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

```
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Job #1, processed 2360/10000 permutations (23.60%, 19.822246838424167 seconds remaining)
Job #1, processed 2370/10000 permutations (23.70%, 19.80897349647329 seconds remaining)
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Job #1, processed 2390/10000 permutations (23.90%, 19.776666224252228 seconds remaining)
Job #1, processed 2400/10000 permutations (24.00%, 19.74250308672587 seconds remaining)
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Job #1, processed 2480/10000 permutations (24.80%, 19.595540046691895 seconds remaining)
Job #1, processed 2490/10000 permutations (24.90%, 19.573463186202755 seconds remaining)
Job #1, processed 2500/10000 permutations (25.00%, 19.537829160690308 seconds remaining)
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Job #1, processed 2540/10000 permutations (25.40%, 19.428964637395904 seconds remaining)
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Job #1, processed 2640/10000 permutations (26.40%, 19.236429705764305 seconds remaining)
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Job #1, processed 2680/10000 permutations (26.80%, 19.14029748404204 seconds remaining)
Job #1, processed 2690/10000 permutations (26.90%, 19.13953704993521 seconds remaining)
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Job #1, processed 2840/10000 permutations (28.40%, 18.753101886158255 seconds remaining)
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Job #1, processed 2940/10000 permutations (29.40%, 18.45970230037663 seconds remaining)
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Job #1, processed 2960/10000 permutations (29.60%, 18.449296487344277 seconds remaining)
Job #1, processed 2970/10000 permutations (29.70%, 18.41564448192866 seconds remaining)
Job #1, processed 2980/10000 permutations (29.80%, 18.38011577785415 seconds remaining)
Job #1, processed 2990/10000 permutations (29.90%, 18.35625837718364 seconds remaining)
Job #1, processed 3000/10000 permutations (30.00%, 18.32162650426229 seconds remaining)
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Job #1, processed 3030/10000 permutations (30.30%, 18.247320557584857 seconds remaining)
Job #1, processed 3040/10000 permutations (30.40%, 18.238773427511514 seconds remaining)
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Job #1, processed 3060/10000 permutations (30.60%, 18.20283067927641 seconds remaining)
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Job #1, processed 3080/10000 permutations (30.80%, 18.137290530390555 seconds remaining)
Job #1, processed 3090/10000 permutations (30.90%, 18.10210289924276 seconds remaining)
Job #1, processed 3100/10000 permutations (31.00%, 18.07727611449457 seconds remaining)
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Job #1, processed 3120/10000 permutations (31.20%, 18.043527529789852 seconds remaining)
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Job #1, processed 3140/10000 permutations (31.40%, 17.976422063863957 seconds remaining)
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Job #1, processed 3200/10000 permutations (32.00%, 17.823137670755386 seconds remaining)
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Job #1, processed 3220/10000 permutations (32.20%, 17.791194952793 seconds remaining)
Job #1, processed 3230/10000 permutations (32.30%, 17.75919924579538 seconds remaining)
Job #1, processed 3240/10000 permutations (32.40%, 17.72287952458417 seconds remaining)
Job #1, processed 3250/10000 permutations (32.50%, 17.688266900869518 seconds remaining)
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Job #1, processed 3270/10000 permutations (32.70%, 17.664277444921133 seconds remaining)
Job #1, processed 3280/10000 permutations (32.80%, 17.63067738602801 seconds remaining)
Job #1, processed 3290/10000 permutations (32.90%, 17.617303125764096 seconds remaining)
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Job #1, processed 3340/10000 permutations (33.40%, 17.467840120464025 seconds remaining)
Job #1, processed 3350/10000 permutations (33.50%, 17.434130942643577 seconds remaining)
Job #1, processed 3360/10000 permutations (33.60%, 17.399356058665685 seconds remaining)
Job #1, processed 3370/10000 permutations (33.70%, 17.375390581278133 seconds remaining)
Job #1, processed 3380/10000 permutations (33.80%, 17.342861126160482 seconds remaining)
Job #1, processed 3390/10000 permutations (33.90%, 17.31038754949879 seconds remaining)
Job #1, processed 3400/10000 permutations (34.00%, 17.27485972292283 seconds remaining)
Job #1, processed 3410/10000 permutations (34.10%, 17.250455071150032 seconds remaining)
Job #1, processed 3420/10000 permutations (34.20%, 17.228226901494967 seconds remaining)
Job #1, processed 3430/10000 permutations (34.30%, 17.195007091360957 seconds remaining)
