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    filename: test_example_tfce20220113.m
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% MEM 2gb
% WALLTIME 00:10:00
% DATA public

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%% Using threshold-free cluster enhancement for cluster statistics
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% This example explains how the threshold-free cluster enhancement (TFCE) )method works for cluster statistics.
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%% # Why is it useful?
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% When using clusting to correct for multiple comparisons, we need to define the cluster-forming threshold using the `cfg.clusterthreshold` and the `cfg.clusteralpha` options in **[ft_statistics_montecarlo](https://github.com/fieldtrip/fieldtrip/blob/release/ft_statistics_montecarlo.m)**. Different clusteralpha thresholds lead to clusters with a different spatial ot temporal extent, and thereby potentially to a different sensitivity of the subsequent permutation test. The threshold-free cluster enhancement method (TFCE) was introduced by [Smith and Nichols (2009)](https://doi.org/10.1016/j.neuroimage.2008.03.061) to overcome this arbitrary threshold.
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function test_example_threshold_free_cluster_enhancement

% MEM 2gb
% WALLTIME 00:10:00
% DATA public

%
%% Using threshold-free cluster enhancement for cluster statistics
%
% This example explains how the threshold-free cluster enhancement (TFCE) )method works for cluster statistics.
%
%% # Why is it useful?
%
% When using clusting to correct for multiple comparisons, we need to define the cluster-forming threshold using the `cfg.clusterthreshold` and the `cfg.clusteralpha` options in **[ft_statistics_montecarlo](https://github.com/fieldtrip/fieldtrip/blob/release/ft_statistics_montecarlo.m)**. Different clusteralpha thresholds lead to clusters with a different spatial ot temporal extent, and thereby potentially to a different sensitivity of the subsequent permutation test. The threshold-free cluster enhancement method (TFCE) was introduced by [Smith and Nichols (2009)](https://doi.org/10.1016/j.neuroimage.2008.03.061) to overcome this arbitrary threshold.
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%% # How does it work?
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% Each voxel’s TFCE score is given by the sum of the scores of all “supporting sections” underneath it; as the height  is incrementally raised from zero up to the height (signal intensity) <sub>p</sub> of a given point , the image is thresholded at , and the single contiguous cluster containing p is used to define the score for that height . This score is simply the height  (raised to some power , which is by default set to 2 in FieldTrip and can be adjusted via `cfg.tfce_H`) multiplied by the cluster extent  (raised to some power , which is by default set to 0.5 in FieldTrip and can be adjusted via `cfg.tfce_E`). For more detailed information, see [Smith and Nichols (2009)](https://doi.org/10.1016/j.neuroimage.2008.03.061).
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%% # Example code
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% The following MATLAB code gives an example of the TFCE method. Moreover, we will compare the statistical output of the TFCE method with the conventional threshold based on `cfg.clusteralpha`.
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% The data used in this example is available from our [FTP server](ftp://ftp.fieldtriptoolbox.org/pub/fieldtrip/example/threshold_free_cluster_enhancement/).
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load(dccnpath('/home/common/matlab/fieldtrip/data/ftp/example/threshold_free_cluster_enhancement/ERF_orig.mat'));

Nsubj       = 10;
design      = zeros(2, Nsubj*2);
design(1,:) = [1:Nsubj 1:Nsubj];                % this is the uvar (unit-of-observation variable)
design(2,:) = [ones(1,Nsubj) ones(1,Nsubj)*2];  % this is the ivar (independ