square/Fisher exact test or t-test for the comparison of methylation rate of each CpG site between the two groups. In my case, each CpG site in one colony is either methylated or not methylated, whereas when calculating methylation of one individual (experimental unit), I need to average the methylation from the colonies, e.g. 4 out of 6 colonies were methylated at CpG site 1, then the methylation of this site in this individual is 66.67%. However, by calculating like this, the percentages are not really continuous, but can only be 16.67% (1/6), 33.33% (2/6), 50% (3/6), 66.67% (4/6), 83.33% (5/6) and 100%. I know that Chi-square is normally used for counts. So my question is, is t-test valid here or there are better methods for data analysis?
I would run the chisquare test. In attachment, a SAS program on fabricated data with a logistic regression as well as a chisquare test. They both yield the same results. I also added an R script for the chisquare test on the same fabricated data. One can run SAS (with SAS Studio) online for free on the "SAS on demands website". You only need to register once: https://odamid.oda.sas.com/SASStudio
You can't use chi-square on the percentages. You can use a test for a difference in binomial proportions.
Newcombe R.G. (1998). Interval Estimation for the Difference Between Independent Proportions: Comparison of Eleven Methods. Statistics in Medicine, 17, 873--890.
I agree with Thom. Looks like your data is binomial ("x 'successes' in "n" 'trials': here, x is the number of clones you observed a site being methylated, and n is the number of clones analyzed - per individual). Attaches is an example how you could do that in R.
As an aside I don't think the Fisher's exact test is ever a good choice outside of the highly unusual case of fixed marginals. I'd recommend Egon Pearson's N-1 corrected chi-square test.
Hi all, thank you so much for your kind replies! I greatly appreciate it! Our lab continuously use JMP for data analysis, and I re-organized data as Jos Feys suggested, but in the end I only found "Nominal Logistic regression" instead of "Binomial test" as suggested by Jochen Wilhelm and Thom Baguley . I am confused if these two are using the same testing method / testing the same hypothesis. Could you please help me to understand it according to my case?
In the 2x2 case logistic regression and a chi-square are essentially equivalent - if you set up the model to compare a main effects only model with a model containing the two-way interaction. The test statistic that logistic regression gives is the likelihood chi-square and the 2x2 chi-square test usually gives a Pearson chi-square test statistic - but you can obtain both from either analysis with a bit of further work (depending on software). The two statistics will tend to be similar in smaller samples (and identical in very large samples).
I don't fully understand your data structure so I'm not sure if it could be readily analysed with a chi-square test. Logistic regression is a bit more flexible (e.g., you can have multiple continuous and categorical predictors).
Thank you very much Thom Baguley ! I sincerely appreciate your kind explanations. One last question I promise. Would it also be a reasonable analysis to average the methylation rate from each CpG site (like stated in the question, calculated as percentages), then use non-parametric test (as the data were not normally distributed) to compare the means between two treatment groups?
Possibly - you might be losing information by averaging. It depends a lot on the structure of the data - how many repeated observations on each individual and so on.