Massively univariate analysis of face vs house recognition

A permuted Ordinary Least Squares algorithm is run at each voxel in order to determine whether or not it behaves differently under a “face viewing” condition and a “house viewing” condition. We consider the mean image per session and per condition. Otherwise, the observations cannot be exchanged at random because a time dependence exists between observations within a same session (see [1] for more detailed explanations).

The example shows the small differences that exist between Bonferroni-corrected p-values and family-wise corrected p-values obtained from a permutation test combined with a max-type procedure [2]. Bonferroni correction is a bit conservative, as revealed by the presence of a few false negative.

Note

If you are using Nilearn with a version older than 0.9.0, then you should either upgrade your version or import maskers from the input_data module instead of the maskers module.

That is, you should manually replace in the following example all occurrences of:

from nilearn.maskers import NiftiMasker

with:

from nilearn.input_data import NiftiMasker

References

[1] Winkler, A. M. et al. (2014).

Permutation inference for the general linear model. Neuroimage.

[2] Anderson, M. J. & Robinson, J. (2001).

Permutation tests for linear models. Australian & New Zealand Journal of Statistics, 43(1), 75-88. (http://avesbiodiv.mncn.csic.es/estadistica/permut2.pdf)

Load Haxby dataset

from nilearn import datasets, image

haxby_dataset = datasets.fetch_haxby(subjects=[2])

# print basic information on the dataset
print(f"Mask nifti image (3D) is located at: {haxby_dataset.mask}")
print(f"Functional nifti image (4D) is located at: {haxby_dataset.func[0]}")

Mask nifti image (3D) is located at: /home/remi/nilearn_data/haxby2001/mask.nii.gz
Functional nifti image (4D) is located at: /home/remi/nilearn_data/haxby2001/subj2/bold.nii.gz

Restrict to faces and houses

import numpy as np
import pandas as pd

labels = pd.read_csv(haxby_dataset.session_target[0], sep=" ")
conditions = labels["labels"]
categories = conditions.unique()
conditions_encoded = np.zeros_like(conditions)
for c, category in enumerate(categories):
    conditions_encoded[conditions == category] = c
sessions = labels["chunks"]
condition_mask = conditions.isin(["face", "house"])
conditions_encoded = conditions_encoded[condition_mask]

Mask data

from nilearn.image import index_img
from nilearn.maskers import NiftiMasker

mask_filename = haxby_dataset.mask

nifti_masker = NiftiMasker(
    smoothing_fwhm=8,
    mask_img=mask_filename,
    memory="nilearn_cache",  # cache options
    memory_level=1,
)
func_filename = haxby_dataset.func[0]
func_reduced = index_img(func_filename, condition_mask)
fmri_masked = nifti_masker.fit_transform(func_reduced)

# We consider the mean image per session and per condition.
# Otherwise, the observations cannot be exchanged at random because
# a time dependence exists between observations within a same session.
n_sessions = np.unique(sessions).size
conditions_per_session = 2
grouped_fmri_masked = np.empty(
    (conditions_per_session * n_sessions, fmri_masked.shape[1])
)
grouped_conditions_encoded = np.empty((conditions_per_session * n_sessions, 1))

for s in range(n_sessions):
    session_mask = sessions[condition_mask] == s
    session_house_mask = np.logical_and(
        session_mask, conditions[condition_mask] == "house"
    )
    session_face_mask = np.logical_and(
        session_mask, conditions[condition_mask] == "face"
    )
    grouped_fmri_masked[2 * s] = fmri_masked[session_house_mask].mean(0)
    grouped_fmri_masked[2 * s + 1] = fmri_masked[session_face_mask].mean(0)
    grouped_conditions_encoded[2 * s] = conditions_encoded[session_house_mask][
        0
    ]
    grouped_conditions_encoded[2 * s + 1] = conditions_encoded[
        session_face_mask
    ][0]

Perform massively univariate analysis with permuted OLS

We use a two-sided t-test to compute p-values, but we keep trace of the effect sign to add it back at the end and thus observe the signed effect

from nilearn.mass_univariate import permuted_ols

# Note that an intercept as a covariate is used by default
neg_log_pvals, t_scores_original_data, _ = permuted_ols(
    grouped_conditions_encoded,
    grouped_fmri_masked,
    n_perm=10000,
    two_sided_test=True,
    verbose=1,  # display progress bar
    n_jobs=1,  # can be changed to use more CPUs
)
signed_neg_log_pvals = neg_log_pvals * np.sign(t_scores_original_data)
signed_neg_log_pvals_unmasked = nifti_masker.inverse_transform(
    signed_neg_log_pvals
)

