Hi all,
I'm interested in comparing the ratios of yes/ no results between 2 strains:
yes no
strain a 10 20
strain b 50 50
For each experiment, I have 3 biological replicates (same strains, same protocol, different days).
I was wondering whether I can use the
Cochran–Mantel–Haenszel test for repeated tests of independence to answer whether there is a difference between the yes/no proportion of strain a and b?
If so-
what is the best way to graph it?
Thanks!
Hello Chen,
Yes, you may use the CMH test, with day replications representing the "matching" variable.
How to graph? You could plot odds ratios by day and group, if you felt that it was helpful to do so. A simple table could convey the same information.
Good luck with your work.
David Morse Thanks for your help!
Just to better understand-
would it make sense to present also each replica's p-val (chi- square/ Fisher's exact test)...? Or that only the the p-val retrieved from the CMH test is the relevant one in case of replicates...? What happen if out of several replicates, one is not significant (but shows the same "trend" of different, possibly due to several reasons...?) Thanks again!
Hello again Chen,
I'd say it depends on what research question you're trying to answer. The MH test will address the comparison of strains (across replications). If you're more worried about whether replications yielded consistent results, you could:
1. Run three FIsher exact tests, one for each day. The collective likelihood could be computed via Fisher's method for combining independent outcomes:
= -2(SUM(ln(prob_i)), which is approximately distributed as a chi-square with 2*k df (where k = number of probabilities being combined; ln = natural log; and SUM is the summation operator). Of course, if the trends differ, your next chore is to try to figure out plausible explanation/s!
2. Switch gears and use log-linear analysis, with a 2 x 2 x 3 design. In this approach, the main effect of replication could be evaluated (along with the other main effects and interactions). Here's a good starting resource: http://userwww.sfsu.edu/efc/classes/biol710/loglinear/Log%20Linear%20Models.htm
Good luck with your work.
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