Job #1, processed 3440/10000 permutations (34.40%, 17.161516744037005 seconds remaining)
Job #1, processed 3450/10000 permutations (34.50%, 17.135857181272645 seconds remaining)
Job #1, processed 3460/10000 permutations (34.60%, 17.104259453756963 seconds remaining)
Job #1, processed 3470/10000 permutations (34.70%, 17.071466827942242 seconds remaining)
Job #1, processed 3480/10000 permutations (34.80%, 17.03880231955956 seconds remaining)
Job #1, processed 3490/10000 permutations (34.90%, 17.012823374018627 seconds remaining)
Job #1, processed 3500/10000 permutations (35.00%, 16.994707686560496 seconds remaining)
Job #1, processed 3510/10000 permutations (35.10%, 16.960683777121737 seconds remaining)
Job #1, processed 3520/10000 permutations (35.20%, 16.927479808980767 seconds remaining)
Job #1, processed 3530/10000 permutations (35.30%, 16.91541185122374 seconds remaining)
Job #1, processed 3540/10000 permutations (35.40%, 16.88398670342009 seconds remaining)
Job #1, processed 3550/10000 permutations (35.50%, 16.849676259806458 seconds remaining)
Job #1, processed 3560/10000 permutations (35.60%, 16.81668691152937 seconds remaining)
Job #1, processed 3570/10000 permutations (35.70%, 16.791540967316184 seconds remaining)
Job #1, processed 3580/10000 permutations (35.80%, 16.79074400896467 seconds remaining)
Job #1, processed 3590/10000 permutations (35.90%, 16.75792756386122 seconds remaining)
Job #1, processed 3600/10000 permutations (36.00%, 16.72556601630317 seconds remaining)
Job #1, processed 3610/10000 permutations (36.10%, 16.691863939702674 seconds remaining)
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Job #1, processed 3640/10000 permutations (36.40%, 16.60437201143621 seconds remaining)
Job #1, processed 3650/10000 permutations (36.50%, 16.570917122984586 seconds remaining)
Job #1, processed 3660/10000 permutations (36.60%, 16.55700494031437 seconds remaining)
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Job #1, processed 3690/10000 permutations (36.90%, 16.501850152080298 seconds remaining)
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Job #1, processed 3760/10000 permutations (37.60%, 16.31606136484349 seconds remaining)
Job #1, processed 3770/10000 permutations (37.70%, 16.29342086372072 seconds remaining)
Job #1, processed 3780/10000 permutations (37.80%, 16.28234397923505 seconds remaining)
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Job #1, processed 3800/10000 permutations (38.00%, 16.257844222219365 seconds remaining)
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Job #1, processed 3820/10000 permutations (38.20%, 16.222723575162636 seconds remaining)
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Job #1, processed 3840/10000 permutations (38.40%, 16.16088157395522 seconds remaining)
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Job #1, processed 3860/10000 permutations (38.60%, 16.10548803102167 seconds remaining)
Job #1, processed 3870/10000 permutations (38.70%, 16.091978577680365 seconds remaining)
Job #1, processed 3880/10000 permutations (38.80%, 16.105748515768152 seconds remaining)
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Job #1, processed 3900/10000 permutations (39.00%, 16.04155081969041 seconds remaining)
Job #1, processed 3910/10000 permutations (39.10%, 16.008705508678464 seconds remaining)
Job #1, processed 3920/10000 permutations (39.20%, 15.98601185545629 seconds remaining)
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Job #1, processed 3940/10000 permutations (39.40%, 15.933645268987279 seconds remaining)
Job #1, processed 3950/10000 permutations (39.50%, 15.908274756202214 seconds remaining)
Job #1, processed 3960/10000 permutations (39.60%, 15.886918494195648 seconds remaining)
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Job #1, processed 3980/10000 permutations (39.80%, 15.847527022337797 seconds remaining)
Job #1, processed 3990/10000 permutations (39.90%, 15.814676196354077 seconds remaining)
Job #1, processed 4000/10000 permutations (40.00%, 15.78954792022705 seconds remaining)
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Job #1, processed 4060/10000 permutations (40.60%, 15.637238210057976 seconds remaining)
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Job #1, processed 4080/10000 permutations (40.80%, 15.575831553515268 seconds remaining)
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Job #1, processed 4100/10000 permutations (41.00%, 15.52933064902701 seconds remaining)
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Job #1, processed 4120/10000 permutations (41.20%, 15.476834584208365 seconds remaining)
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Job #1, processed 4200/10000 permutations (42.00%, 15.24771077292306 seconds remaining)
