I'm currently doing some analysis for my dissertation project and I was wondering what statistical test is best to perform. I have to compare the SDs of each participant (64 participants with 64 individual responses each) to check if there were any differences. My study has two conditions which each participant was tested in. I've calculated the SDs and plotted them to see the spread visually.
I don't know if a t-test is the right method for comparing all of my values and have read that it may be better to use an F-test, but I have never done this before. I'd really appreciate any opinion or guidance on this as my R skills are beginner level.
Thanks!
Hello Abigail,
There are a number of tests available to compare two or more variances (= SD^2). If only two variances, the tests aren't much different. If more than two variances, they do differ in the amount of information used and the relative power/type I error trade-off. Levene's test, based on deviations from sample medians (not means), is pretty robust against non-normality as a measure of variance equality.
It's not clear from your query whether you have one observation per case within condition, or multiple observations (e.g., trials) per case within condition. If the former, then all you could do is compare variance of condition 1 to condition 2 (and 64 scores contributing to each variance estimate).
However, if you have multiple observations per participant, you'll have to decide whether you're more interested in:
1. comparing variance of condition 1 vs. condition 2;
2. comparing variance of participant i vs. participant j within a condition;
3. comparing variances of participant i vs. participant j across combined conditions;
4. an omnibus test of variance (Participant 1 = P2 = ... = P64), within or across conditions.
Multiple trials scores within persons/participants would not be statistically independent, so that adds another wrinkle to the picture. As well, you'd want a sufficient number of within condition trials/observations/scores per case in order to have any hope of a stable variance estimate per participant.
Good luck with your work.
Hello Abigail,
There are a number of tests available to compare two or more variances (= SD^2). If only two variances, the tests aren't much different. If more than two variances, they do differ in the amount of information used and the relative power/type I error trade-off. Levene's test, based on deviations from sample medians (not means), is pretty robust against non-normality as a measure of variance equality.
It's not clear from your query whether you have one observation per case within condition, or multiple observations (e.g., trials) per case within condition. If the former, then all you could do is compare variance of condition 1 to condition 2 (and 64 scores contributing to each variance estimate).
However, if you have multiple observations per participant, you'll have to decide whether you're more interested in:
1. comparing variance of condition 1 vs. condition 2;
2. comparing variance of participant i vs. participant j within a condition;
3. comparing variances of participant i vs. participant j across combined conditions;
4. an omnibus test of variance (Participant 1 = P2 = ... = P64), within or across conditions.
Multiple trials scores within persons/participants would not be statistically independent, so that adds another wrinkle to the picture. As well, you'd want a sufficient number of within condition trials/observations/scores per case in order to have any hope of a stable variance estimate per participant.
Good luck with your work.
If you are looking for the R code to run F-test, please check the following.
https://www.r-bloggers.com/2017/08/f-test-compare-two-variances-in-r/
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