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rigor-mcp

rigor-mcp

by mrnh
OverviewSchemaSourceRelated ServersDiscussionsAdmin
Python
Remote

paired_t_test

Read-onlyIdempotent

Test whether the mean difference between paired observations equals zero, returning t-statistic, degrees of freedom, p-value, confidence interval, and assumption warnings.

Instructions

Test whether the mean difference between paired observations (e.g. before/after measurements on the same subjects, or matched pairs) is zero. a[i] and b[i] must be the two measurements of the same pair -- use two_sample_t_test instead if the two samples are independent (different subjects in each group). Returns the t-statistic, degrees of freedom (n-1), two-tailed p-value, a confidence interval for the mean difference, a citation, and assumption warnings.

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": "paired_t_test"
  }
}

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. Changed3 schema fields changedv0.3.0
    • addedInput schema / properties / a / description
      Added value: +"first measurement of each pair, e.g. 'before'"
    • addedInput schema / properties / alpha / description
      Added value: +"significance level for the test (and any confidence interval); default 0.05"
    • addedInput schema / properties / b / description
      Added value: +"second measurement of each pair, e.g. 'after' -- same length and pairing order as a"
  2. First observedv0.1.0

TDQS

A4.7/5.0
Behavior4/5

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

Annotations already declare readOnlyHint=true, openWorldHint=false, idempotentHint=true, and destructiveHint=false, covering the safety profile. The description adds value by specifying the return values (t-statistic, df, p-value, CI, citation, assumption warnings), which goes beyond annotations. It does not contradict any annotation.

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 a single, well-structured paragraph that starts with the purpose, explains usage constraints, and lists outputs. It is concise with no filler, every sentence provides essential information.

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

Completeness5/5

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

The description is thorough for a statistical test with no output schema. It states all key outputs, mentions assumption warnings, clarifies the two-tailed nature, and contrasts with alternatives. No critical information is missing for an agent to decide and use the tool correctly.

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

Parameters4/5

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

Despite 100% schema description coverage, the description adds critical context for parameters 'a' and 'b' by emphasizing the pairing requirement and order ('a[i] and b[i] must be the two measurements of the same pair') which is not fully conveyed by the schema alone. This enhances understanding beyond the baseline.

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's purpose: testing whether the mean difference between paired observations is zero. It provides concrete examples ('before/after measurements on the same subjects, or matched pairs') and distinguishes itself from the sibling tool 'two_sample_t_test' by specifying when to use which, making it unambiguous.

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?

The description explicitly instructs when to use this tool (paired observations) and when not to ('use two_sample_t_test instead if the two samples are independent'). It also provides context on pairing requirements, which serves as clear guidance for selection.

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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