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Mann-Whitney U Test

stats_mann_whitney
Read-onlyIdempotent

Perform a Mann-Whitney U test on two independent groups to assess whether their underlying distributions differ significantly.

Instructions

Run a Mann-Whitney U test on two independent groups.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
group_aYesFirst group of numeric observations (at least 2 values).
group_bYesSecond group of numeric observations (at least 2 values).
alternativeNoAlternative hypothesis: 'two-sided', 'less', or 'greater'.two-sided

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
n_aYesSize of the first group.
n_bYesSize of the second group.
methodYesHow the p-value was computed: 'exact' when both groups have n <= 8 and there are no ties, else 'asymptotic'.
p_valueYesp-value.
statisticYesThe Mann-Whitney U statistic (for the first group).
alternativeYesAlternative hypothesis tested.
Behavior3/5

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

Annotations already provide safety profile (read-only, idempotent). The description adds minimal context ('independent groups') but does not elaborate on assumptions, handling of ties, or interpretation. No contradiction with annotations.

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, direct sentence with no redundant information. It is front-loaded with the action and clearly expresses the core function.

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?

Given comprehensive schema descriptions, annotations, and an output schema, the description is nearly sufficient for a well-known statistical test. However, it lacks explicit guidance on when to select it over alternative tests, which is a minor gap.

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?

Schema description coverage is 100%; all parameters (group_a, group_b, alternative) are well-documented in the schema. The tool description adds no parameter-level detail, so the baseline of 3 applies.

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 explicitly states the statistical test name ('Mann-Whitney U test') and data context ('two independent groups'), making it highly specific and distinguishing it from sibling tools like t-test or chi-square.

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

Usage Guidelines3/5

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

The phrase 'on two independent groups' implies a use case but does not explicitly state when to prefer this over alternatives (e.g., t-test, chi-square) or mention assumptions like non-normality. This leaves the agent to infer from the test name.

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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