.. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_03_second_level_models_plot_second_level_association_test.py: Example of generic design in second-level models ================================================ This example shows the results obtained in a group analysis using a more complex contrast than a one- or two-sample t test. We use the [left button press (auditory cue)] task from the Localizer dataset and seek association between the contrast values and a variate that measures the speed of pseudo-word reading. No confounding variate is included in the model. .. code-block:: default # Author: Virgile Fritsch, Bertrand Thirion, 2014 -- 2018 # Jerome-Alexis Chevalier, 2019 At first, we need to load the Localizer contrasts. .. code-block:: default from nilearn import datasets n_samples = 94 localizer_dataset = datasets.fetch_localizer_contrasts( ['left button press (auditory cue)'], n_subjects=n_samples) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none /home/kshitij/miniconda3/envs/nistats-py36-latest/lib/python3.6/site-packages/numpy/lib/npyio.py:2372: VisibleDeprecationWarning: Reading unicode strings without specifying the encoding argument is deprecated. Set the encoding, use None for the system default. output = genfromtxt(fname, **kwargs) Let's print basic information on the dataset. .. code-block:: default print('First contrast nifti image (3D) is located at: %s' % localizer_dataset.cmaps[0]) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none First contrast nifti image (3D) is located at: /home/kshitij/nilearn_data/brainomics_localizer/brainomics_data/S01/cmaps_LeftAuditoryClick.nii.gz we also need to load the behavioral variable. .. code-block:: default tested_var = localizer_dataset.ext_vars['pseudo'] print(tested_var) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none [b'15.0' b'16.0' b'14.0' b'19.0' b'16.0' b'18.0' b'22.0' b'19.0' b'17.0' b'15.0' b'10.0' b'21.0' b'17.0' b'21.0' b'n/a' b'14.0' b'22.0' b'17.0' b'23.0' b'15.0' b'15.0' b'18.0' b'17.0' b'18.0' b'20.0' b'27.0' b'18.0' b'16.0' b'18.0' b'17.0' b'19.0' b'22.0' b'15.0' b'16.0' b'21.0' b'20.0' b'12.0' b'n/a' b'19.0' b'19.0' b'16.0' b'22.0' b'23.0' b'14.0' b'24.0' b'22.0' b'20.0' b'25.0' b'23.0' b'15.0' b'12.0' b'16.0' b'20.0' b'18.0' b'14.0' b'14.0' b'18.0' b'20.0' b'19.0' b'14.0' b'27.0' b'n/a' b'13.0' b'17.0' b'19.0' b'19.0' b'14.0' b'17.0' b'15.0' b'15.0' b'14.0' b'20.0' b'16.0' b'15.0' b'15.0' b'15.0' b'19.0' b'17.0' b'14.0' b'15.0' b'n/a' b'20.0' b'15.0' b'17.0' b'18.0' b'17.5' b'n/a' b'15.0' b'23.0' b'12.0' b'16.0' b'13.0' b'25.0' b'21.0'] It is worth to do a auality check and remove subjects with missing values. .. code-block:: default import numpy as np mask_quality_check = np.where(tested_var != b'n/a')[0] n_samples = mask_quality_check.size contrast_map_filenames = [localizer_dataset.cmaps[i] for i in mask_quality_check] tested_var = tested_var[mask_quality_check].astype(float).reshape((-1, 1)) print("Actual number of subjects after quality check: %d" % n_samples) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none Actual number of subjects after quality check: 89 Estimate second level model --------------------------- We define the input maps and the design matrix for the second level model and fit it. .. code-block:: default import pandas as pd design_matrix = pd.DataFrame( np.hstack((tested_var, np.ones_like(tested_var))), columns=['fluency', 'intercept']) Fit of the second-level model .. code-block:: default from nistats.second_level_model import SecondLevelModel model = SecondLevelModel(smoothing_fwhm=5.0) model.fit(contrast_map_filenames, design_matrix=design_matrix) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none SecondLevelModel(mask_img=None, memory=Memory(location=None), memory_level=1, minimize_memory=True, n_jobs=1, smoothing_fwhm=5.0, verbose=0) To estimate the contrast is very simple. We can just provide the column name of the design matrix. .. code-block:: default z_map = model.compute_contrast('fluency', output_type='z_score') We compute the fdr-corrected p = 0.05 threshold for these data .. code-block:: default from nistats.thresholding import map_threshold _, threshold = map_threshold(z_map, alpha=.05, height_control='fdr') Let us plot the second level contrast at the computed thresholds .. code-block:: default from nilearn import plotting plotting.plot_stat_map( z_map, threshold=threshold, colorbar=True, title='Group-level association between motor activity \n' 'and reading fluency (fdr=0.05)') plotting.show() .. image:: /auto_examples/03_second_level_models/images/sphx_glr_plot_second_level_association_test_001.png :class: sphx-glr-single-img Computing the (corrected) p-values with parametric test to compare with non parametric test .. code-block:: default from nilearn.image import math_img from nilearn.input_data import NiftiMasker from nistats.utils import get_data p_val = model.compute_contrast('fluency', output_type='p_value') n_voxels = np.sum(get_data(model.masker_.mask_img_)) # Correcting the p-values for multiple testing and taking negative logarithm neg_log_pval = math_img("-np.log10(np.minimum(1, img * {}))" .format(str(n_voxels)), img=p_val) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none :1: RuntimeWarning: divide by zero encountered in log10 Let us plot the (corrected) negative log p-values for the parametric test .. code-block:: default cut_coords = [38, -17, -3] # Since we are plotting negative log p-values and using a threshold equal to 1, # it corresponds to corrected p-values lower than 10%, meaning that there # is less than 10% probability to make a single false discovery # (90% chance that we make no false discoveries at all). # This threshold is much more conservative than the previous one. threshold = 1 title = ('Group-level association between motor activity and reading: \n' 'neg-log of parametric corrected p-values (FWER < 10%)') plotting.plot_stat_map(neg_log_pval, colorbar=True, cut_coords=cut_coords, threshold=threshold, title=title) plotting.show() .. image:: /auto_examples/03_second_level_models/images/sphx_glr_plot_second_level_association_test_002.png :class: sphx-glr-single-img Computing the (corrected) negative log p-values with permutation test .. code-block:: default from nistats.second_level_model import non_parametric_inference neg_log_pvals_permuted_ols_unmasked = \ non_parametric_inference(contrast_map_filenames, design_matrix=design_matrix, second_level_contrast='fluency', model_intercept=True, n_perm=1000, two_sided_test=False, mask=None, smoothing_fwhm=5.0, n_jobs=1) Let us plot the (corrected) negative log p-values .. code-block:: default title = ('Group-level association between motor activity and reading: \n' 'neg-log of non-parametric corrected p-values (FWER < 10%)') plotting.plot_stat_map(neg_log_pvals_permuted_ols_unmasked, colorbar=True, cut_coords=cut_coords, threshold=threshold, title=title) plotting.show() # The neg-log p-values obtained with non parametric testing are capped at 3 # since the number of permutations is 1e3. # The non parametric test yields a few more discoveries # and is then more powerful than the usual parametric procedure. .. image:: /auto_examples/03_second_level_models/images/sphx_glr_plot_second_level_association_test_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 12.721 seconds) .. _sphx_glr_download_auto_examples_03_second_level_models_plot_second_level_association_test.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download :download:`Download Python source code: plot_second_level_association_test.py ` .. container:: sphx-glr-download :download:`Download Jupyter notebook: plot_second_level_association_test.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_