I collected data on the monthly occurrence of a parasite and the monthly occurrence of a histological lesion in the tissues where the parasite infects. The parasite is strongly seasonal - peak prevalence and intensities occur in March and April. The lesions are more spread out throughout the year but appear to be more common in those months. So for each (lesion or parasite), I can construct a contingency table (2x12) to demonstrate the months where the prevalence of lesions and parasites are highest. What I would like to do is test how closely the parasites and lesions agree. Is there a test of agreement to compare monthly lesion and parasite prevalence?
I can disregard month and construct a contingency table of parasite and lesion. The results show a Kappa of 0.0248 with a P = 0.5804. Also, Bowker's test for symmetry (greater than 2x2 contingency table) indicates symmetry of disagreement chisq =22.6, P <0.001. I would take these results that there is no strong measure of agreement between the lesion and parasite overall. However, this doesn't account for month.
Agreement is for Y and X with the same scale. Your description mentions counts (lesions, parasites) but not the scales used for either one.
Association is more general. You could stratefy your contingency table by Month. One of the CMH tests should cover your hypothesis.
Ok, I think it is the Cochran Mantel Haenzsel test you're referring too. I found an example and understand how to run it now. So I chose the presence/absence of lesion and parasite as the X and Y and then in the pop-up window chose month as the grouping variable. Is the default that the null hypothesis is no correlation between parasite and lesion?
You are way ahead of me! Yes, the null is no association. You test the overall association (unstratified) first with the Contingency platform, then select CMH from the red triangle for stratification by Month.
I tried running the CMH test with parasite and lesion as X and Y stratified by month. Correlation scores are blank in the results box followed by a message that the statistic was not computed as the covariance matrix was singular. What does that mean?
I have another question or 2. I also ran general agreement statistics between the parasite and lesion, ignoring month. The Kappa score was high (0.66) and was significant P<0.001. Bowker's test was also significant chisq 5.4, P=0.196. Does Bowker's test confirm the Kappa? I'm not sure how to take Bowker's result as it seems like it is testing disagreement rather than agreement. Can you explain?
Also, after thinking about this a bit, I don't know that it matters that I include month in the analysis. Perhaps Kappa and Bowker's would be sufficient. However, I would like to understand if the CMH test provides any additional useful information beyond Kappa and Bowkers.
Kappa measures agreement between raters or ratings. For McNemar's / Bowker's test of symmetry, the null hypothesis is that the probabilities in the square table satisfy symmetry or that pij = pji for all pairs of table cells.
The CMH tests are about association and the choice among the four alternatives depends on the modeling type of the X and Y variables. From JMP Help:
Singularity usually means that the model behind this test is over-specified. It would be like including a quadratic term in the linear predictor when the X variable has only two levels. Such data does not support estimating the model. Can you post the Contingency platform with your data before and after applying the CMH tests?
Here is the contingency table and CMH results. I set lesion and parasite presence/absence as ordinal and it worked. I stratified by month. I think I had my columns set as nominal previously.
I believe the null hypothesis is that there is no association between lesions and parasites. Therefore it looks like I have a highly significant association between them. So what I'm wondering is what added information does the CMH and stratification provide above that of the standard ChiSquare?
Thanks for your help!