In [ ]:
%matplotlib inline

Second-level fMRI model: true positive proportion in clusters

This script showcases the so-called "All resolution inference" procedure, in which the proportion of true discoveries in arbitrary clusters is estimated. The clusters can be defined from the input image, i.e. in a circular way, as the error control accounts for arbitrary cluster selection.

Rosenblatt JD, Finos L, Weeda WD, Solari A, Goeman JJ. All-Resolutions Inference for brain imaging. Neuroimage. 2018 Nov 1;181:786-796. doi: 10.1016/j.neuroimage.2018.07.060

Fetch dataset

We download a list of left vs right button press contrasts from a localizer dataset. Note that we fetch individual t-maps that represent the BOLD activity estimate divided by the uncertainty about this estimate.

In [ ]:
from nilearn.datasets import fetch_localizer_contrasts
n_subjects = 16
data = fetch_localizer_contrasts(["left vs right button press"], n_subjects,

from nilearn import plotting

Estimate second level model

We define the input maps and the design matrix for the second level model and fit it.

In [ ]:
import pandas as pd
second_level_input = data['cmaps']
design_matrix = pd.DataFrame([1] * len(second_level_input),

Model specification and fit

In [ ]:
from nilearn.glm.second_level import SecondLevelModel
second_level_model = SecondLevelModel(smoothing_fwhm=8.0)
second_level_model =,

To estimate the contrast is very simple. We can just provide the column name of the design matrix.

In [ ]:
z_map = second_level_model.compute_contrast(output_type='z_score')

We threshold the second level contrast at uncorrected p < 0.001 and plot

In [ ]:
from scipy.stats import norm
p_val = 0.001
p001_uncorrected = norm.isf(p_val)

from nilearn.glm import cluster_level_inference
proportion_true_discoveries_img = cluster_level_inference(
    z_map, threshold=[3, 4, 5], alpha=.05)

    proportion_true_discoveries_img, threshold=0.,
    display_mode='z', vmax=1, colorbar=True,
    title='group left-right button press, proportion true positives')

    z_map, threshold=p001_uncorrected, colorbar=True, display_mode='z',
    title='group left-right button press (uncorrected p < 0.001)')