Dear Andrew,

I’d like to check two different ways of a two-group comparison with covariates in NBS and understand why they give different results.

My data: Two groups (Group vs Control), N ≈ 1500

Covariates: 2 binary, 2 continuous (all continuous covariates demeaned across all subjects)

NBS settings
Extent, primary t = 4.5, permutations = 5000.

Design A (t-test; no explicit intercept)
Columns: [Group, Control, cov1, cov2, cov3, cov4]

Group > Control: [ 1 -1 0 0 0 0 ]

Control > Group: [ -1 1 0 0 0 0 ]
(Group/Control coded 0/1.)

Design B (GLM; with intercept)
Columns: [Intercept(=1), Group, cov1, cov2, cov3, cov4]

Group > Control: [0 1 0 0 0 0]

Control > Group: [0 -1 0 0 0 0]

Design A yields significant networks at t=4.5; Design B does not (same matrices, order, and permutations). 

My question is: Are Designs A and B equivalent in NBS for testing the adjusted group effect (assuming continuous covariates are mean-centered across all subjects)? If yes, what could explain the discrepancy?

Many thanks :)

Best,

Aslı