Note

Click here to download the full example code or to run this example in your browser via Binder

# 9.8.9. 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.

## 9.8.9.1. 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('Mask nifti image (3D) is located at: %s' % haxby_dataset.mask)
print('Functional nifti image (4D) is located at: %s' % haxby_dataset.func[0])
```

Out:

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

```
mask_filename = haxby_dataset.mask
from nilearn.image import index_img
from nilearn.input_data import NiftiMasker
nifti_masker = NiftiMasker(
smoothing_fwhm=8,
mask_img=mask_filename,
memory='nilearn_cache', memory_level=1) # cache options
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
grouped_fmri_masked = np.empty((2 * n_sessions, # two conditions per session
fmri_masked.shape[1]))
grouped_conditions_encoded = np.empty((2 * 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
neg_log_pvals, t_scores_original_data, _ = permuted_ols(
grouped_conditions_encoded, grouped_fmri_masked,
# + intercept as a covariate by default
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)
```

Out:

```
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Job #1, processed 3260/10000 permutations (32.60%, 8 seconds remaining)
Job #1, processed 3270/10000 permutations (32.70%, 8 seconds remaining)
Job #1, processed 3280/10000 permutations (32.80%, 8 seconds remaining)
Job #1, processed 3290/10000 permutations (32.90%, 8 seconds remaining)
Job #1, processed 3300/10000 permutations (33.00%, 8 seconds remaining)
Job #1, processed 3310/10000 permutations (33.10%, 8 seconds remaining)
Job #1, processed 3320/10000 permutations (33.20%, 8 seconds remaining)
Job #1, processed 3330/10000 permutations (33.30%, 8 seconds remaining)
Job #1, processed 3340/10000 permutations (33.40%, 8 seconds remaining)
Job #1, processed 3350/10000 permutations (33.50%, 8 seconds remaining)
Job #1, processed 3360/10000 permutations (33.60%, 8 seconds remaining)
Job #1, processed 3370/10000 permutations (33.70%, 8 seconds remaining)
Job #1, processed 3380/10000 permutations (33.80%, 8 seconds remaining)
Job #1, processed 3390/10000 permutations (33.90%, 8 seconds remaining)
Job #1, processed 3400/10000 permutations (34.00%, 8 seconds remaining)
Job #1, processed 3410/10000 permutations (34.10%, 8 seconds remaining)
Job #1, processed 3420/10000 permutations (34.20%, 8 seconds remaining)
Job #1, processed 3430/10000 permutations (34.30%, 8 seconds remaining)
Job #1, processed 3440/10000 permutations (34.40%, 8 seconds remaining)
Job #1, processed 3450/10000 permutations (34.50%, 8 seconds remaining)
Job #1, processed 3460/10000 permutations (34.60%, 8 seconds remaining)
Job #1, processed 3470/10000 permutations (34.70%, 8 seconds remaining)
Job #1, processed 3480/10000 permutations (34.80%, 8 seconds remaining)
Job #1, processed 3490/10000 permutations (34.90%, 8 seconds remaining)
Job #1, processed 3500/10000 permutations (35.00%, 8 seconds remaining)
Job #1, processed 3510/10000 permutations (35.10%, 8 seconds remaining)
Job #1, processed 3520/10000 permutations (35.20%, 8 seconds remaining)
Job #1, processed 3530/10000 permutations (35.30%, 8 seconds remaining)
Job #1, processed 3540/10000 permutations (35.40%, 8 seconds remaining)
Job #1, processed 3550/10000 permutations (35.50%, 8 seconds remaining)
Job #1, processed 3560/10000 permutations (35.60%, 8 seconds remaining)
Job #1, processed 3570/10000 permutations (35.70%, 8 seconds remaining)
Job #1, processed 3580/10000 permutations (35.80%, 8 seconds remaining)
Job #1, processed 3590/10000 permutations (35.90%, 8 seconds remaining)
Job #1, processed 3600/10000 permutations (36.00%, 8 seconds remaining)