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Job #1, processed 4220/10000 permutations (42.20%, 15.18480144631806 seconds remaining)
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Job #1, processed 4240/10000 permutations (42.40%, 15.140301542462044 seconds remaining)
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Job #1, processed 4370/10000 permutations (43.70%, 14.807560611916898 seconds remaining)
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Job #1, processed 4390/10000 permutations (43.90%, 14.767774700303828 seconds remaining)
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Job #1, processed 5220/10000 permutations (52.20%, 12.749842011608838 seconds remaining)
Job #1, processed 5230/10000 permutations (52.30%, 12.72465388314446 seconds remaining)
Job #1, processed 5240/10000 permutations (52.40%, 12.693834736147 seconds remaining)
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Job #1, processed 5270/10000 permutations (52.70%, 12.654559259848982 seconds remaining)
Job #1, processed 5280/10000 permutations (52.80%, 12.632315371975755 seconds remaining)
Job #1, processed 5290/10000 permutations (52.90%, 12.614861715944143 seconds remaining)
Job #1, processed 5300/10000 permutations (53.00%, 12.631569974827316 seconds remaining)
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Job #1, processed 5320/10000 permutations (53.20%, 12.63946911625396 seconds remaining)
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Job #1, processed 5360/10000 permutations (53.60%, 12.599702408064656 seconds remaining)
Job #1, processed 5370/10000 permutations (53.70%, 12.582569864653118 seconds remaining)
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Job #1, processed 5390/10000 permutations (53.90%, 12.555102407158195 seconds remaining)
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Job #1, processed 5500/10000 permutations (55.00%, 12.42412929101424 seconds remaining)
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Job #1, processed 5520/10000 permutations (55.20%, 12.446583125902258 seconds remaining)
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Job #1, processed 5580/10000 permutations (55.80%, 12.400384430389678 seconds remaining)
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Job #1, processed 5600/10000 permutations (56.00%, 12.352137071745735 seconds remaining)
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Job #1, processed 5620/10000 permutations (56.20%, 12.294487069934288 seconds remaining)
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Job #1, processed 5680/10000 permutations (56.80%, 12.205306140469835 seconds remaining)
Job #1, processed 5690/10000 permutations (56.90%, 12.183133422385621 seconds remaining)
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Job #1, processed 5720/10000 permutations (57.20%, 12.120476139175306 seconds remaining)
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Job #1, processed 5870/10000 permutations (58.70%, 11.737620490576175 seconds remaining)
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Job #1, processed 5910/10000 permutations (59.10%, 11.619310771955046 seconds remaining)
Job #1, processed 5920/10000 permutations (59.20%, 11.591277934409476 seconds remaining)
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Job #1, processed 5940/10000 permutations (59.40%, 11.527419673071968 seconds remaining)
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Job #1, processed 5970/10000 permutations (59.70%, 11.449594944565739 seconds remaining)
Job #1, processed 5980/10000 permutations (59.80%, 11.417608474807997 seconds remaining)
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Job #1, processed 6000/10000 permutations (60.00%, 11.359352429707844 seconds remaining)
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Job #1, processed 6060/10000 permutations (60.60%, 11.173671869554928 seconds remaining)
Job #1, processed 6070/10000 permutations (60.70%, 11.163536628349215 seconds remaining)
Job #1, processed 6080/10000 permutations (60.80%, 11.145858275262935 seconds remaining)
Job #1, processed 6090/10000 permutations (60.90%, 11.116283808631458 seconds remaining)
Job #1, processed 6100/10000 permutations (61.00%, 11.088012750031519 seconds remaining)
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Job #1, processed 6120/10000 permutations (61.20%, 11.040292373669692 seconds remaining)
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Job #1, processed 6140/10000 permutations (61.40%, 10.982262584984497 seconds remaining)
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Job #1, processed 6180/10000 permutations (61.80%, 10.86523781933831 seconds remaining)
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Job #1, processed 6200/10000 permutations (62.00%, 10.806225830508817 seconds remaining)
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Job #1, processed 6220/10000 permutations (62.20%, 10.74191768453052 seconds remaining)
