vlt.stats.power.simulate_lme_data_shuffled

  SIMULATE_LME_DATA_SHUFFLED - (Helper) Generates data using the 'shuffle' method.

    Methodology:
    This is a non-parametric method that simulates data under the null
    hypothesis by shuffling the model's residuals. It makes no assumption
    about the shape of the error distribution, instead using the empirical
    distribution of the errors observed in the data.

    Process:
    1.  Calculates the composite residuals from the baseline model (Residual =
        Observed_Y - Grand_Mean). This residual combines the random effect
        and the individual error term.
    2.  Pools all residuals together and shuffles them randomly.
    3.  Creates a simulated null dataset by adding the shuffled residuals back
        to the grand mean. This breaks any relationship between predictors
        and the outcome.
    4.  Injects the `effect_size` to create the alternative hypothesis dataset.

    Assumptions:
    -   Assumes "exchangeability" of the composite residuals across the entire
        dataset. This means it assumes any error could have occurred for any
        observation, regardless of its group membership.

    Pros/Cons:
    +   Robust to violations of normality.
    -   The exchangeability assumption is strong and often inappropriate for
        mixed models, as it ignores the dependency within groups. This can
        make it less accurate than the hierarchical method.