Visualising statistical significance thresholds on EEG data

MNE-Python provides a range of tools for statistical hypothesis testing and the visualisation of the results. Here, we show a few options for exploratory and confirmatory tests - e.g., targeted t-tests, cluster-based permutation approaches (here with Threshold-Free Cluster Enhancement); and how to visualise the results.

The underlying data comes from [1]; we contrast long vs. short words. TFCE is described in [2].

# Authors: The MNE-Python contributors.
# License: BSD-3-Clause
# Copyright the MNE-Python contributors.

import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import ttest_ind

import mne
from mne.channels import find_ch_adjacency, make_1020_channel_selections
from mne.stats import spatio_temporal_cluster_test

np.random.seed(0)

# Load the data
path = mne.datasets.kiloword.data_path() / "kword_metadata-epo.fif"
epochs = mne.read_epochs(path)
# These data are quite smooth, so to speed up processing we'll (unsafely!) just
# decimate them
epochs.decimate(4, verbose="error")
name = "NumberOfLetters"

# Split up the data by the median length in letters via the attached metadata
median_value = str(epochs.metadata[name].median())
long_words = epochs[name + " > " + median_value]
short_words = epochs[name + " < " + median_value]

If we have a specific point in space and time we wish to test, it can be convenient to convert the data into Pandas Dataframe format. In this case, the mne.Epochs object has a convenient mne.Epochs.to_data_frame() method, which returns a dataframe. This dataframe can then be queried for specific time windows and sensors. The extracted data can be submitted to standard statistical tests. Here, we conduct t-tests on the difference between long and short words.

time_windows = ((0.2, 0.25), (0.35, 0.45))
elecs = ["Fz", "Cz", "Pz"]
index = ["condition", "epoch", "time"]

# display the EEG data in Pandas format (first 5 rows)
print(epochs.to_data_frame(index=index)[elecs].head())

report = "{elec}, time: {tmin}-{tmax} s; t({df})={t_val:.3f}, p={p:.3f}"
print("\nTargeted statistical test results:")
for tmin, tmax in time_windows:
    long_df = long_words.copy().crop(tmin, tmax).to_data_frame(index=index)
    short_df = short_words.copy().crop(tmin, tmax).to_data_frame(index=index)
    for elec in elecs:
        # extract data
        A = long_df[elec].groupby("condition").mean()
        B = short_df[elec].groupby("condition").mean()

        # conduct t test
        t, p = ttest_ind(A, B)

        # display results
        format_dict = dict(
            elec=elec, tmin=tmin, tmax=tmax, df=len(epochs.events) - 2, t_val=t, p=p
        )
        print(report.format(**format_dict))

Absent specific hypotheses, we can also conduct an exploratory mass-univariate analysis at all sensors and time points. This requires correcting for multiple tests. MNE offers various methods for this; amongst them, cluster-based permutation methods allow deriving power from the spatio-temoral correlation structure of the data. Here, we use TFCE.

# Calculate adjacency matrix between sensors from their locations
adjacency, _ = find_ch_adjacency(epochs.info, "eeg")

# Extract data: transpose because the cluster test requires channels to be last
# In this case, inference is done over items. In the same manner, we could
# also conduct the test over, e.g., subjects.
X = [
    long_words.get_data(copy=False).transpose(0, 2, 1),
    short_words.get_data(copy=False).transpose(0, 2, 1),
]
tfce = dict(start=0.4, step=0.4)  # ideally start and step would be smaller

# Calculate statistical thresholds
t_obs, clusters, cluster_pv, h0 = spatio_temporal_cluster_test(
    X, tfce, adjacency=adjacency, n_permutations=100
)  # a more standard number would be 1000+
significant_points = cluster_pv.reshape(t_obs.shape).T < 0.05
print(str(significant_points.sum()) + " points selected by TFCE ...")

The results of these mass univariate analyses can be visualised by plotting mne.Evoked objects as images (via mne.Evoked.plot_image) and masking points for significance. Here, we group channels by Regions of Interest to facilitate localising effects on the head.

# We need an evoked object to plot the image to be masked
evoked = mne.combine_evoked(
    [long_words.average(), short_words.average()], weights=[1, -1]
)  # calculate difference wave
time_unit = dict(time_unit="s")
evoked.plot_joint(
    title="Long vs. short words", ts_args=time_unit, topomap_args=time_unit
)  # show difference wave

# Create ROIs by checking channel labels
selections = make_1020_channel_selections(evoked.info, midline="12z")

# Visualize the results
fig, axes = plt.subplots(nrows=3, figsize=(8, 8))
axes = {sel: ax for sel, ax in zip(selections, axes.ravel())}
evoked.plot_image(
    axes=axes,
    group_by=selections,
    colorbar=False,
    show=False,
    mask=significant_points,
    show_names="all",
    titles=None,
    **time_unit,
)
plt.colorbar(axes["Left"].images[-1], ax=list(axes.values()), shrink=0.3, label="µV")

plt.show()

References

[1]

Stéphane Dufau, Jonathan Grainger, Katherine J. Midgley, and Phillip J. Holcomb. A thousand words are worth a picture: snapshots of printed-word processing in an event-related potential megastudy. Psychological Science, 26(12):1887–1897, 2015. doi:10.1177/0956797615603934.

[2]

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.

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