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Job #1, processed 2420/10000 permutations (24.20%, 23.567773643603996 seconds remaining)
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Job #1, processed 2450/10000 permutations (24.50%, 23.44024159470383 seconds remaining)
Job #1, processed 2460/10000 permutations (24.60%, 23.401982871497548 seconds remaining)
Job #1, processed 2470/10000 permutations (24.70%, 23.39876545296024 seconds remaining)
Job #1, processed 2480/10000 permutations (24.80%, 23.71622105567686 seconds remaining)
Job #1, processed 2490/10000 permutations (24.90%, 24.0712777064986 seconds remaining)
Job #1, processed 2500/10000 permutations (25.00%, 24.077673196792603 seconds remaining)
Job #1, processed 2510/10000 permutations (25.10%, 24.079736530068388 seconds remaining)
Job #1, processed 2520/10000 permutations (25.20%, 24.097924100028145 seconds remaining)
Job #1, processed 2530/10000 permutations (25.30%, 24.123746185905848 seconds remaining)
Job #1, processed 2540/10000 permutations (25.40%, 24.15601488736671 seconds remaining)
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Job #1, processed 2580/10000 permutations (25.80%, 24.445874256681105 seconds remaining)
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Job #1, processed 2600/10000 permutations (26.00%, 24.547617527154777 seconds remaining)
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Job #1, processed 2690/10000 permutations (26.90%, 24.67778892765258 seconds remaining)
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Job #1, processed 2780/10000 permutations (27.80%, 24.446597955209743 seconds remaining)
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Job #1, processed 2800/10000 permutations (28.00%, 24.453191348484587 seconds remaining)
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Job #1, processed 2820/10000 permutations (28.20%, 24.3979284171517 seconds remaining)
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Job #1, processed 2880/10000 permutations (28.80%, 24.21405116054747 seconds remaining)
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Job #1, processed 2900/10000 permutations (29.00%, 24.11460291106125 seconds remaining)
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Job #1, processed 2920/10000 permutations (29.20%, 24.019002983014875 seconds remaining)
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Job #1, processed 2960/10000 permutations (29.60%, 23.90182649767077 seconds remaining)
Job #1, processed 2970/10000 permutations (29.70%, 23.852567531444407 seconds remaining)
Job #1, processed 2980/10000 permutations (29.80%, 23.81756768770666 seconds remaining)
Job #1, processed 2990/10000 permutations (29.90%, 23.831403334403916 seconds remaining)
Job #1, processed 3000/10000 permutations (30.00%, 23.819154977798462 seconds remaining)
Job #1, processed 3010/10000 permutations (30.10%, 23.810536009924753 seconds remaining)
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Job #1, processed 3030/10000 permutations (30.30%, 23.8419829791922 seconds remaining)
Job #1, processed 3040/10000 permutations (30.40%, 23.938009425213462 seconds remaining)
Job #1, processed 3050/10000 permutations (30.50%, 23.98532605952904 seconds remaining)
Job #1, processed 3060/10000 permutations (30.60%, 23.98200192794301 seconds remaining)
Job #1, processed 3070/10000 permutations (30.70%, 24.067033944766763 seconds remaining)
Job #1, processed 3080/10000 permutations (30.80%, 24.054875005375255 seconds remaining)
Job #1, processed 3090/10000 permutations (30.90%, 24.054312381929563 seconds remaining)
Job #1, processed 3100/10000 permutations (31.00%, 24.062450847318093 seconds remaining)
Job #1, processed 3110/10000 permutations (31.10%, 24.047153662255344 seconds remaining)
Job #1, processed 3120/10000 permutations (31.20%, 24.02010220747728 seconds remaining)
Job #1, processed 3130/10000 permutations (31.30%, 24.108593599483992 seconds remaining)
Job #1, processed 3140/10000 permutations (31.40%, 24.129923445403954 seconds remaining)
Job #1, processed 3150/10000 permutations (31.50%, 24.148108160684977 seconds remaining)
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Job #1, processed 3170/10000 permutations (31.70%, 24.12367040351362 seconds remaining)
Job #1, processed 3180/10000 permutations (31.80%, 24.121197019732975 seconds remaining)
Job #1, processed 3190/10000 permutations (31.90%, 24.11920702569537 seconds remaining)
Job #1, processed 3200/10000 permutations (32.00%, 24.114632844924927 seconds remaining)
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Job #1, processed 3220/10000 permutations (32.20%, 24.109578605023966 seconds remaining)
Job #1, processed 3230/10000 permutations (32.30%, 24.117374001641764 seconds remaining)