Job #1, processed 3610/10000 permutations (36.10%, 8 seconds remaining)
Job #1, processed 3620/10000 permutations (36.20%, 8 seconds remaining)
Job #1, processed 3630/10000 permutations (36.30%, 8 seconds remaining)
Job #1, processed 3640/10000 permutations (36.40%, 8 seconds remaining)
Job #1, processed 3650/10000 permutations (36.50%, 8 seconds remaining)
Job #1, processed 3660/10000 permutations (36.60%, 8 seconds remaining)
Job #1, processed 3670/10000 permutations (36.70%, 8 seconds remaining)
Job #1, processed 3680/10000 permutations (36.80%, 8 seconds remaining)
Job #1, processed 3690/10000 permutations (36.90%, 8 seconds remaining)
Job #1, processed 3700/10000 permutations (37.00%, 8 seconds remaining)
Job #1, processed 3710/10000 permutations (37.10%, 8 seconds remaining)
Job #1, processed 3720/10000 permutations (37.20%, 8 seconds remaining)
Job #1, processed 3730/10000 permutations (37.30%, 8 seconds remaining)
Job #1, processed 3740/10000 permutations (37.40%, 8 seconds remaining)
Job #1, processed 3750/10000 permutations (37.50%, 8 seconds remaining)
Job #1, processed 3760/10000 permutations (37.60%, 8 seconds remaining)
Job #1, processed 3770/10000 permutations (37.70%, 8 seconds remaining)
Job #1, processed 3780/10000 permutations (37.80%, 8 seconds remaining)
Job #1, processed 3790/10000 permutations (37.90%, 8 seconds remaining)
Job #1, processed 3800/10000 permutations (38.00%, 8 seconds remaining)
Job #1, processed 3810/10000 permutations (38.10%, 8 seconds remaining)
Job #1, processed 3820/10000 permutations (38.20%, 8 seconds remaining)
Job #1, processed 3830/10000 permutations (38.30%, 8 seconds remaining)
Job #1, processed 3840/10000 permutations (38.40%, 8 seconds remaining)
Job #1, processed 3850/10000 permutations (38.50%, 8 seconds remaining)
Job #1, processed 3860/10000 permutations (38.60%, 8 seconds remaining)
Job #1, processed 3870/10000 permutations (38.70%, 8 seconds remaining)
Job #1, processed 3880/10000 permutations (38.80%, 8 seconds remaining)
Job #1, processed 3890/10000 permutations (38.90%, 8 seconds remaining)
Job #1, processed 3900/10000 permutations (39.00%, 8 seconds remaining)
Job #1, processed 3910/10000 permutations (39.10%, 8 seconds remaining)
Job #1, processed 3920/10000 permutations (39.20%, 8 seconds remaining)
Job #1, processed 3930/10000 permutations (39.30%, 8 seconds remaining)
Job #1, processed 3940/10000 permutations (39.40%, 8 seconds remaining)
Job #1, processed 3950/10000 permutations (39.50%, 8 seconds remaining)
Job #1, processed 3960/10000 permutations (39.60%, 8 seconds remaining)
Job #1, processed 3970/10000 permutations (39.70%, 8 seconds remaining)
Job #1, processed 3980/10000 permutations (39.80%, 8 seconds remaining)
Job #1, processed 3990/10000 permutations (39.90%, 8 seconds remaining)
Job #1, processed 4000/10000 permutations (40.00%, 8 seconds remaining)
Job #1, processed 4010/10000 permutations (40.10%, 7 seconds remaining)
Job #1, processed 4020/10000 permutations (40.20%, 7 seconds remaining)
Job #1, processed 4030/10000 permutations (40.30%, 7 seconds remaining)
Job #1, processed 4040/10000 permutations (40.40%, 7 seconds remaining)
Job #1, processed 4050/10000 permutations (40.50%, 7 seconds remaining)
Job #1, processed 4060/10000 permutations (40.60%, 7 seconds remaining)
Job #1, processed 4070/10000 permutations (40.70%, 7 seconds remaining)
Job #1, processed 4080/10000 permutations (40.80%, 7 seconds remaining)
Job #1, processed 4090/10000 permutations (40.90%, 7 seconds remaining)
Job #1, processed 4100/10000 permutations (41.00%, 7 seconds remaining)
Job #1, processed 4110/10000 permutations (41.10%, 7 seconds remaining)
Job #1, processed 4120/10000 permutations (41.20%, 7 seconds remaining)
Job #1, processed 4130/10000 permutations (41.30%, 7 seconds remaining)
