Could you explain in more detail about your data structure? Could you list your variables? This may help people understand exactly what kind of data you have.

@J.Patrick Kelley,

I have four variables ,for example A , B , C , D (these varaibles are four sinuses in patients who are suffering from sinusitis disease) . Information for these varaibles are collected from 100 patients . For instance If a patient had an infection in his A_sinuse, we use No.1 and if not use No.0 and this information is checked separately for other three sinuses in each patient.

Now I want to compare these four variables (infection in four sinuses) by using a statistical test (not descriptive statistics )

Hello!

Thanks for the clarification. I thought that you may be speaking about multiple sinuses within a single patient. So, it seems like your question is: "Does the probability of vary among different sinuses?"

Because your data are clustered (i.e. replicated) within patients, you are in the realm of mixed-effect models. There are many ways to implement mixed effect models. My preferred method is using the "lme4" package in R. In your case, you will want to include a single random effect of patient ID. (You will need to change the random effect structure a bit if you measured each patient multiple times).

The simplest option is the following, I think. Take note that I haven't thought in-depth about this, so there may be other considerations. Other contributors may jump in. You use one variable (sinus ID) with four variables. This simplifies everything, for sure. This is sort of like applying a treatment (single variable in your model), just as you would if you ran a control treatment against three experimental conditions. So, you are testing the influence of sinus ID on the probability of overall infection (yes/no for the patient). This assumes that sinuses themselves are not interacting to influence infection.

Of course sinuses may influence each other in terms of probability of infection. It seems that you are sampling the patients at a single time point, so you might have no information about which sinus was infected first. So, you may want to consider examining probability of infection for groups of sinuses. Community ecologists (or epidemiologists) may know better how to conduct these association analyses...

Sounds like a great data set you have!

Dear Patrick,

Thank you for your consideration and guidance.what you get from my question is what I have asked exactly .

Maybe any one else add another suggestion for solving the problem :)

If the infection of the 4 siuses are dependent to each other which I think this is right, then you have to employ nonparametric Cochran's Q test.

However, if you want to consider the effect of other possible independent variable, the linear mixed model with GEE estimation (package nlme or lme4 in R) is also useful. But for the univariate analysis I prefer Cochran's Q test.

Dear Dr.Vossoughi,

Thank you very much for your answer,I used Cochran 's Q test and get the answer.