Issue A1: Stats Tutorial Rework — Proper Statistical Testing for PSDs

[Ramdam17]

Description:

Rework the statistical analysis in getting_started.ipynb to use appropriate tests instead of basic t-tests on epoch-averaged PSDs.

Context:
The current tutorial computes PSDs averaged across epochs, then runs t-tests. This approach is statistically problematic because:

• Averaging across epochs loses trial-level variance information
• Simple t-tests don't account for the repeated-measures structure
• Multiple comparisons across channels/frequencies need proper correction

Current problematic code (in stats.py):

# averaging across frequencies (compute stats only in ch space)
power = np.mean(data, axis=2)
T_obs, p_values, H0 = mne.stats.permutation_t_test(power, n_permutations, tail=0)

Tasks:

1. Analysis & Documentation

   • Document why current approach is problematic
   • Review appropriate alternatives (repeated-measures ANOVA, mixed-effects, cluster-based)

2. Implementation

   • Implement proper group-level statistics for PSD data
   • Options to consider:
     • Repeated-measures ANOVA (if comparing conditions)
     • Mixed-effects models (for hierarchical data)
     • Non-parametric cluster-based permutation (already partially in HyPyP)
   • Add to stats.py or create new module

3. Tutorial

   • Create new notebook section or mini-notebook: "Proper Statistics for Hyperscanning"
   • Show correct workflow: epochs → stats (not epochs → average → stats)
   • Include interpretation guidelines

Acceptance Criteria:

• Document explaining the statistical issue
• New function(s) in stats.py with proper tests
• Tutorial notebook demonstrating correct usage
• Comparison showing difference between old and new approach
• Docstrings with statistical assumptions clearly stated

References:

• MNE cluster-based permutation: https://mne.tools/stable/auto_tutorials/stats-sensor-space/
• scipy.stats.f_oneway, pingouin library for ANOVA

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