Experiment Design: Is Your Array Shuffle Truly Random?

You're given a shuffle(arr) function that takes an array of n distinct items and returns a random permutation. Design a rigorous test plan to assess whether the shuffle is uniform and independent across runs.

Requirements:

1. State hypotheses
   • Null and alternative hypotheses for uniformity over permutations and independence across runs.
2. Specify tests
   • Position uniformity (e.g., chi-square goodness-of-fit/independence on item-by-position counts).
   • Pairwise order/adjacency tests to probe correlations between items.
   • Any additional tests to catch common implementation bugs.
3. Choose sample size and significance level
   • Derive or justify trial counts T, alpha, power, and multiple-testing correction.
4. Bias/correlation detection
   • How to localize and diagnose nonuniformity or dependence.
5. Implementation and automation in JavaScript
   • Outline data collection, statistics, p-values, pass/fail logic, and CI strategy.

Assume: We can call shuffle repeatedly as a black box. We can choose n (e.g., 10–52) and run T trials.