mne.stats.permutation_cluster_test#

mne.stats.permutation_cluster_test(X, threshold=None, n_permutations=1024, tail=0, stat_fun=None, adjacency=None, n_jobs=1, seed=None, max_step=1, exclude=None, step_down_p=0, t_power=1, out_type='indices', check_disjoint=False, buffer_size=1000, verbose=None)[source]#

Cluster-level statistical permutation test.

For a list of NumPy arrays of data, calculate some statistics corrected for multiple comparisons using permutations and cluster-level correction. Each element of the list X should contain the data for one group of observations (e.g., 2D arrays for time series, 3D arrays for time-frequency power values). Permutations are generated with random partitions of the data. For details, see 1 2.

Parameters

Xlist of array, shape (n_observations, p[, q][, r]): The data to be clustered. Each array in X should contain the observations for one group. The first dimension of each array is the number of observations from that group; remaining dimensions comprise the size of a single observation. For example if X = [X1, X2] with X1.shape = (20, 50, 4) and X2.shape = (17, 50, 4), then X has 2 groups with respectively 20 and 17 observations in each, and each data point is of shape (50, 4). Note: that the last dimension of each element of X should correspond to the dimension represented in the adjacency parameter (e.g., spectral data should be provided as (observations, frequencies, channels/vertices)).
thresholdfloat | dict | None: The so-called “cluster forming threshold” in the form of a test statistic (note: this is not an alpha level / “p-value”). If numeric, vertices with data values more extreme than threshold will be used to form clusters. If None, an F-threshold will be chosen automatically that corresponds to a p-value of 0.05 for the given number of observations (only valid when using an F-statistic). If threshold is a dict (with keys 'start' and 'step') then threshold-free cluster enhancement (TFCE) will be used (see the TFCE example and 3). See Notes for an example on how to compute a threshold based on a particular p-value for one-tailed or two-tailed tests.
n_permutationsint: The number of permutations to compute.
tailint: If tail is 1, the statistic is thresholded above threshold. If tail is -1, the statistic is thresholded below threshold. If tail is 0, the statistic is thresholded on both sides of the distribution.
stat_funcallable() | None: Function called to calculate the test statistic. Must accept 1D-array as input and return a 1D array. If None (the default), uses mne.stats.f_oneway.
adjacencyscipy.sparse.spmatrix | None | False: Defines adjacency between locations in the data, where “locations” can be spatial vertices, frequency bins, time points, etc. For spatial vertices, see: mne.channels.find_ch_adjacency(). If False, assumes no adjacency (each location is treated as independent and unconnected). If None, a regular lattice adjacency is assumed, connecting each location to its neighbor(s) along the last dimension of each group X[k] (or the last two dimensions if X[k] is 2D). If adjacency is a matrix, it is assumed to be symmetric (only the upper triangular half is used) and must be square with dimension equal to X[k].shape[-1] (for 2D data) or X[k].shape[-1] * X[k].shape[-2] (for 3D data) or (optionally) X[k].shape[-1] * X[k].shape[-2] * X[k].shape[-3] (for 4D data). The function mne.stats.combine_adjacency may be useful for 4D data.
n_jobsint: The number of jobs to run in parallel (default 1). If -1, it is set to the number of CPU cores. Requires the joblib package.
seedNone | int | instance of RandomState: A seed for the NumPy random number generator (RNG). If None (default), the seed will be obtained from the operating system (see RandomState for details), meaning it will most likely produce different output every time this function or method is run. To achieve reproducible results, pass a value here to explicitly initialize the RNG with a defined state.
max_stepint: Maximum distance between samples along the second axis of X to be considered adjacent (typically the second axis is the “time” dimension). Only used when adjacency has shape (n_vertices, n_vertices), that is, when adjacency is only specified for sensors (e.g., via mne.channels.find_ch_adjacency()), and not via sensors and further dimensions such as time points (e.g., via an additional call of mne.stats.combine_adjacency()).
excludebool array or None: Mask to apply to the data to exclude certain points from clustering (e.g., medial wall vertices). Should be the same shape as X. If None, no points are excluded.
step_down_pfloat: To perform a step-down-in-jumps test, pass a p-value for clusters to exclude from each successive iteration. Default is zero, perform no step-down test (since no clusters will be smaller than this value). Setting this to a reasonable value, e.g. 0.05, can increase sensitivity but costs computation time.
t_powerfloat: Power to raise the statistical values (usually F-values) by before summing (sign will be retained). Note that t_power=0 will give a count of locations in each cluster, t_power=1 will weight each location by its statistical score.
out_type‘mask’ | ‘indices’: Output format of clusters within a list. If 'mask', returns a list of boolean arrays, each with the same shape as the input data (or slices if the shape is 1D and adjacency is None), with True values indicating locations that are part of a cluster. If 'indices', returns a list of tuple of ndarray, where each ndarray contains the indices of locations that together form the given cluster along the given dimension. Note that for large datasets, 'indices' may use far less memory than 'mask'. Default is 'indices'.
check_disjointbool: Whether to check if the connectivity matrix can be separated into disjoint sets before clustering. This may lead to faster clustering, especially if the second dimension of X (usually the “time” dimension) is large.
buffer_sizeint | None: Block size to use when computing test statistics. This can significantly reduce memory usage when n_jobs > 1 and memory sharing between processes is enabled (see mne.set_cache_dir()), because X will be shared between processes and each process only needs to allocate space for a small block of locations at a time.
verbosebool | str | int | None: Control verbosity of the logging output. If None, use the default verbosity level. See the logging documentation and mne.verbose() for details. Should only be passed as a keyword argument.

Returns

F_obsarray, shape (p[, q][, r]): Statistic (F by default) observed for all variables.
clusterslist: List type defined by out_type above.
cluster_pvarray: P-value for each cluster.
H0array, shape (n_permutations,): Max cluster level stats observed under permutation.

Notes

For computing a threshold based on a p-value, use the conversion from scipy.stats.rv_continuous.ppf():

pval = 0.001  # arbitrary
dfn = n_conditions - 1  # degrees of freedom numerator
dfd = n_observations - n_conditions  # degrees of freedom denominator
thresh = scipy.stats.f.ppf(1 - pval, dfn=dfn, dfd=dfd)  # F distribution

References

1: Eric Maris and Robert Oostenveld. Nonparametric statistical testing of EEG- and MEG-data. Journal of Neuroscience Methods, 164(1):177–190, 2007. doi:10.1016/j.jneumeth.2007.03.024.
2: Jona Sassenhagen and Dejan Draschkow. Cluster-based permutation tests of meg/eeg data do not establish significance of effect latency or location. Psychophysiology, 56(6):e13335, 2019. doi:10.1111/psyp.13335.
3: Stephen M. Smith and Thomas E. Nichols. Threshold-free cluster enhancement: addressing problems of smoothing, threshold dependence and localisation in cluster inference. NeuroImage, 44(1):83–98, 2009. doi:10.1016/j.neuroimage.2008.03.061.