Job #1, processed 4140/10000 permutations (41.40%, 7 seconds remaining)
Job #1, processed 4150/10000 permutations (41.50%, 7 seconds remaining)
Job #1, processed 4160/10000 permutations (41.60%, 7 seconds remaining)
Job #1, processed 4170/10000 permutations (41.70%, 7 seconds remaining)
Job #1, processed 4180/10000 permutations (41.80%, 7 seconds remaining)
Job #1, processed 4190/10000 permutations (41.90%, 7 seconds remaining)
Job #1, processed 4200/10000 permutations (42.00%, 7 seconds remaining)
Job #1, processed 4210/10000 permutations (42.10%, 7 seconds remaining)
Job #1, processed 4220/10000 permutations (42.20%, 7 seconds remaining)
Job #1, processed 4230/10000 permutations (42.30%, 7 seconds remaining)
Job #1, processed 4240/10000 permutations (42.40%, 7 seconds remaining)
Job #1, processed 4250/10000 permutations (42.50%, 7 seconds remaining)
Job #1, processed 4260/10000 permutations (42.60%, 7 seconds remaining)
Job #1, processed 4270/10000 permutations (42.70%, 7 seconds remaining)
Job #1, processed 4280/10000 permutations (42.80%, 7 seconds remaining)
Job #1, processed 4290/10000 permutations (42.90%, 7 seconds remaining)
Job #1, processed 4300/10000 permutations (43.00%, 7 seconds remaining)
Job #1, processed 4310/10000 permutations (43.10%, 7 seconds remaining)
Job #1, processed 4320/10000 permutations (43.20%, 7 seconds remaining)
Job #1, processed 4330/10000 permutations (43.30%, 7 seconds remaining)
Job #1, processed 4340/10000 permutations (43.40%, 7 seconds remaining)
Job #1, processed 4350/10000 permutations (43.50%, 7 seconds remaining)
Job #1, processed 4360/10000 permutations (43.60%, 7 seconds remaining)
Job #1, processed 4370/10000 permutations (43.70%, 7 seconds remaining)
Job #1, processed 4380/10000 permutations (43.80%, 7 seconds remaining)
Job #1, processed 4390/10000 permutations (43.90%, 7 seconds remaining)
Job #1, processed 4400/10000 permutations (44.00%, 7 seconds remaining)
Job #1, processed 4410/10000 permutations (44.10%, 7 seconds remaining)
Job #1, processed 4420/10000 permutations (44.20%, 7 seconds remaining)
Job #1, processed 4430/10000 permutations (44.30%, 7 seconds remaining)
Job #1, processed 4440/10000 permutations (44.40%, 7 seconds remaining)
Job #1, processed 4450/10000 permutations (44.50%, 7 seconds remaining)
Job #1, processed 4460/10000 permutations (44.60%, 7 seconds remaining)
Job #1, processed 4470/10000 permutations (44.70%, 7 seconds remaining)
Job #1, processed 4480/10000 permutations (44.80%, 7 seconds remaining)
Job #1, processed 4490/10000 permutations (44.90%, 7 seconds remaining)
Job #1, processed 4500/10000 permutations (45.00%, 7 seconds remaining)
Job #1, processed 4510/10000 permutations (45.10%, 7 seconds remaining)
Job #1, processed 4520/10000 permutations (45.20%, 7 seconds remaining)
Job #1, processed 4530/10000 permutations (45.30%, 7 seconds remaining)
Job #1, processed 4540/10000 permutations (45.40%, 7 seconds remaining)
Job #1, processed 4550/10000 permutations (45.50%, 7 seconds remaining)
Job #1, processed 4560/10000 permutations (45.60%, 7 seconds remaining)
Job #1, processed 4570/10000 permutations (45.70%, 7 seconds remaining)
Job #1, processed 4580/10000 permutations (45.80%, 7 seconds remaining)
Job #1, processed 4590/10000 permutations (45.90%, 7 seconds remaining)
Job #1, processed 4600/10000 permutations (46.00%, 7 seconds remaining)
Job #1, processed 4610/10000 permutations (46.10%, 7 seconds remaining)
Job #1, processed 4620/10000 permutations (46.20%, 7 seconds remaining)
Job #1, processed 4630/10000 permutations (46.30%, 7 seconds remaining)
Job #1, processed 4640/10000 permutations (46.40%, 7 seconds remaining)
Job #1, processed 4650/10000 permutations (46.50%, 7 seconds remaining)
