Connectomestats: Three groups ANOVA

MakaniP · April 22, 2022, 12:54pm

Daer MRtrix experts,

I have a similar question. I have three groups. I would like to perform one-way ANOVA followed by t-test. I am not sure if my model is correct or not. Maybe you can help me out.

My design matrix:
1 0 0
1 0 0
0 1 0
0 1 0
0 0 1
0 0 1

My group-effect contrast matrix:
1 -1 0
0 1 -1

Now I am using this command:
connectomestats connectome_name.txt tfnbs design_matrix.txt group-effect_contrast_matrix.txt tfnbs_output

Thank you!

Best wishes,
Punit

rsmith · April 27, 2022, 7:49am

Hi Punit,

Decided to move this to a separate topic: if things stray too far from the original content of a topic it makes it harder for subsequent readers to find. Can always add links to other topics if you think they are related.

I would like to perform one-way ANOVA followed by t-test.

We need to be very careful here up-front before we even get to the matrices. When you say “followed by”, are you referring to a post hoc test to identify source / direction of effect only where the ANOVA assigned statistical significance? Because that can be done, but:

It involves running the command twice, not once.
To do it “properly” (at least as far as I can ascertain) requires utilising a software feature that is implemented but not published and not yet part of a tagged MRtrix3 release.

I am not sure if my model is correct or not.

The “model” in terms of combination of design and contrast matrices is fine; there are multiple possible solutions and this is one of them.

However you are currently performing two t-tests, corresponding to the two rows of your contrast matrix. The first tests the hypothesis that group 1 is greater than group 2; the second tests the hypothesis that group 2 is greater than group 3. In neuroimaging-GLM-speak, an ANOVA is achieved using an F-test. You need two additions:

-ftests option, where you provide a text file specifying the set of F-tests you wish to perform and how to construct each. In your case the content of that file should simply be “1 1”: A single row for a single F-test, and that F-test incorporates both of the two rows of the contrast matrix.
-fonly option, since you don’t actually want to perform those two t-tests, you’re only specifying them to facilitate construction of the F-test.

(I’m currently in an argument with myself as to whether this interface should change)

Cheers
Rob

MakaniP · April 28, 2022, 7:27am

Dear Rob,

Thank you very much for your clear answers.

I have a question about the text file for -ftests. When you want to run a ANOVA, we usually use a two-line contast matrix [1 -1 0 ; 0 1 -1]. I did not understand how it is [1 1 0]. Can you please explain it to me?

Thank you!

Best wishes,
Punit

rsmith · April 29, 2022, 7:18am

The F-test is [1 1], not [1 1 0].

Each row of the F-test file corresponds to a single F-test. Here, there’s one F-test, so there’s one row.

Each column of the F-test file corresponds to a row in the contrast matrix, and contains a 0 or 1 to indicate if that row is or is not included in this F-test.

This is intended to mimic the FSL GLM GUI, where each t-test appears on a row, and each F-test is a column of checkboxes controlling which contrast matrix rows are a part of that F-test.

If you find this confusing, that’s more motivation for me to make the proposed interface change linked above (and external comments are quite welcome):

github.com/MRtrix3/mrtrix3

*stats: F-test interface

opened 10:53PM - 11 Nov 20 UTC

Lestropie

question

Currently, the interface for defining F-tests for statistical inference operates… as follows: - The contrast matrix for t-tests is a compulsory positional argument; - The set of F-tests is optionally provided as a text file, where each row contains 1's and 0's indicating which rows of the contrast matrix are included in the F-test and which are not; - If one is only using the contrast matrix for the purpose of constructing F-tests, and does not actually want / need to perform the t-tests indicated by each row of the contrast matrix, one can use the `-fonly` option. This builds on the `*stats` interface prior to `3.0.0` without perturbing it, and is consistent with the FSL GUI (where each F-test is a column of checkboxes selecting contrast matrix rows). There is however a potential weakness here that arises particularly in the context of the `-strong` option. In the absence of that functionality, if one wanted to perform *some* of the t-tests present in the contrast matrix, in addition to F-tests (where some of those F-tests necessitated additional rows in the contrast matrix in order to construct them), then one would simply *not* use the `-fonly` option, perform all t-tests and F-tests, and just ignore the outputs for those t-tests that are not of interest (and swallow the computational penalty). However if one wishes to the `-strong`, then those not-of-interest t-tests would decrease statistical power. The interface that would provide maximal flexibility would be: - The contrast matrix for t-tests becomes a command-line *option*, which can be specified only once; - F-tests are provided via command-line option `-ftest`, which *can* be specified multiple times; each individual F-test being provided as the matrix *C* in its full form rather than referencing rows of the t-test contrast matrix; - The `-fonly` option would be removed; - Command exits if no t-test contrast matrix is provided and no F-tests are specified. This guarantees that strong FWE correction is only ever applied across inferences that are explicitly of interest. It would however deviate from both prior *MRtrix3* and FSL interfaces.

MakaniP · April 30, 2022, 6:40pm

Dear Rob,

Thank you very much for your clear explanation! Now there is no more confusion.

Best wishes,
Punit