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rigor-mcp

rigor-mcp

by mrnh
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Python
Remote

wilcoxon_signed_rank

Read-onlyIdempotent

Test whether the median difference between paired samples is zero by ranking absolute differences. Nonparametric alternative to the paired t-test for small or non-normal samples.

Instructions

The non-parametric alternative to paired_t_test -- use when that test's own small-n warning makes a normal-theory result suspect. Tests whether the median of the paired differences is zero, by ranking the absolute differences rather than assuming they're normally distributed. Pairs with a zero difference are dropped (and counted in a warning), the standard procedure. statistic is T = min(W+, W-).

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "a": "<a>",
      "b": "<b>"
    },
    "name": "wilcoxon_signed_rank"
  }
}

Input Schema

NameRequiredDescriptionDefault
aYesfirst measurement of each pair, e.g. 'before'
bYessecond measurement of each pair, e.g. 'after' -- same length and pairing order as a
alphaNosignificance level for the test (and any confidence interval); default 0.05

Schema Changelog

Changes observed during successful MCP inspections.

  1. Addedv0.3.0

TDQS

A4.6/5.0
Behavior5/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare readOnlyHint=true, idempotentHint=true, and destructiveHint=false, so the safety profile is covered. The description adds valuable behavioral details: pairs with zero difference are dropped and counted in a warning, and the statistic formula is disclosed (T = min(W+, W−)). This goes beyond annotations to clarify handling of edge cases.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is three concise sentences that immediately state the core purpose, usage condition, and key behavioral details. No fluff, each sentence earns its place, and it is front-loaded with the most important information.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a statistical test with no output schema, the description explains the test type, when to use it, handling of zero differences, and the statistic formula. It does not explicitly state return values (e.g., p-value, statistic), but the mention of 'statistic' and the test context make the output reasonably inferred. It is nearly complete for the complexity involved.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The input schema has 100% description coverage for all three parameters (a, b, alpha), already explaining that a and b are paired first/second measurements with same length and pairing order. The description does not add new parameter-level meaning beyond restating the paired nature; it focuses on the test itself, so baseline 3 is appropriate.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool is the non-parametric alternative to paired_t_test, and specifies it tests whether the median of paired differences is zero by ranking absolute differences. This verb+resource+statistical purpose is specific and distinguishes it from sibling tests like one_sample_t_test and mann_whitney_u.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines5/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Explicitly says to use this tool when paired_t_test's small-n warning makes normal-theory results suspect. It also names the alternative (paired_t_test) and implies it's for paired data, providing clear context for when to choose this over other statistical tests.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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