Job #1, processed 4660/10000 permutations (46.60%, 7 seconds remaining)
Job #1, processed 4670/10000 permutations (46.70%, 7 seconds remaining)
Job #1, processed 4680/10000 permutations (46.80%, 7 seconds remaining)
Job #1, processed 4690/10000 permutations (46.90%, 7 seconds remaining)
Job #1, processed 4700/10000 permutations (47.00%, 7 seconds remaining)
Job #1, processed 4710/10000 permutations (47.10%, 7 seconds remaining)
Job #1, processed 4720/10000 permutations (47.20%, 7 seconds remaining)
Job #1, processed 4730/10000 permutations (47.30%, 7 seconds remaining)
Job #1, processed 4740/10000 permutations (47.40%, 6 seconds remaining)
Job #1, processed 4750/10000 permutations (47.50%, 6 seconds remaining)
Job #1, processed 4760/10000 permutations (47.60%, 6 seconds remaining)
Job #1, processed 4770/10000 permutations (47.70%, 6 seconds remaining)
Job #1, processed 4780/10000 permutations (47.80%, 6 seconds remaining)
Job #1, processed 4790/10000 permutations (47.90%, 6 seconds remaining)
Job #1, processed 4800/10000 permutations (48.00%, 6 seconds remaining)
Job #1, processed 4810/10000 permutations (48.10%, 6 seconds remaining)
Job #1, processed 4820/10000 permutations (48.20%, 6 seconds remaining)
Job #1, processed 4830/10000 permutations (48.30%, 6 seconds remaining)
Job #1, processed 4840/10000 permutations (48.40%, 6 seconds remaining)
Job #1, processed 4850/10000 permutations (48.50%, 6 seconds remaining)
Job #1, processed 4860/10000 permutations (48.60%, 6 seconds remaining)
Job #1, processed 4870/10000 permutations (48.70%, 6 seconds remaining)
Job #1, processed 4880/10000 permutations (48.80%, 6 seconds remaining)
Job #1, processed 4890/10000 permutations (48.90%, 6 seconds remaining)
Job #1, processed 4900/10000 permutations (49.00%, 6 seconds remaining)
Job #1, processed 4910/10000 permutations (49.10%, 6 seconds remaining)
Job #1, processed 4920/10000 permutations (49.20%, 6 seconds remaining)
Job #1, processed 4930/10000 permutations (49.30%, 6 seconds remaining)
Job #1, processed 4940/10000 permutations (49.40%, 6 seconds remaining)
Job #1, processed 4950/10000 permutations (49.50%, 6 seconds remaining)
Job #1, processed 4960/10000 permutations (49.60%, 6 seconds remaining)
Job #1, processed 4970/10000 permutations (49.70%, 6 seconds remaining)
Job #1, processed 4980/10000 permutations (49.80%, 6 seconds remaining)
Job #1, processed 4990/10000 permutations (49.90%, 6 seconds remaining)
Job #1, processed 5000/10000 permutations (50.00%, 6 seconds remaining)
Job #1, processed 5010/10000 permutations (50.10%, 6 seconds remaining)
Job #1, processed 5020/10000 permutations (50.20%, 6 seconds remaining)
Job #1, processed 5030/10000 permutations (50.30%, 6 seconds remaining)
Job #1, processed 5040/10000 permutations (50.40%, 6 seconds remaining)
Job #1, processed 5050/10000 permutations (50.50%, 6 seconds remaining)
Job #1, processed 5060/10000 permutations (50.60%, 6 seconds remaining)
Job #1, processed 5070/10000 permutations (50.70%, 6 seconds remaining)
Job #1, processed 5080/10000 permutations (50.80%, 6 seconds remaining)
Job #1, processed 5090/10000 permutations (50.90%, 6 seconds remaining)
Job #1, processed 5100/10000 permutations (51.00%, 6 seconds remaining)
Job #1, processed 5110/10000 permutations (51.10%, 6 seconds remaining)
Job #1, processed 5120/10000 permutations (51.20%, 6 seconds remaining)
Job #1, processed 5130/10000 permutations (51.30%, 6 seconds remaining)
Job #1, processed 5140/10000 permutations (51.40%, 6 seconds remaining)
Job #1, processed 5150/10000 permutations (51.50%, 6 seconds remaining)
Job #1, processed 5160/10000 permutations (51.60%, 6 seconds remaining)
Job #1, processed 5170/10000 permutations (51.70%, 6 seconds remaining)