Job #1, processed 3240/10000 permutations (32.40%, 24.075737823674707 seconds remaining)
Job #1, processed 3250/10000 permutations (32.50%, 24.03472186968877 seconds remaining)
Job #1, processed 3260/10000 permutations (32.60%, 23.987148306852472 seconds remaining)
Job #1, processed 3270/10000 permutations (32.70%, 23.944661386880664 seconds remaining)
Job #1, processed 3280/10000 permutations (32.80%, 23.900963527400318 seconds remaining)
Job #1, processed 3290/10000 permutations (32.90%, 23.85956179769568 seconds remaining)
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Job #1, processed 3310/10000 permutations (33.10%, 23.76793180779748 seconds remaining)
Job #1, processed 3320/10000 permutations (33.20%, 23.71415161511984 seconds remaining)
Job #1, processed 3330/10000 permutations (33.30%, 23.6678444830863 seconds remaining)
Job #1, processed 3340/10000 permutations (33.40%, 23.785613566815496 seconds remaining)
Job #1, processed 3350/10000 permutations (33.50%, 23.839957767458102 seconds remaining)
Job #1, processed 3360/10000 permutations (33.60%, 23.802348443440028 seconds remaining)
Job #1, processed 3370/10000 permutations (33.70%, 23.75777812456872 seconds remaining)
Job #1, processed 3380/10000 permutations (33.80%, 23.746020152018623 seconds remaining)
Job #1, processed 3390/10000 permutations (33.90%, 23.719372252095763 seconds remaining)
Job #1, processed 3400/10000 permutations (34.00%, 23.70129595083349 seconds remaining)
Job #1, processed 3410/10000 permutations (34.10%, 23.687259349655196 seconds remaining)
Job #1, processed 3420/10000 permutations (34.20%, 23.64535409525821 seconds remaining)
Job #1, processed 3430/10000 permutations (34.30%, 23.64484575677544 seconds remaining)
Job #1, processed 3440/10000 permutations (34.40%, 23.60769032323083 seconds remaining)
Job #1, processed 3450/10000 permutations (34.50%, 23.557937542597454 seconds remaining)
Job #1, processed 3460/10000 permutations (34.60%, 23.52118408611055 seconds remaining)
Job #1, processed 3470/10000 permutations (34.70%, 23.478153092716884 seconds remaining)
Job #1, processed 3480/10000 permutations (34.80%, 23.504774477290013 seconds remaining)
Job #1, processed 3490/10000 permutations (34.90%, 23.46113188970396 seconds remaining)
Job #1, processed 3500/10000 permutations (35.00%, 23.411307913916453 seconds remaining)
Job #1, processed 3510/10000 permutations (35.10%, 23.366017557616928 seconds remaining)
Job #1, processed 3520/10000 permutations (35.20%, 23.319496051831674 seconds remaining)
Job #1, processed 3530/10000 permutations (35.30%, 23.27170092458428 seconds remaining)
Job #1, processed 3540/10000 permutations (35.40%, 23.231638475999993 seconds remaining)
Job #1, processed 3550/10000 permutations (35.50%, 23.181616030948263 seconds remaining)
Job #1, processed 3560/10000 permutations (35.60%, 23.13938277758909 seconds remaining)
Job #1, processed 3570/10000 permutations (35.70%, 23.09671386750806 seconds remaining)
Job #1, processed 3580/10000 permutations (35.80%, 23.049056640550415 seconds remaining)
Job #1, processed 3590/10000 permutations (35.90%, 23.175155797044546 seconds remaining)
Job #1, processed 3600/10000 permutations (36.00%, 23.13116243150499 seconds remaining)
Job #1, processed 3610/10000 permutations (36.10%, 23.129274403289415 seconds remaining)
Job #1, processed 3620/10000 permutations (36.20%, 23.08163505496241 seconds remaining)
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Job #1, processed 3640/10000 permutations (36.40%, 22.996463243777935 seconds remaining)
Job #1, processed 3650/10000 permutations (36.50%, 22.958592859033036 seconds remaining)
Job #1, processed 3660/10000 permutations (36.60%, 22.91322022839322 seconds remaining)
Job #1, processed 3670/10000 permutations (36.70%, 22.891403565939502 seconds remaining)
Job #1, processed 3680/10000 permutations (36.80%, 22.900178593137994 seconds remaining)
Job #1, processed 3690/10000 permutations (36.90%, 22.92000345938251 seconds remaining)
Job #1, processed 3700/10000 permutations (37.00%, 22.882157834800513 seconds remaining)
Job #1, processed 3710/10000 permutations (37.10%, 22.845012004806023 seconds remaining)
Job #1, processed 3720/10000 permutations (37.20%, 22.802770840224397 seconds remaining)
Job #1, processed 3730/10000 permutations (37.30%, 22.74244804740272 seconds remaining)
Job #1, processed 3740/10000 permutations (37.40%, 22.67512375275719 seconds remaining)
Job #1, processed 3750/10000 permutations (37.50%, 22.606921195983887 seconds remaining)
Job #1, processed 3760/10000 permutations (37.60%, 22.562707870564562 seconds remaining)
Job #1, processed 3770/10000 permutations (37.70%, 22.516602022262084 seconds remaining)
