Hi there!
If I want to examine whether the variance of a sample changes significantly through a treatment, how would I do that?
In this case I would not be interested in the change/difference of the mean values between T1 and T2, but rather in the variance within the group.
To be more specific: In educational research, I am interested if a certain teaching method can significantly reduce differences between the students, measured in a pre-/post-test design. I assume that there will be a general effect of teaching, meaning that the mean score will be higher in the post test, but that is not what I am interested in. I want to know if I can close the "gap" between the low- and high-achieving students rather than just increasing performance.
Thanks a lot :-)
Is this what you are looking for? Denote whether it is pre or post with time_ij, the score be score_ij, and subject_j.
score_ij ~ beta0 + beta1 time_ij + time_ij e1_ij + e0_ij + u_j
and testing this against
score_ij ~ beta0 + beta1 time_ij + e_ij + u_j
I assume you have an actual control group also as fan effects (i.e., the Matthew effect) can occur.
You can have a look at Brown-Forsythe test ( The Levene's test using medians).
Please check the following links:
https://online.stat.psu.edu/stat500/lesson/7/7.4
https://opentextbc.ca/introbusinessstatopenstax/chapter/test-of-two-variances/
Hello Andreas Dengel. I believe that the best known tests for homogeneity of variance (e.g., Levene's test and the Brown-Forsythe modifications to it) are meant for use with independent samples. I just found an article describing a method for "clustered" data. It uses data from twins as an example, so I think it ought to be applicable to your
paired data too. DISCLAIMER: I just found it, and have not read it yet, so I am not (at this point) vouching for it. But you may find it helpful.
Article Robust tests for the equality of variances for clustered data
HTH.
Maybe a totally different approach: using bayesian parameter estimation. You could use a model to assess the correlation between the measures and herein estimating the sigmas for each measrurement time. After that you could use the posterior distributions of both sigmas and compare them, e.g. calculating the difference and inspect the posterior of the difference. With approaches like Region Of Practical Equivalence (ROPE) you could test if you have enough evidence to claim a difference. In the brms package in R you could use a model like this (with a t-distribution to be more robust against outliers)
f1
The model I showed above, as Rainer Duesing shows, can be represented as a Bayesian (I hadn't specified how to estimate it and at this point imo it is not the first question to address). Reading the second half of question again, it suggested another approach that might seem okay, but has a difficulty. You might think predict post from pre with a regression and test if beta1 is less than one. The issue here is again regression towards the mean, as you will tend to find these. Rainer used R, so I assumed you played with the data in that. If so, try:
lv
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