in the last 5 years, each year 4 different learning tests were administered to groups of people, not homogeneous in total number and gender difference.
having the number of men and women that each year and for each test have achieved the highest score range, which statistical test I can use to relate gender (dichotomous variable, male - female) with the learning test (polychotomous variable, 4 tests) for each year (stratification variable, 5 years).
thank you in advance...
If you don't have a priori knowledge on the effect of type of learning test on gender issue you can simply use mixed model with YEAR as random variable and GENDER and TEST as fixed factor using library such as lme4
If you have some a priori knowlegde it could be better to go for path analysis or structural equation modeling
If the YEAR is also a variable you are interested in studying, you could include it also as a fixed factor and test its interactions with the other variables
Denis and Bruno, thank you for your reply. The year variable is to be considered in a context useful to the time series
more questions from me, what makes them a group, and what do you want to know. Eg has the gender gap changed differentially from different learning outcomes over the last 5 years. I am also unclear on the meaning of highest score range.
If you plot the data can you see an effect? Maybe try plotting the data and ask a friend if they see a pattern (sometimes we see a pattern because we want to find one). If the friend sees the same pattern (without any hints), then maybe it is real.
There are a few problems (or I don't understand the experiment correctly).
1) You have categorized the scores rather than using the score itself. The way that you categorize can introduce artifacts into the data. If "high score" is defined as anything above 37 then you get one answer, but if high score is 47 you get a different answer.
2) You are only interested in the highest category. Thus you have one data value for men and another for women for each test per year. There is no replication. You can further condense the data by taking the difference between men and women and then there is but one number per test per year.
Hierarchical linear modeling (aka multilevel model) would be a way I would recommend. Check Bryk and Raudenbush's ' Hierarchical Linear Models: Applications and Data Analysis Methods ' book for your reference. Another approach would be structural equation modeling.
Dear Dr Piazza, your description of your data is quite short and I am not sure I understood your problem correctly, but I am not convinced that you are in a situation where hierarchical model would be recommended.
I understand that you have records about different individuals according to Gender (2 levels), Year (5 levels) and Tests (4 levels), producing 2*5*4 = 40 groups, each with different individuals. If individuals are different from group to group, I don't see how to "hierarchize" the model.
The nature of the "response" for each individual is not clear : is it a score at the test, is this response binary, categorical, continuous... or some other data? Do you have the individual's response or rather a summary by the groups ?
I would suggest that you communicate a significant subset of your data to let the community figure out more precisely what your problem is.
Best.
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