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vlt.stats.power.run_lme_power_analysisValidation

  RUN_LME_POWER_ANALYSISVALIDATION - Validate the LME power analysis against analytical results

    vlt.stats.power.run_lme_power_analysisValidation

    Validates the simulation-based power curve from vlt.stats.power.run_lme_power_analysis
    against the analytical solution for a simple 1-way ANOVA case provided by
    vlt.stats.power.calculateTukeyPairwisePower.

    It performs the following steps:
    1. Creates a simple, balanced 1-way ANOVA dataset using vlt.stats.artificialAnovaTable.
    2. Calls `run_lme_power_analysis` to generate a simulated power curve across a
       range of effect sizes.
    3. For each effect size tested in the simulation, it calculates the corresponding
       theoretical power using the analytical Tukey HSD power formula.
    4. Plots the simulated power curve (blue circles) and the theoretical power
       curve (red line) on the same axes for visual comparison.
    5. Displays a table comparing the simulated and analytical power values.

    See also: vlt.stats.power.anovaposthocValidation

    Optional Name-Value Pairs:
    'numShuffles' - The number of shuffles for the simulation (default 1000).
                    Higher numbers give more precise results but take longer.
    'alpha'       - The significance level (default 0.05).