Note

Go to the end to download the full example code or to run this example in your browser via Binder

# 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)

```
# Author: Virgile Fritsch, <virgile.fritsch@inria.fr>, Feb. 2014
```

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/runner/work/nilearn/nilearn/nilearn_data/haxby2001/mask.nii.gz
Functional nifti image (4D) is located at: /home/runner/work/nilearn/nilearn/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
)
```

```
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
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Job #1, processed 2350/10000 permutations (23.50%, 7.653558239023736 seconds remaining)
Job #1, processed 2360/10000 permutations (23.60%, 7.643992335109388 seconds remaining)
Job #1, processed 2370/10000 permutations (23.70%, 7.6333976506180905 seconds remaining)
Job #1, processed 2380/10000 permutations (23.80%, 7.6242872847228496 seconds remaining)
Job #1, processed 2390/10000 permutations (23.90%, 7.6135083601564535 seconds remaining)
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Job #1, processed 2430/10000 permutations (24.30%, 7.575410237528169 seconds remaining)
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Job #1, processed 2470/10000 permutations (24.70%, 7.537149273914847 seconds remaining)
Job #1, processed 2480/10000 permutations (24.80%, 7.527697270916354 seconds remaining)
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Job #1, processed 2500/10000 permutations (25.00%, 7.507174730300903 seconds remaining)
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Job #1, processed 2530/10000 permutations (25.30%, 7.47897172445365 seconds remaining)
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Job #1, processed 2580/10000 permutations (25.80%, 7.429536965466285 seconds remaining)
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Job #1, processed 2620/10000 permutations (26.20%, 7.390622666773906 seconds remaining)
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Job #1, processed 2680/10000 permutations (26.80%, 7.338164187189359 seconds remaining)
Job #1, processed 2690/10000 permutations (26.90%, 7.327831544840646 seconds remaining)
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Job #1, processed 2780/10000 permutations (27.80%, 7.2428757321062704 seconds remaining)
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Job #1, processed 2820/10000 permutations (28.20%, 7.20324875446076 seconds remaining)
Job #1, processed 2830/10000 permutations (28.30%, 7.195327618939296 seconds remaining)
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Job #1, processed 2870/10000 permutations (28.70%, 7.15687688385568 seconds remaining)
Job #1, processed 2880/10000 permutations (28.80%, 7.148526032765707 seconds remaining)
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Job #1, processed 2900/10000 permutations (29.00%, 7.128731242541608 seconds remaining)
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Job #1, processed 2920/10000 permutations (29.20%, 7.108802612513712 seconds remaining)
Job #1, processed 2930/10000 permutations (29.30%, 7.099090039119786 seconds remaining)
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Job #1, processed 2960/10000 permutations (29.60%, 7.071589856534391 seconds remaining)
Job #1, processed 2970/10000 permutations (29.70%, 7.061325318082815 seconds remaining)
Job #1, processed 2980/10000 permutations (29.80%, 7.052032835531555 seconds remaining)
Job #1, processed 2990/10000 permutations (29.90%, 7.042297191843141 seconds remaining)
Job #1, processed 3000/10000 permutations (30.00%, 7.030979235967001 seconds remaining)
Job #1, processed 3010/10000 permutations (30.10%, 7.021231379619865 seconds remaining)
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Job #1, processed 3030/10000 permutations (30.30%, 7.001152503608477 seconds remaining)
Job #1, processed 3040/10000 permutations (30.40%, 6.992865179714403 seconds remaining)
Job #1, processed 3050/10000 permutations (30.50%, 6.981631923894414 seconds remaining)
Job #1, processed 3060/10000 permutations (30.60%, 6.972692771674761 seconds remaining)
Job #1, processed 3070/10000 permutations (30.70%, 6.961908547031763 seconds remaining)
Job #1, processed 3080/10000 permutations (30.80%, 6.952108822859727 seconds remaining)
