Hello everyone, I have had some hesitation on which test I should use: ANOVA or mixed models.
Here is the procedure I followed,
Hence, I opted for a mixed model, I have two independent variables: (time: pre/post) and groups (control/experiment); and one dependent variable (comprehension of the presented material); but I have some hesitation, because, from what I have learnt, ANOVA also could be used.
Hence, what is the one that should be used in my work?
NB: Even if the groups ctrl-pre/ctrl-post and exp-pre/exp-post are the same, the subjects have not been paired between pre and post (The test was anonymous).
Attached is an example of what my data has as form.
PS: the study is in the field of applied linguistics.
Thank you.
That's a classical BACI design (before-after control-impact). As you don't have any pairing, there is no known common variance structure, and so using random effects don't make sense here.
Given the conditional distribution of the response is roughly normal, then the interesting coefficient for you is the interaction (Time:Treat) in a 2x2 model. This gives you the (expected) difference in post-pre-changes between the treated and the control group.
I wrote that you can't sepcify a mixed models, as you don't have a variable that would make sense as random effect. I further wrote that the interaction in a 2x2 model is what I think you should test. This is very concretely the answer to your question.
If you now ask "which test?", then the answer is "a t-test" (all coefficients in linear models are tested this way). But that shouldn't bother you; if you use some software to fit/analyze a 2x2 ANOVA model, you will get the estimate, the standard error, the t-value and the p-value (and sometimes also the confidence interval) of interaction.
Again: that is the way to go when the assumption makes sense that the conditional distribution of the response is normal. If not, you may have to go for some other tools that allow to use an appropriate probability model for the response. The functional model would still be the 2x2 model and you still would like to test the interaction. -- The data you posted would be ok for an ANOVA model.
http://data.library.virginia.edu/understanding-2-way-interactions/
You can get help from these references. Simply explained.
Article Towards understanding and use of mixed-model analysis of agr...
https://www.sas.com/store/books/categories/usage-and-reference/sas-for-mixed-models-second-edition/prodBK_59882_en.html
Hello again,
I have collected a new version of data, applied mixed models, implemented in XLSTAT package, and obtained the attached results. I also joined the ANOVA test results.
NB: I chose the mixed models statistics mainly because I have had some randomness in choosing my samples: two groups of 25, from a population of about 300 students.
Could you please help in interpreting the attached results?
Thanks a lot.
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