test: migrate stats/bartlett-test to ULP-based assertions

[kgryte]

Description

What is the purpose of this pull request?

This pull request:

• migrates the tests for stats/bartlett-test from EPS-scaled relative tolerance comparisons to ULP-based assertions, as described in [RFC]: Migrate math/base/special packages from relative tolerance testing to ULP difference testing (tracking issue) #11352.

Specifically, in test/test.js, the following idiom

delta = abs( out.pValue - expected );
tol = 10.0 * EPS * abs( expected );
t.ok( delta <= tol, 'within tolerance. ...' );

is replaced by

t.strictEqual( isAlmostSameValue( out.pValue, expected, 9 ), true, 'returns expected value' );

The abs and EPS requires are dropped in favor of @stdlib/assert/is-almost-same-value.

ULP bounds

The ULP constants were tightened to the measured minimum which still passes over the full fixture set (fixtures generated against R):

Assertion	ULP bound	Measured ULP difference
out.pValue	9	9
out.statistic	4	4

Each bound is minimal: lowering pValue to 8 or statistic to 3 causes the respective assertion to fail. The suite was run twice at the final bounds to confirm deterministic results.

The package has no test/test.native.js, so only test/test.js required changes.

Related Issues

Does this pull request have any related issues?

This pull request has the following related issues:

• [RFC]: Migrate math/base/special packages from relative tolerance testing to ULP difference testing (tracking issue) #11352

Questions

Any questions for reviewers of this pull request?

No.

Other

Any other information relevant to this pull request? This may include screenshots, references, and/or implementation notes.

• Only test files are modified; no implementation, documentation, or benchmark changes are included.
• The conversion mirrors the idiom already established in the same family (e.g., stats/levene-test and stats/fligner-test).

Checklist

Please ensure the following tasks are completed before submitting this pull request.

• Read, understood, and followed the contributing guidelines.

AI Assistance

When authoring the changes proposed in this PR, did you use any kind of AI assistance?

• Yes
• No

If you answered "yes" above, how did you use AI assistance?

• Code generation (e.g., when writing an implementation or fixing a bug)
• Test/benchmark generation
• Documentation (including examples)
• Research and understanding

Disclosure

If you answered "yes" to using AI assistance, please provide a short disclosure indicating how you used AI assistance. This helps reviewers determine how much scrutiny to apply when reviewing your contribution. Example disclosures: "This PR was written primarily by Claude Code." or "I consulted ChatGPT to understand the codebase, but the proposed changes were fully authored manually by myself.".

This PR was written primarily by Claude Code. The ULP bounds were determined empirically by measuring the actual ULP differences against the fixture values and then verifying that each bound is the minimum integer which still passes.

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@stdlib-js/reviewers

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Generated by Claude Code

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
stats/bartlett-test	$\\color{green}414/414$ $\\color{green}+100.00\\%$	$\\color{green}54/54$ $\\color{green}+100.00\\%$	$\\color{green}4/4$ $\\color{green}+100.00\\%$	$\\color{green}414/414$ $\\color{green}+100.00\\%$

The above coverage report was generated for the changes in this PR.