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Job #1, processed 3100/10000 permutations (31.00%, 6.933580283195741 seconds remaining)
Job #1, processed 3110/10000 permutations (31.10%, 6.924765934131537 seconds remaining)
Job #1, processed 3120/10000 permutations (31.20%, 6.9160804748535165 seconds remaining)
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Job #1, processed 3140/10000 permutations (31.40%, 6.896602203891534 seconds remaining)
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Job #1, processed 3200/10000 permutations (32.00%, 6.834590405225754 seconds remaining)
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Job #1, processed 3220/10000 permutations (32.20%, 6.814216681889124 seconds remaining)
Job #1, processed 3230/10000 permutations (32.30%, 6.804467188684565 seconds remaining)
Job #1, processed 3240/10000 permutations (32.40%, 6.79463486318235 seconds remaining)
Job #1, processed 3250/10000 permutations (32.50%, 6.783974592502301 seconds remaining)
Job #1, processed 3260/10000 permutations (32.60%, 6.775087985524371 seconds remaining)
Job #1, processed 3270/10000 permutations (32.70%, 6.76427614506596 seconds remaining)
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Job #1, processed 3290/10000 permutations (32.90%, 6.74540095995987 seconds remaining)
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Job #1, processed 3310/10000 permutations (33.10%, 6.725660875844812 seconds remaining)
Job #1, processed 3320/10000 permutations (33.20%, 6.715690265218894 seconds remaining)
Job #1, processed 3330/10000 permutations (33.30%, 6.706044602322508 seconds remaining)
Job #1, processed 3340/10000 permutations (33.40%, 6.6964566065165805 seconds remaining)
Job #1, processed 3350/10000 permutations (33.50%, 6.6864607262967235 seconds remaining)
Job #1, processed 3360/10000 permutations (33.60%, 6.6765232142947974 seconds remaining)
Job #1, processed 3370/10000 permutations (33.70%, 6.666502100070081 seconds remaining)
Job #1, processed 3380/10000 permutations (33.80%, 6.657022826064974 seconds remaining)
Job #1, processed 3390/10000 permutations (33.90%, 6.647788526737584 seconds remaining)
Job #1, processed 3400/10000 permutations (34.00%, 6.637087204877068 seconds remaining)
Job #1, processed 3410/10000 permutations (34.10%, 6.627462404564329 seconds remaining)
Job #1, processed 3420/10000 permutations (34.20%, 6.617301670431393 seconds remaining)
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Job #1, processed 3440/10000 permutations (34.40%, 6.598523794218551 seconds remaining)
Job #1, processed 3450/10000 permutations (34.50%, 6.587968352912129 seconds remaining)
Job #1, processed 3460/10000 permutations (34.60%, 6.57896663825636 seconds remaining)
Job #1, processed 3470/10000 permutations (34.70%, 6.568177100217307 seconds remaining)
Job #1, processed 3480/10000 permutations (34.80%, 6.55987134199033 seconds remaining)
Job #1, processed 3490/10000 permutations (34.90%, 6.5504748233751435 seconds remaining)
Job #1, processed 3500/10000 permutations (35.00%, 6.540579659598214 seconds remaining)
Job #1, processed 3510/10000 permutations (35.10%, 6.531301525583295 seconds remaining)
Job #1, processed 3520/10000 permutations (35.20%, 6.521944544532081 seconds remaining)
Job #1, processed 3530/10000 permutations (35.30%, 6.5121457076950735 seconds remaining)
Job #1, processed 3540/10000 permutations (35.40%, 6.5027770187895175 seconds remaining)
Job #1, processed 3550/10000 permutations (35.50%, 6.492443621998102 seconds remaining)
Job #1, processed 3560/10000 permutations (35.60%, 6.4824450819679855 seconds remaining)
Job #1, processed 3570/10000 permutations (35.70%, 6.472459268837081 seconds remaining)
Job #1, processed 3580/10000 permutations (35.80%, 6.462654898286532 seconds remaining)
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Job #1, processed 3600/10000 permutations (36.00%, 6.443160163031684 seconds remaining)
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Job #1, processed 3620/10000 permutations (36.20%, 6.424626324058237 seconds remaining)
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Job #1, processed 3650/10000 permutations (36.50%, 6.3953803304123555 seconds remaining)
Job #1, processed 3660/10000 permutations (36.60%, 6.385469196924094 seconds remaining)
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Job #1, processed 3680/10000 permutations (36.80%, 6.365276341852936 seconds remaining)
