.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/05_glm_second_level/plot_thresholding.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_05_glm_second_level_plot_thresholding.py: Statistical testing of a second-level analysis ============================================== Perform a one-sample t-test on a bunch of images (a.k.a. second-level analysis in fMRI) and threshold the resulting statistical map. This example is based on the so-called localizer dataset. It shows activation related to a mental computation task, as opposed to narrative sentence reading/listening. .. GENERATED FROM PYTHON SOURCE LINES 15-18 Prepare some images for a simple t test ---------------------------------------- This is a simple manually performed second level analysis. .. GENERATED FROM PYTHON SOURCE LINES 18-24 .. code-block:: default from nilearn import datasets n_samples = 20 localizer_dataset = datasets.fetch_localizer_calculation_task( n_subjects=n_samples, legacy_format=False ) .. GENERATED FROM PYTHON SOURCE LINES 25-26 Get the set of individual statstical maps (contrast estimates) .. GENERATED FROM PYTHON SOURCE LINES 26-28 .. code-block:: default cmap_filenames = localizer_dataset.cmaps .. GENERATED FROM PYTHON SOURCE LINES 29-34 Perform the second level analysis ---------------------------------- First, we define a design matrix for the model. As the model is trivial (one-sample test), the design matrix is just one column with ones. .. GENERATED FROM PYTHON SOURCE LINES 34-37 .. code-block:: default import pandas as pd design_matrix = pd.DataFrame([1] * n_samples, columns=['intercept']) .. GENERATED FROM PYTHON SOURCE LINES 38-39 Next, we specify and estimate the model. .. GENERATED FROM PYTHON SOURCE LINES 39-43 .. code-block:: default from nilearn.glm.second_level import SecondLevelModel second_level_model = SecondLevelModel().fit( cmap_filenames, design_matrix=design_matrix) .. GENERATED FROM PYTHON SOURCE LINES 44-46 Compute the only possible contrast: the one-sample test. Since there is only one possible contrast, we don't need to specify it in detail. .. GENERATED FROM PYTHON SOURCE LINES 46-48 .. code-block:: default z_map = second_level_model.compute_contrast(output_type='z_score') .. GENERATED FROM PYTHON SOURCE LINES 49-51 Threshold the resulting map without multiple comparisons correction, abs(z) > 3.29 (equivalent to p < 0.001), cluster size > 10 voxels. .. GENERATED FROM PYTHON SOURCE LINES 51-59 .. code-block:: default from nilearn.image import threshold_img thresholded_map = threshold_img( z_map, threshold=3.29, cluster_threshold=10, two_sided=True, ) .. GENERATED FROM PYTHON SOURCE LINES 60-62 This is equivalent to thresholding a z-statistic image with a false positive rate < .001, cluster size > 10 voxels. .. GENERATED FROM PYTHON SOURCE LINES 62-71 .. code-block:: default from nilearn.glm import threshold_stats_img thresholded_map1, threshold1 = threshold_stats_img( z_map, alpha=.001, height_control='fpr', cluster_threshold=10, two_sided=True, ) .. GENERATED FROM PYTHON SOURCE LINES 72-73 Now use FDR <.05 (False Discovery Rate) and no cluster-level threshold. .. GENERATED FROM PYTHON SOURCE LINES 73-77 .. code-block:: default thresholded_map2, threshold2 = threshold_stats_img( z_map, alpha=.05, height_control='fdr') print('The FDR=.05 threshold is %.3g' % threshold2) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none The FDR=.05 threshold is 2.37 .. GENERATED FROM PYTHON SOURCE LINES 78-81 Now use FWER <.05 (Family-Wise Error Rate) and no cluster-level threshold. As the data has not been intensively smoothed, we can use a simple Bonferroni correction. .. GENERATED FROM PYTHON SOURCE LINES 81-85 .. code-block:: default thresholded_map3, threshold3 = threshold_stats_img( z_map, alpha=.05, height_control='bonferroni') print('The p<.05 Bonferroni-corrected threshold is %.3g' % threshold3) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none The p<.05 Bonferroni-corrected threshold is 4.88 .. GENERATED FROM PYTHON SOURCE LINES 86-90 Visualize the results --------------------- First, the unthresholded map. .. GENERATED FROM PYTHON SOURCE LINES 90-93 .. code-block:: default from nilearn import plotting display = plotting.plot_stat_map(z_map, title='Raw z map') .. image-sg:: /auto_examples/05_glm_second_level/images/sphx_glr_plot_thresholding_001.png :alt: plot thresholding :srcset: /auto_examples/05_glm_second_level/images/sphx_glr_plot_thresholding_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 94-96 Second, the p<.001 uncorrected-thresholded map (with only clusters > 10 voxels). .. GENERATED FROM PYTHON SOURCE LINES 96-100 .. code-block:: default plotting.plot_stat_map( thresholded_map1, cut_coords=display.cut_coords, threshold=threshold1, title='Thresholded z map, fpr <.001, clusters > 10 voxels') .. image-sg:: /auto_examples/05_glm_second_level/images/sphx_glr_plot_thresholding_002.png :alt: plot thresholding :srcset: /auto_examples/05_glm_second_level/images/sphx_glr_plot_thresholding_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 101-102 Third, the fdr-thresholded map. .. GENERATED FROM PYTHON SOURCE LINES 102-106 .. code-block:: default plotting.plot_stat_map(thresholded_map2, cut_coords=display.cut_coords, title='Thresholded z map, expected fdr = .05', threshold=threshold2) .. image-sg:: /auto_examples/05_glm_second_level/images/sphx_glr_plot_thresholding_003.png :alt: plot thresholding :srcset: /auto_examples/05_glm_second_level/images/sphx_glr_plot_thresholding_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 107-108 Fourth, the Bonferroni-thresholded map. .. GENERATED FROM PYTHON SOURCE LINES 108-112 .. code-block:: default plotting.plot_stat_map(thresholded_map3, cut_coords=display.cut_coords, title='Thresholded z map, expected fwer < .05', threshold=threshold3) .. image-sg:: /auto_examples/05_glm_second_level/images/sphx_glr_plot_thresholding_004.png :alt: plot thresholding :srcset: /auto_examples/05_glm_second_level/images/sphx_glr_plot_thresholding_004.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 113-119 These different thresholds correspond to different statistical guarantees: in the FWER-corrected image there is only a probability smaller than .05 of observing any false positive voxel. In the FDR-corrected image, 5% of the voxels found are likely to be false positive. In the uncorrected image, one expects a few tens of false positive voxels. .. GENERATED FROM PYTHON SOURCE LINES 119-121 .. code-block:: default plotting.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 23.246 seconds) **Estimated memory usage:** 9 MB .. _sphx_glr_download_auto_examples_05_glm_second_level_plot_thresholding.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/nilearn/nilearn.github.io/main?filepath=examples/auto_examples/05_glm_second_level/plot_thresholding.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_thresholding.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_thresholding.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_