How would you test whether your array shuffling function is truly random? Outline an experiment: define null and alternative hypotheses, select statistical tests (e.g., chi-square goodness-of-fit on position frequencies and tests for pairwise independence), determine sample size and significance level, and describe how you'd detect bias or correlations. Explain how you would implement and automate these tests in JavaScript.

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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This is a hard difficulty Statistics & Math question, commonly asked during Technical Screen rounds at Sybill.

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This question is commonly asked for Software Engineer candidates at Sybill during technical interviews.

Design tests to verify shuffle randomness | Sybill Interview 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.

Experiment Design: Is Your Array Shuffle Truly Random?

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

Quick Overview

Experiment Design: Is Your Array Shuffle Truly Random?

Solution

Submit Your Answer to Earn 20XP

Design tests to verify shuffle randomness

Quick Overview

Experiment Design: Is Your Array Shuffle Truly Random?

Solution

Submit Your Answer to Earn 20XP