Job #1, processed 3690/10000 permutations (36.90%, 6.35582745947489 seconds remaining)
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Job #1, processed 3720/10000 permutations (37.20%, 6.328033393429171 seconds remaining)
Job #1, processed 3730/10000 permutations (37.30%, 6.317286474775054 seconds remaining)
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Job #1, processed 3760/10000 permutations (37.60%, 6.2877189859430835 seconds remaining)
Job #1, processed 3770/10000 permutations (37.70%, 6.27791326811206 seconds remaining)
Job #1, processed 3780/10000 permutations (37.80%, 6.267550904914817 seconds remaining)
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Job #1, processed 3800/10000 permutations (38.00%, 6.247327842210469 seconds remaining)
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Job #1, processed 3840/10000 permutations (38.40%, 6.209417159358661 seconds remaining)
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Job #1, processed 3860/10000 permutations (38.60%, 6.189467561059665 seconds remaining)
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Job #1, processed 3900/10000 permutations (39.00%, 6.151621861335559 seconds remaining)
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Job #1, processed 3960/10000 permutations (39.60%, 6.095771380145139 seconds remaining)
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Job #1, processed 3990/10000 permutations (39.90%, 6.068163008916946 seconds remaining)
Job #1, processed 4000/10000 permutations (40.00%, 6.059394836425781 seconds remaining)
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Job #1, processed 4030/10000 permutations (40.30%, 6.030639285780952 seconds remaining)
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Job #1, processed 4050/10000 permutations (40.50%, 6.011243811360112 seconds remaining)
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Job #1, processed 4080/10000 permutations (40.80%, 5.981898017958099 seconds remaining)
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Job #1, processed 4100/10000 permutations (41.00%, 5.963965590407208 seconds remaining)
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Job #1, processed 4120/10000 permutations (41.20%, 5.943735643497948 seconds remaining)
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Job #1, processed 4140/10000 permutations (41.40%, 5.92414643338337 seconds remaining)
Job #1, processed 4150/10000 permutations (41.50%, 5.91430309019893 seconds remaining)
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Job #1, processed 4170/10000 permutations (41.70%, 5.89410186557175 seconds remaining)
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Job #1, processed 4240/10000 permutations (42.40%, 5.826200089364682 seconds remaining)
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Job #1, processed 4290/10000 permutations (42.90%, 5.776436078798521 seconds remaining)
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Job #1, processed 4370/10000 permutations (43.70%, 5.699740300735019 seconds remaining)
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Job #1, processed 4390/10000 permutations (43.90%, 5.680908020102082 seconds remaining)
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Job #1, processed 5100/10000 permutations (51.00%, 4.994224165000167 seconds remaining)
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Job #1, processed 5190/10000 permutations (51.90%, 4.906266395756275 seconds remaining)
Job #1, processed 5200/10000 permutations (52.00%, 4.896139658414401 seconds remaining)
Job #1, processed 5210/10000 permutations (52.10%, 4.8863501191825645 seconds remaining)
Job #1, processed 5220/10000 permutations (52.20%, 4.8766618706714135 seconds remaining)
Job #1, processed 5230/10000 permutations (52.30%, 4.867200666814188 seconds remaining)
Job #1, processed 5240/10000 permutations (52.40%, 4.857990395931798 seconds remaining)
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Job #1, processed 5260/10000 permutations (52.60%, 4.8380403863159875 seconds remaining)
Job #1, processed 5270/10000 permutations (52.70%, 4.828562700318656 seconds remaining)
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Job #1, processed 5300/10000 permutations (53.00%, 4.799066566071421 seconds remaining)
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Job #1, processed 5360/10000 permutations (53.60%, 4.7422042960551245 seconds remaining)