Job #1, processed 6230/10000 permutations (62.30%, 10.71021334355754 seconds remaining)
Job #1, processed 6240/10000 permutations (62.40%, 10.68551822197743 seconds remaining)
Job #1, processed 6250/10000 permutations (62.50%, 10.653594017028809 seconds remaining)
Job #1, processed 6260/10000 permutations (62.60%, 10.621137315853716 seconds remaining)
Job #1, processed 6270/10000 permutations (62.70%, 10.589647834570973 seconds remaining)
Job #1, processed 6280/10000 permutations (62.80%, 10.560873880507842 seconds remaining)
Job #1, processed 6290/10000 permutations (62.90%, 10.529486167980492 seconds remaining)
Job #1, processed 6300/10000 permutations (63.00%, 10.497248683656965 seconds remaining)
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Job #1, processed 6320/10000 permutations (63.20%, 10.445467924769918 seconds remaining)
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Job #1, processed 6340/10000 permutations (63.40%, 10.399473247467908 seconds remaining)
Job #1, processed 6350/10000 permutations (63.50%, 10.37337194840739 seconds remaining)
Job #1, processed 6360/10000 permutations (63.60%, 10.348516467232374 seconds remaining)
Job #1, processed 6370/10000 permutations (63.70%, 10.32264399491075 seconds remaining)
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Job #1, processed 6390/10000 permutations (63.90%, 10.275636871469226 seconds remaining)
Job #1, processed 6400/10000 permutations (64.00%, 10.249181315302849 seconds remaining)
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Job #1, processed 6420/10000 permutations (64.20%, 10.195639986858188 seconds remaining)
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Job #1, processed 6470/10000 permutations (64.70%, 10.07383598242145 seconds remaining)
Job #1, processed 6480/10000 permutations (64.80%, 10.04875393855719 seconds remaining)
Job #1, processed 6490/10000 permutations (64.90%, 10.020637622783287 seconds remaining)
Job #1, processed 6500/10000 permutations (65.00%, 9.988789521730864 seconds remaining)
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Job #1, processed 6520/10000 permutations (65.20%, 9.927787121088226 seconds remaining)
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Job #1, processed 6560/10000 permutations (65.60%, 9.802619282792257 seconds remaining)
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Job #1, processed 6580/10000 permutations (65.80%, 9.746589341062183 seconds remaining)
Job #1, processed 6590/10000 permutations (65.90%, 9.723143817079626 seconds remaining)
Job #1, processed 6600/10000 permutations (66.00%, 9.69533853819876 seconds remaining)
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Job #1, processed 6670/10000 permutations (66.70%, 9.483524108040278 seconds remaining)
Job #1, processed 6680/10000 permutations (66.80%, 9.454636863605707 seconds remaining)
Job #1, processed 6690/10000 permutations (66.90%, 9.423488897058458 seconds remaining)
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Job #1, processed 6720/10000 permutations (67.20%, 9.340153197447458 seconds remaining)
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Job #1, processed 6760/10000 permutations (67.60%, 9.214090812841112 seconds remaining)
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Job #1, processed 6780/10000 permutations (67.80%, 9.166852873686844 seconds remaining)
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Job #1, processed 6820/10000 permutations (68.20%, 9.05907320207165 seconds remaining)
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Job #1, processed 7000/10000 permutations (70.00%, 8.606587375913348 seconds remaining)
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Job #1, processed 7070/10000 permutations (70.70%, 8.395002688848988 seconds remaining)
Job #1, processed 7080/10000 permutations (70.80%, 8.365434976620863 seconds remaining)
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Job #1, processed 7100/10000 permutations (71.00%, 8.303148571874054 seconds remaining)
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Job #1, processed 7240/10000 permutations (72.40%, 7.892590011680981 seconds remaining)
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Job #1, processed 7370/10000 permutations (73.70%, 7.50678466230105 seconds remaining)
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Job #1, processed 7390/10000 permutations (73.90%, 7.450511484571978 seconds remaining)
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[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 28.7s 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
)
```

```
/home/yasmin/miniconda3/envs/nilearn-dev/lib/python3.10/site-packages/sklearn/utils/validation.py:1141: 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 48.699 seconds)

**Estimated memory usage:** 945 MB