5 different subjects; each subject has 8, 11, 4, 6, and 3 sessions collected; the same measurement is made in every session. What statistical test to use to show significant measurement? one sample t-test is not suitable due to dependent sessions (acquired in the same subject)?
If I understand it well, you have to compare your five subjects with each other. If is this what you want, then I suggest you use a nonparametric method, i.e., Kruskal Wallis test. The sample size for each subject/group is too small to perform a parametric test, which in this case would be an one-way ANOVA.
I would like to help be I do not really understand what you did. You say you had 5 subjects. Each subject was involved in 8, 11, 4, 6 and 3 sessions. In each session, the same measurement was taken from your subjects. It seems to me you had a repeated measures design, but why were there 8, 11, 4, 6 and 3 sessions. What do you mean by sessions.
Hard to say for sure based on the description but I’d suggest looking into a mixed model. SAS’s PROC MIXED might prove useful or nparlLD in R.
Jos Feys, The study involves MRI acquisition from subjects over several MR sessions. Here, subjects had 8,11, 4, 6, and 3 MR data acquisitions done from them. I believe I cannot consider all sessions to be independent and thus cannot use n=32(8+11+6+4+3). Practical issues prevent me from acquiring more data. So would require a suitable method to show the significance of measured metric, U in all subjects. Due to the statistical non-independent nature of data, t-test to show significant difference from U0 would not work.
I think you can compare the measurements of the MRI sessions wiht either parametric one-way repeated measures ANOVAs or non-parametric Friedman ranks tests. The choice between parametric and non-parametric depends on the severity of deviation from the normality of the distributions of your measures. Inspect the histograms of these and/or run the Shapiro test.
You can test differences in correlation (either independent or dependent or from a specific value(e.g. 0)) online , e.g.: https://www.psychometrica.de/correlation.html For testing whether a correlation is different from zero, most statistical packages include this test when calculating correlations. As I understand the differences in correlations between your subjects 1-5 (= between sessions 8,11,4,6 and 3) would be for independent correlations, since they are from different brains. The differences in correlations within each subject (for differences regions within a particular brain) would be for differences in dependent correlations.
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