Job #1, processed 3780/10000 permutations (37.80%, 22.473693311529818 seconds remaining)
Job #1, processed 3790/10000 permutations (37.90%, 22.428788338613387 seconds remaining)
Job #1, processed 3800/10000 permutations (38.00%, 22.38089941677294 seconds remaining)
Job #1, processed 3810/10000 permutations (38.10%, 22.339143556559804 seconds remaining)
Job #1, processed 3820/10000 permutations (38.20%, 22.290295600891113 seconds remaining)
Job #1, processed 3830/10000 permutations (38.30%, 22.246449071495714 seconds remaining)
Job #1, processed 3840/10000 permutations (38.40%, 22.19738408923149 seconds remaining)
Job #1, processed 3850/10000 permutations (38.50%, 22.151442103571707 seconds remaining)
Job #1, processed 3860/10000 permutations (38.60%, 22.106516910958163 seconds remaining)
Job #1, processed 3870/10000 permutations (38.70%, 22.060758435448932 seconds remaining)
Job #1, processed 3880/10000 permutations (38.80%, 22.067614125222278 seconds remaining)
Job #1, processed 3890/10000 permutations (38.90%, 22.02807473278291 seconds remaining)
Job #1, processed 3900/10000 permutations (39.00%, 21.977514083568867 seconds remaining)
Job #1, processed 3910/10000 permutations (39.10%, 21.92524583260421 seconds remaining)
Job #1, processed 3920/10000 permutations (39.20%, 21.951933335284792 seconds remaining)
Job #1, processed 3930/10000 permutations (39.30%, 21.934671991654024 seconds remaining)
Job #1, processed 3940/10000 permutations (39.40%, 21.897289291856254 seconds remaining)
Job #1, processed 3950/10000 permutations (39.50%, 21.839315055291863 seconds remaining)
Job #1, processed 3960/10000 permutations (39.60%, 21.7770077146665 seconds remaining)
Job #1, processed 3970/10000 permutations (39.70%, 21.718505533276034 seconds remaining)
Job #1, processed 3980/10000 permutations (39.80%, 21.654377896582066 seconds remaining)
Job #1, processed 3990/10000 permutations (39.90%, 21.590170087073382 seconds remaining)
Job #1, processed 4000/10000 permutations (40.00%, 21.53122580051422 seconds remaining)
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Job #1, processed 4030/10000 permutations (40.30%, 21.382740273960767 seconds remaining)
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Job #1, processed 4050/10000 permutations (40.50%, 21.300732500759175 seconds remaining)
Job #1, processed 4060/10000 permutations (40.60%, 21.263144136062394 seconds remaining)
Job #1, processed 4070/10000 permutations (40.70%, 21.226683911293083 seconds remaining)
Job #1, processed 4080/10000 permutations (40.80%, 21.191621584050797 seconds remaining)
Job #1, processed 4090/10000 permutations (40.90%, 21.146784910071453 seconds remaining)
Job #1, processed 4100/10000 permutations (41.00%, 21.104998815350417 seconds remaining)
Job #1, processed 4110/10000 permutations (41.10%, 21.06333194799957 seconds remaining)
Job #1, processed 4120/10000 permutations (41.20%, 21.02838461144456 seconds remaining)
Job #1, processed 4130/10000 permutations (41.30%, 20.984413006115194 seconds remaining)
Job #1, processed 4140/10000 permutations (41.40%, 20.943452388192146 seconds remaining)
Job #1, processed 4150/10000 permutations (41.50%, 20.895881514951405 seconds remaining)
Job #1, processed 4160/10000 permutations (41.60%, 20.849881571072796 seconds remaining)
Job #1, processed 4170/10000 permutations (41.70%, 20.819614501879936 seconds remaining)
Job #1, processed 4180/10000 permutations (41.80%, 20.78118572394814 seconds remaining)
Job #1, processed 4190/10000 permutations (41.90%, 20.742005962176084 seconds remaining)
Job #1, processed 4200/10000 permutations (42.00%, 20.717260440190632 seconds remaining)
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Job #1, processed 4220/10000 permutations (42.20%, 20.629321091547958 seconds remaining)
Job #1, processed 4230/10000 permutations (42.30%, 20.58567948995189 seconds remaining)
Job #1, processed 4240/10000 permutations (42.40%, 20.54106870687233 seconds remaining)
Job #1, processed 4250/10000 permutations (42.50%, 20.495420638252707 seconds remaining)
Job #1, processed 4260/10000 permutations (42.60%, 20.451056224079757 seconds remaining)
Job #1, processed 4270/10000 permutations (42.70%, 20.40488844565541 seconds remaining)
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Job #1, processed 4290/10000 permutations (42.90%, 20.33247224211971 seconds remaining)
Job #1, processed 4300/10000 permutations (43.00%, 20.29088827621105 seconds remaining)
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Job #1, processed 4360/10000 permutations (43.60%, 20.200883158850015 seconds remaining)
Job #1, processed 4370/10000 permutations (43.70%, 20.145962039720548 seconds remaining)