Job #1, processed 5180/10000 permutations (51.80%, 6 seconds remaining)
Job #1, processed 5190/10000 permutations (51.90%, 6 seconds remaining)
Job #1, processed 5200/10000 permutations (52.00%, 6 seconds remaining)
Job #1, processed 5210/10000 permutations (52.10%, 6 seconds remaining)
Job #1, processed 5220/10000 permutations (52.20%, 6 seconds remaining)
Job #1, processed 5230/10000 permutations (52.30%, 6 seconds remaining)
Job #1, processed 5240/10000 permutations (52.40%, 6 seconds remaining)
Job #1, processed 5250/10000 permutations (52.50%, 6 seconds remaining)
Job #1, processed 5260/10000 permutations (52.60%, 6 seconds remaining)
Job #1, processed 5270/10000 permutations (52.70%, 6 seconds remaining)
Job #1, processed 5280/10000 permutations (52.80%, 6 seconds remaining)
Job #1, processed 5290/10000 permutations (52.90%, 6 seconds remaining)
Job #1, processed 5300/10000 permutations (53.00%, 6 seconds remaining)
Job #1, processed 5310/10000 permutations (53.10%, 6 seconds remaining)
Job #1, processed 5320/10000 permutations (53.20%, 6 seconds remaining)
Job #1, processed 5330/10000 permutations (53.30%, 6 seconds remaining)
Job #1, processed 5340/10000 permutations (53.40%, 6 seconds remaining)
Job #1, processed 5350/10000 permutations (53.50%, 6 seconds remaining)
Job #1, processed 5360/10000 permutations (53.60%, 6 seconds remaining)
Job #1, processed 5370/10000 permutations (53.70%, 6 seconds remaining)
Job #1, processed 5380/10000 permutations (53.80%, 6 seconds remaining)
Job #1, processed 5390/10000 permutations (53.90%, 6 seconds remaining)
Job #1, processed 5400/10000 permutations (54.00%, 6 seconds remaining)
Job #1, processed 5410/10000 permutations (54.10%, 6 seconds remaining)
Job #1, processed 5420/10000 permutations (54.20%, 6 seconds remaining)
Job #1, processed 5430/10000 permutations (54.30%, 6 seconds remaining)
Job #1, processed 5440/10000 permutations (54.40%, 6 seconds remaining)
Job #1, processed 5450/10000 permutations (54.50%, 6 seconds remaining)
Job #1, processed 5460/10000 permutations (54.60%, 6 seconds remaining)
Job #1, processed 5470/10000 permutations (54.70%, 5 seconds remaining)
Job #1, processed 5480/10000 permutations (54.80%, 5 seconds remaining)
Job #1, processed 5490/10000 permutations (54.90%, 5 seconds remaining)
Job #1, processed 5500/10000 permutations (55.00%, 5 seconds remaining)
Job #1, processed 5510/10000 permutations (55.10%, 5 seconds remaining)
Job #1, processed 5520/10000 permutations (55.20%, 5 seconds remaining)
Job #1, processed 5530/10000 permutations (55.30%, 5 seconds remaining)
Job #1, processed 5540/10000 permutations (55.40%, 5 seconds remaining)
Job #1, processed 5550/10000 permutations (55.50%, 5 seconds remaining)
Job #1, processed 5560/10000 permutations (55.60%, 5 seconds remaining)
Job #1, processed 5570/10000 permutations (55.70%, 5 seconds remaining)
Job #1, processed 5580/10000 permutations (55.80%, 5 seconds remaining)
Job #1, processed 5590/10000 permutations (55.90%, 5 seconds remaining)
Job #1, processed 5600/10000 permutations (56.00%, 5 seconds remaining)
Job #1, processed 5610/10000 permutations (56.10%, 5 seconds remaining)
Job #1, processed 5620/10000 permutations (56.20%, 5 seconds remaining)
Job #1, processed 5630/10000 permutations (56.30%, 5 seconds remaining)
Job #1, processed 5640/10000 permutations (56.40%, 5 seconds remaining)
Job #1, processed 5650/10000 permutations (56.50%, 5 seconds remaining)
Job #1, processed 5660/10000 permutations (56.60%, 5 seconds remaining)
Job #1, processed 5670/10000 permutations (56.70%, 5 seconds remaining)
Job #1, processed 5680/10000 permutations (56.80%, 5 seconds remaining)
Job #1, processed 5690/10000 permutations (56.90%, 5 seconds remaining)
