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one_way_anova

Read-onlyIdempotent

Test whether three or more independent groups have different means, returning F-statistic, p-value, and citation to identify if any group stands out.

Instructions

Test whether three or more independent groups have different means -- e.g. comparing average order value across three marketing channels. A significant result means at least one group differs from the others, not which one -- follow up with pairwise two_sample_t_test calls (correcting for multiple comparisons via bonferroni_correction or benjamini_hochberg_correction) to find which. Returns the F-statistic, between/within degrees of freedom, p-value, a citation, and a warning if within-group df is small.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
alphaNosignificance level for the test (and any confidence interval); default 0.05
groupsYesone list of observations per group; at least 3 groups, each with at least 2 observations

Schema Changelog

Changes observed during successful MCP inspections. Dates show when Glama detected each change.

  1. Changed2 schema fields changedv0.3.0
    • addedInput schema / properties / alpha / description
      Added value: +"significance level for the test (and any confidence interval); default 0.05"
    • addedInput schema / properties / groups / description
      Added value: +"one list of observations per group; at least 3 groups, each with at least 2 observations"
  2. First observedv0.1.0

TDQS

A4.2/5.0
Behavior4/5

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

The description lists the return values (F-statistic, degrees of freedom, p-value, citation, warning) and mentions a potential warning for small within-group df. It doesn't contradict the annotations (readOnly, idempotent), and the nature of a statistical test implies no side effects.

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 concise and well-structured, starting with the primary purpose, then explaining interpretation and follow-up, and finally listing the outputs. It contains no unnecessary words.

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?

The description covers the main aspects: purpose, interpretation, follow-up, and outputs. It lacks assumptions (e.g., normality, homogeneity of variance) but provides a warning for small df, which is a key check. Overall, it is sufficiently comprehensive for a statistical test.

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 description does not elaborate on the parameters beyond what the schema already provides. It mentions 'significance level' but does not explicitly tie it to the 'alpha' parameter, and it gives no additional detail on the 'groups' parameter beyond the schema's description.

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: to test whether three or more independent groups have different means, with a concrete example. It also explains the interpretation of a significant result.

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

Usage Guidelines4/5

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

The description indicates when to use this test (three or more groups) and suggests follow-up pairwise t-tests with correction methods, which helps guide usage. However, it does not explicitly differentiate from other tests like ANOVA variants or non-parametric 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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