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Job #1, processed 4390/10000 permutations (43.90%, 20.03780501687174 seconds remaining)
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Job #1, processed 4470/10000 permutations (44.70%, 19.616383481612406 seconds remaining)
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Job #1, processed 4490/10000 permutations (44.90%, 19.512533592487497 seconds remaining)
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Job #1, processed 4520/10000 permutations (45.20%, 19.394421195561904 seconds remaining)
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Job #1, processed 4690/10000 permutations (46.90%, 18.53336162506136 seconds remaining)
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Job #1, processed 5100/10000 permutations (51.00%, 16.884131398855473 seconds remaining)
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Job #1, processed 5140/10000 permutations (51.40%, 16.807488761523356 seconds remaining)
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Job #1, processed 5240/10000 permutations (52.40%, 16.385722911994876 seconds remaining)
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Job #1, processed 5270/10000 permutations (52.70%, 16.25256750932002 seconds remaining)
Job #1, processed 5280/10000 permutations (52.80%, 16.206110004222754 seconds remaining)
Job #1, processed 5290/10000 permutations (52.90%, 16.16240266004898 seconds remaining)
Job #1, processed 5300/10000 permutations (53.00%, 16.1145454442726 seconds remaining)
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Job #1, processed 5370/10000 permutations (53.70%, 16.08251133488987 seconds remaining)
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Job #1, processed 5390/10000 permutations (53.90%, 16.111571027971596 seconds remaining)
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Job #1, processed 5450/10000 permutations (54.50%, 15.967722030954624 seconds remaining)
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Job #1, processed 5480/10000 permutations (54.80%, 15.850570563852354 seconds remaining)
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Job #1, processed 5690/10000 permutations (56.90%, 15.138391542099484 seconds remaining)
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Job #1, processed 5760/10000 permutations (57.60%, 15.00084219707383 seconds remaining)
Job #1, processed 5770/10000 permutations (57.70%, 14.964196581154596 seconds remaining)
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Job #1, processed 5920/10000 permutations (59.20%, 14.704600163408227 seconds remaining)
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Job #1, processed 5960/10000 permutations (59.60%, 14.570175967760532 seconds remaining)
Job #1, processed 5970/10000 permutations (59.70%, 14.587189424776751 seconds remaining)
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Job #1, processed 6000/10000 permutations (60.00%, 14.53808291753133 seconds remaining)
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Job #1, processed 6060/10000 permutations (60.60%, 14.33672840130998 seconds remaining)
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Job #1, processed 6100/10000 permutations (61.00%, 14.212879810176913 seconds remaining)
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Job #1, processed 6270/10000 permutations (62.70%, 14.080609590813301 seconds remaining)
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Job #1, processed 6290/10000 permutations (62.90%, 14.016109096605941 seconds remaining)
Job #1, processed 6300/10000 permutations (63.00%, 13.987179495039442 seconds remaining)
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Job #1, processed 6360/10000 permutations (63.60%, 13.839818224217156 seconds remaining)
Job #1, processed 6370/10000 permutations (63.70%, 13.81122500368714 seconds remaining)
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Job #1, processed 6390/10000 permutations (63.90%, 13.743837874819976 seconds remaining)
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Job #1, processed 6560/10000 permutations (65.60%, 13.360410844407435 seconds remaining)
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Job #1, processed 6800/10000 permutations (68.00%, 12.429609298706055 seconds remaining)
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Job #1, processed 7000/10000 permutations (70.00%, 11.675904239927018 seconds remaining)
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Job #1, processed 7370/10000 permutations (73.70%, 10.277852650413356 seconds remaining)
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Job #1, processed 7390/10000 permutations (73.90%, 10.195160426370826 seconds remaining)
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scikit-learn F-scores for comparison