Job #1, processed 5700/10000 permutations (57.00%, 5 seconds remaining)
Job #1, processed 5710/10000 permutations (57.10%, 5 seconds remaining)
Job #1, processed 5720/10000 permutations (57.20%, 5 seconds remaining)
Job #1, processed 5730/10000 permutations (57.30%, 5 seconds remaining)
Job #1, processed 5740/10000 permutations (57.40%, 5 seconds remaining)
Job #1, processed 5750/10000 permutations (57.50%, 5 seconds remaining)
Job #1, processed 5760/10000 permutations (57.60%, 5 seconds remaining)
Job #1, processed 5770/10000 permutations (57.70%, 5 seconds remaining)
Job #1, processed 5780/10000 permutations (57.80%, 5 seconds remaining)
Job #1, processed 5790/10000 permutations (57.90%, 5 seconds remaining)
Job #1, processed 5800/10000 permutations (58.00%, 5 seconds remaining)
Job #1, processed 5810/10000 permutations (58.10%, 5 seconds remaining)
Job #1, processed 5820/10000 permutations (58.20%, 5 seconds remaining)
Job #1, processed 5830/10000 permutations (58.30%, 5 seconds remaining)
Job #1, processed 5840/10000 permutations (58.40%, 5 seconds remaining)
Job #1, processed 5850/10000 permutations (58.50%, 5 seconds remaining)
Job #1, processed 5860/10000 permutations (58.60%, 5 seconds remaining)
Job #1, processed 5870/10000 permutations (58.70%, 5 seconds remaining)
Job #1, processed 5880/10000 permutations (58.80%, 5 seconds remaining)
Job #1, processed 5890/10000 permutations (58.90%, 5 seconds remaining)
Job #1, processed 5900/10000 permutations (59.00%, 5 seconds remaining)
Job #1, processed 5910/10000 permutations (59.10%, 5 seconds remaining)
Job #1, processed 5920/10000 permutations (59.20%, 5 seconds remaining)
Job #1, processed 5930/10000 permutations (59.30%, 5 seconds remaining)
Job #1, processed 5940/10000 permutations (59.40%, 5 seconds remaining)
Job #1, processed 5950/10000 permutations (59.50%, 5 seconds remaining)
Job #1, processed 5960/10000 permutations (59.60%, 5 seconds remaining)
Job #1, processed 5970/10000 permutations (59.70%, 5 seconds remaining)
Job #1, processed 5980/10000 permutations (59.80%, 5 seconds remaining)
Job #1, processed 5990/10000 permutations (59.90%, 5 seconds remaining)
Job #1, processed 6000/10000 permutations (60.00%, 5 seconds remaining)
Job #1, processed 6010/10000 permutations (60.10%, 5 seconds remaining)
Job #1, processed 6020/10000 permutations (60.20%, 5 seconds remaining)
Job #1, processed 6030/10000 permutations (60.30%, 5 seconds remaining)
Job #1, processed 6040/10000 permutations (60.40%, 5 seconds remaining)
Job #1, processed 6050/10000 permutations (60.50%, 5 seconds remaining)
Job #1, processed 6060/10000 permutations (60.60%, 5 seconds remaining)
Job #1, processed 6070/10000 permutations (60.70%, 5 seconds remaining)
Job #1, processed 6080/10000 permutations (60.80%, 5 seconds remaining)
Job #1, processed 6090/10000 permutations (60.90%, 5 seconds remaining)
Job #1, processed 6100/10000 permutations (61.00%, 5 seconds remaining)
Job #1, processed 6110/10000 permutations (61.10%, 5 seconds remaining)
Job #1, processed 6120/10000 permutations (61.20%, 5 seconds remaining)
Job #1, processed 6130/10000 permutations (61.30%, 5 seconds remaining)
Job #1, processed 6140/10000 permutations (61.40%, 5 seconds remaining)
Job #1, processed 6150/10000 permutations (61.50%, 5 seconds remaining)
Job #1, processed 6160/10000 permutations (61.60%, 5 seconds remaining)
Job #1, processed 6170/10000 permutations (61.70%, 5 seconds remaining)
Job #1, processed 6180/10000 permutations (61.80%, 5 seconds remaining)
Job #1, processed 6190/10000 permutations (61.90%, 5 seconds remaining)
Job #1, processed 6200/10000 permutations (62.00%, 5 seconds remaining)
Job #1, processed 6210/10000 permutations (62.10%, 5 seconds remaining)
