Design tests to verify shuffle randomness

Q: Design tests to verify shuffle randomness

This question evaluates a candidate's skills in statistical experiment design, hypothesis testing, and randomness analysis for algorithmic shuffles, focusing on detecting nonuniformity and inter-run dependence.

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Question

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:

State hypotheses
- Null and alternative hypotheses for uniformity over permutations and independence across runs.
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.
Choose sample size and significance level
- Derive or justify trial counts T, alpha, power, and multiple-testing correction.
Bias/correlation detection
- How to localize and diagnose nonuniformity or dependence.
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.

Design tests to verify shuffle randomness

Experiment Design: Is Your Array Shuffle Truly Random?

Solution

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Design tests to verify shuffle randomness

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Experiment Design: Is Your Array Shuffle Truly Random?

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