Job #1, processed 5370/10000 permutations (53.70%, 4.732461365907551 seconds remaining)
Job #1, processed 5380/10000 permutations (53.80%, 4.723030105399377 seconds remaining)
Job #1, processed 5390/10000 permutations (53.90%, 4.713491968852027 seconds remaining)
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Job #1, processed 5470/10000 permutations (54.70%, 4.634889502847869 seconds remaining)
Job #1, processed 5480/10000 permutations (54.80%, 4.62515190744052 seconds remaining)
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Job #1, processed 5520/10000 permutations (55.20%, 4.588353502577629 seconds remaining)
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Job #1, processed 5600/10000 permutations (56.00%, 4.509862508092608 seconds remaining)
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Job #1, processed 5660/10000 permutations (56.60%, 4.451850342666303 seconds remaining)
Job #1, processed 5670/10000 permutations (56.70%, 4.441697315774476 seconds remaining)
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Job #1, processed 5690/10000 permutations (56.90%, 4.421620234873258 seconds remaining)
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Job #1, processed 5770/10000 permutations (57.70%, 4.342678934077456 seconds remaining)
Job #1, processed 5780/10000 permutations (57.80%, 4.3327562866738925 seconds remaining)
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Job #1, processed 5870/10000 permutations (58.70%, 4.242249470959327 seconds remaining)
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Job #1, processed 5900/10000 permutations (59.00%, 4.212262165748467 seconds remaining)
Job #1, processed 5910/10000 permutations (59.10%, 4.2024042332031195 seconds remaining)
Job #1, processed 5920/10000 permutations (59.20%, 4.191986657477714 seconds remaining)
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Job #1, processed 5960/10000 permutations (59.60%, 4.152404493933555 seconds remaining)
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Job #1, processed 6060/10000 permutations (60.60%, 4.053646429930583 seconds remaining)
Job #1, processed 6070/10000 permutations (60.70%, 4.043427935934931 seconds remaining)
Job #1, processed 6080/10000 permutations (60.80%, 4.033075122456802 seconds remaining)
Job #1, processed 6090/10000 permutations (60.90%, 4.02283918250762 seconds remaining)
Job #1, processed 6100/10000 permutations (61.00%, 4.0133456011287505 seconds remaining)
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Job #1, processed 6140/10000 permutations (61.40%, 3.9721922074544707 seconds remaining)
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Job #1, processed 6200/10000 permutations (62.00%, 3.9122490498327442 seconds remaining)
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Job #1, processed 6220/10000 permutations (62.20%, 3.891219823690089 seconds remaining)
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Job #1, processed 6240/10000 permutations (62.40%, 3.8700147194740104 seconds remaining)
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Job #1, processed 6270/10000 permutations (62.70%, 3.8383899316833343 seconds remaining)
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Job #1, processed 6300/10000 permutations (63.00%, 3.806685220627558 seconds remaining)
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Job #1, processed 6360/10000 permutations (63.60%, 3.74272205994564 seconds remaining)
Job #1, processed 6370/10000 permutations (63.70%, 3.7324204703140853 seconds remaining)
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Job #1, processed 6390/10000 permutations (63.90%, 3.711212749585673 seconds remaining)
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Job #1, processed 6760/10000 permutations (67.60%, 3.3343859593543788 seconds remaining)
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[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 10.3s finished
```

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
)
```

```
/usr/share/miniconda3/envs/testenv/lib/python3.9/site-packages/sklearn/utils/validation.py:1143: 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, y=1.1)
# 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, y=1.1)
show()
```

**Total running time of the script:** ( 0 minutes 26.565 seconds)

**Estimated memory usage:** 1016 MB