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IBM

MCP Math Server

by IBM

anova_one_way

Perform one-way ANOVA to test if means of multiple groups differ significantly. Use this statistical tool to analyze variance across groups and determine statistical significance.

Instructions

Perform one-way ANOVA (Analysis of Variance) to test whether means of multiple groups differ significantly (Domain: statistics, Category: inference)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
groupsYes
alphaNo
Behavior2/5

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool performs a statistical test but does not describe what the tool returns (e.g., F-statistic, p-value), assumptions (e.g., normality, homogeneity of variance), or side effects (e.g., computational cost, error handling). For a statistical inference tool with zero annotation coverage, this is a significant gap in transparency.

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

Conciseness4/5

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

The description is a single, efficient sentence that front-loads the core purpose. It avoids redundancy and waste, though it could be more structured (e.g., separating purpose from domain/category). The brevity is appropriate, but the lack of elaboration on usage or parameters slightly limits its effectiveness.

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

Completeness2/5

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

Given the complexity of statistical testing, no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It does not explain what the tool returns, key assumptions, or how to interpret results. For a tool with 2 parameters and no structured support, the description should provide more context to guide the agent effectively.

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

Parameters2/5

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

Schema description coverage is 0%, meaning parameters are undocumented in the schema. The description does not explain the parameters: 'groups' (array of strings representing data groups) and 'alpha' (significance level, default 0.05). It mentions 'multiple groups' but does not clarify parameter roles, formats, or constraints. With low schema coverage, the description fails to compensate, leaving parameters semantically unclear.

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

Purpose4/5

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

The description clearly states the tool's purpose: 'Perform one-way ANOVA (Analysis of Variance) to test whether means of multiple groups differ significantly.' It specifies the verb ('perform'), resource ('one-way ANOVA'), and statistical goal. However, it does not explicitly differentiate from sibling tools (e.g., kruskal_wallis, t_test_two_sample) that also compare group means, which prevents a perfect score.

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

Usage Guidelines2/5

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

The description provides minimal guidance: it mentions the domain ('statistics') and category ('inference'), implying usage for statistical hypothesis testing. However, it lacks explicit when-to-use criteria (e.g., for normally distributed data, comparing ≥3 groups), when-not-to-use alternatives (e.g., non-parametric tests like kruskal_wallis), or prerequisites. This leaves the agent with insufficient context for optimal tool 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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