Job #1, processed 6220/10000 permutations (62.20%, 4 seconds remaining)
Job #1, processed 6230/10000 permutations (62.30%, 4 seconds remaining)
Job #1, processed 6240/10000 permutations (62.40%, 4 seconds remaining)
Job #1, processed 6250/10000 permutations (62.50%, 4 seconds remaining)
Job #1, processed 6260/10000 permutations (62.60%, 4 seconds remaining)
Job #1, processed 6270/10000 permutations (62.70%, 4 seconds remaining)
Job #1, processed 6280/10000 permutations (62.80%, 4 seconds remaining)
Job #1, processed 6290/10000 permutations (62.90%, 4 seconds remaining)
Job #1, processed 6300/10000 permutations (63.00%, 4 seconds remaining)
Job #1, processed 6310/10000 permutations (63.10%, 4 seconds remaining)
Job #1, processed 6320/10000 permutations (63.20%, 4 seconds remaining)
Job #1, processed 6330/10000 permutations (63.30%, 4 seconds remaining)
Job #1, processed 6340/10000 permutations (63.40%, 4 seconds remaining)
Job #1, processed 6350/10000 permutations (63.50%, 4 seconds remaining)
Job #1, processed 6360/10000 permutations (63.60%, 4 seconds remaining)
Job #1, processed 6370/10000 permutations (63.70%, 4 seconds remaining)
Job #1, processed 6380/10000 permutations (63.80%, 4 seconds remaining)
Job #1, processed 6390/10000 permutations (63.90%, 4 seconds remaining)
Job #1, processed 6400/10000 permutations (64.00%, 4 seconds remaining)
Job #1, processed 6410/10000 permutations (64.10%, 4 seconds remaining)
Job #1, processed 6420/10000 permutations (64.20%, 4 seconds remaining)
Job #1, processed 6430/10000 permutations (64.30%, 4 seconds remaining)
Job #1, processed 6440/10000 permutations (64.40%, 4 seconds remaining)
Job #1, processed 6450/10000 permutations (64.50%, 4 seconds remaining)
Job #1, processed 6460/10000 permutations (64.60%, 4 seconds remaining)
Job #1, processed 6470/10000 permutations (64.70%, 4 seconds remaining)
Job #1, processed 6480/10000 permutations (64.80%, 4 seconds remaining)
Job #1, processed 6490/10000 permutations (64.90%, 4 seconds remaining)
Job #1, processed 6500/10000 permutations (65.00%, 4 seconds remaining)
Job #1, processed 6510/10000 permutations (65.10%, 4 seconds remaining)
Job #1, processed 6520/10000 permutations (65.20%, 4 seconds remaining)
Job #1, processed 6530/10000 permutations (65.30%, 4 seconds remaining)
Job #1, processed 6540/10000 permutations (65.40%, 4 seconds remaining)
Job #1, processed 6550/10000 permutations (65.50%, 4 seconds remaining)
Job #1, processed 6560/10000 permutations (65.60%, 4 seconds remaining)
Job #1, processed 6570/10000 permutations (65.70%, 4 seconds remaining)
Job #1, processed 6580/10000 permutations (65.80%, 4 seconds remaining)
Job #1, processed 6590/10000 permutations (65.90%, 4 seconds remaining)
Job #1, processed 6600/10000 permutations (66.00%, 4 seconds remaining)
Job #1, processed 6610/10000 permutations (66.10%, 4 seconds remaining)
Job #1, processed 6620/10000 permutations (66.20%, 4 seconds remaining)
Job #1, processed 6630/10000 permutations (66.30%, 4 seconds remaining)
Job #1, processed 6640/10000 permutations (66.40%, 4 seconds remaining)
Job #1, processed 6650/10000 permutations (66.50%, 4 seconds remaining)
Job #1, processed 6660/10000 permutations (66.60%, 4 seconds remaining)
Job #1, processed 6670/10000 permutations (66.70%, 4 seconds remaining)
Job #1, processed 6680/10000 permutations (66.80%, 4 seconds remaining)
Job #1, processed 6690/10000 permutations (66.90%, 4 seconds remaining)
Job #1, processed 6700/10000 permutations (67.00%, 4 seconds remaining)
Job #1, processed 6710/10000 permutations (67.10%, 4 seconds remaining)
Job #1, processed 6720/10000 permutations (67.20%, 4 seconds remaining)
Job #1, processed 6730/10000 permutations (67.30%, 4 seconds remaining)