F-test does not allow to observe the effect sign (pure two-sided test)

from sklearn.feature_selection import f_regression

# f_regression implicitly adds intercept
_, pvals_bonferroni = f_regression(
    grouped_fmri_masked, grouped_conditions_encoded
)
pvals_bonferroni *= fmri_masked.shape[1]
pvals_bonferroni[np.isnan(pvals_bonferroni)] = 1
pvals_bonferroni[pvals_bonferroni > 1] = 1
neg_log_pvals_bonferroni = -np.log10(pvals_bonferroni)
neg_log_pvals_bonferroni_unmasked = nifti_masker.inverse_transform(
    neg_log_pvals_bonferroni
)

/home/remi/github/nilearn/env/lib/python3.11/site-packages/sklearn/utils/validation.py:1183: DataConversionWarning:

A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().

Visualization

import matplotlib.pyplot as plt

from nilearn.image import get_data
from nilearn.plotting import plot_stat_map, show

# Use the fmri mean image as a surrogate of anatomical data
mean_fmri_img = image.mean_img(func_filename)

threshold = -np.log10(0.1)  # 10% corrected

vmax = min(signed_neg_log_pvals.max(), neg_log_pvals_bonferroni.max())

# Plot thresholded p-values map corresponding to F-scores
display = plot_stat_map(
    neg_log_pvals_bonferroni_unmasked,
    mean_fmri_img,
    threshold=threshold,
    cmap=plt.cm.RdBu_r,
    display_mode="z",
    cut_coords=[-1],
    vmax=vmax,
)

neg_log_pvals_bonferroni_data = get_data(neg_log_pvals_bonferroni_unmasked)
n_detections = (neg_log_pvals_bonferroni_data > threshold).sum()
title = (
    "Negative $\\log_{10}$ p-values"
    "\n(Parametric two-sided F-test"
    "\n+ Bonferroni correction)"
    f"\n{n_detections} detections"
)

display.title(title, size=10)

# Plot permutation p-values map
display = plot_stat_map(
    signed_neg_log_pvals_unmasked,
    mean_fmri_img,
    threshold=threshold,
    cmap=plt.cm.RdBu_r,
    display_mode="z",
    cut_coords=[-1],
    vmax=vmax,
)

n_detections = (np.abs(signed_neg_log_pvals) > threshold).sum()
title = (
    "Negative $\\log_{10}$ p-values"
    "\n(Non-parametric two-sided test"
    "\n+ max-type correction)"
    f"\n{n_detections} detections"
)

display.title(title, size=10)

show()

• 
• 

Estimated memory usage: 949 MB