"""
===========================================================================
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]_.
"""

import numpy as np
import matplotlib.pyplot as plt
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)
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 :class:`mne.Epochs` object has a convenient
# :meth:`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 = ((.2, .25), (.35, .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().transpose(0, 2, 1),
     short_words.get_data().transpose(0, 2, 1)]
tfce = dict(start=.2, step=.2)

# 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 < .05
print(str(significant_points.sum()) + " points selected by TFCE ...")

##############################################################################
# The results of these mass univariate analyses can be visualised by plotting
# :class:`mne.Evoked` objects as images (via :class:`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=.3,
             label="µV")

plt.show()

###############################################################################
# References
# ----------
# .. [1] Dufau, S., Grainger, J., Midgley, KJ., Holcomb, PJ. A thousand
#    words are worth a picture: Snapshots of printed-word processing in an
#    event-related potential megastudy. Psychological Science, 2015
# .. [2] Smith and Nichols 2009, "Threshold-free cluster enhancement:
#    addressing problems of smoothing, threshold dependence, and
#    localisation in cluster inference", NeuroImage 44 (2009) 83-98.

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 s%0A# 
-----------%0A# .. %5B1%5D Dufau, S., Grainger, J., Midgley, KJ., Holcomb, PJ. A thousand%0A#    words are worth a picture: Snapshots of printed-word processing in an%0A#    event-related potential megastudy. Psychological Science, 2015%0A# .. %5B2%5D Smith and Nichols 2009, %22Threshold-free cluster enhancement:%0A#    addressing problems of smoothing, threshold dependence, and%0A#    localisation in cluster inference%22, NeuroImage 44 (2009) 83-98.
+==========%0A# .. footbibliography::
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update citations with bibtex (#9068)