Job #1, processed 6740/10000 permutations (67.40%, 4 seconds remaining)
Job #1, processed 6750/10000 permutations (67.50%, 4 seconds remaining)
Job #1, processed 6760/10000 permutations (67.60%, 4 seconds remaining)
Job #1, processed 6770/10000 permutations (67.70%, 4 seconds remaining)
Job #1, processed 6780/10000 permutations (67.80%, 4 seconds remaining)
Job #1, processed 6790/10000 permutations (67.90%, 4 seconds remaining)
Job #1, processed 6800/10000 permutations (68.00%, 4 seconds remaining)
Job #1, processed 6810/10000 permutations (68.10%, 4 seconds remaining)
Job #1, processed 6820/10000 permutations (68.20%, 4 seconds remaining)
Job #1, processed 6830/10000 permutations (68.30%, 4 seconds remaining)
Job #1, processed 6840/10000 permutations (68.40%, 4 seconds remaining)
Job #1, processed 6850/10000 permutations (68.50%, 4 seconds remaining)
Job #1, processed 6860/10000 permutations (68.60%, 4 seconds remaining)
Job #1, processed 6870/10000 permutations (68.70%, 4 seconds remaining)
Job #1, processed 6880/10000 permutations (68.80%, 4 seconds remaining)
Job #1, processed 6890/10000 permutations (68.90%, 4 seconds remaining)
Job #1, processed 6900/10000 permutations (69.00%, 4 seconds remaining)
Job #1, processed 6910/10000 permutations (69.10%, 4 seconds remaining)
Job #1, processed 6920/10000 permutations (69.20%, 4 seconds remaining)
Job #1, processed 6930/10000 permutations (69.30%, 4 seconds remaining)
Job #1, processed 6940/10000 permutations (69.40%, 4 seconds remaining)
Job #1, processed 6950/10000 permutations (69.50%, 4 seconds remaining)
Job #1, processed 6960/10000 permutations (69.60%, 4 seconds remaining)
Job #1, processed 6970/10000 permutations (69.70%, 4 seconds remaining)
Job #1, processed 6980/10000 permutations (69.80%, 3 seconds remaining)
Job #1, processed 6990/10000 permutations (69.90%, 3 seconds remaining)
Job #1, processed 7000/10000 permutations (70.00%, 3 seconds remaining)
Job #1, processed 7010/10000 permutations (70.10%, 3 seconds remaining)
Job #1, processed 7020/10000 permutations (70.20%, 3 seconds remaining)
Job #1, processed 7030/10000 permutations (70.30%, 3 seconds remaining)
Job #1, processed 7040/10000 permutations (70.40%, 3 seconds remaining)
Job #1, processed 7050/10000 permutations (70.50%, 3 seconds remaining)
Job #1, processed 7060/10000 permutations (70.60%, 3 seconds remaining)
Job #1, processed 7070/10000 permutations (70.70%, 3 seconds remaining)
Job #1, processed 7080/10000 permutations (70.80%, 3 seconds remaining)
Job #1, processed 7090/10000 permutations (70.90%, 3 seconds remaining)
Job #1, processed 7100/10000 permutations (71.00%, 3 seconds remaining)
Job #1, processed 7110/10000 permutations (71.10%, 3 seconds remaining)
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[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 13.6s 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
_, pvals_bonferroni = f_regression(
grouped_fmri_masked,
grouped_conditions_encoded) # f_regression implicitly adds intercept
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)
```

Out:

```
/home/nicolas/anaconda3/envs/nilearn/lib/python3.8/site-packages/sklearn/utils/validation.py:63: 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().
return f(*args, **kwargs)
```

Visualization

```
import matplotlib.pyplot as plt
from nilearn.plotting import plot_stat_map, show
# Use the fmri mean image as a surrogate of anatomical data
from nilearn import image
from nilearn.image import get_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)'
'\n%d detections') % n_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)'
'\n%d detections') % n_detections
display.title(title, y=1.1)
show()
```

**Total running time of the script:** ( 0 minutes 27.889 seconds)