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IBM

MCP Math Server

by IBM

wilcoxon_signed_rank

Compare paired samples using the Wilcoxon signed-rank test to determine if they differ significantly, a non-parametric alternative to the paired t-test.

Instructions

Perform Wilcoxon signed-rank test (non-parametric paired test) to test whether paired samples differ significantly (Domain: statistics, Category: inference)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
beforeYes
afterYes
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. It mentions the test is non-parametric and for paired samples, but doesn't disclose behavioral traits like what the output contains (e.g., test statistic, p-value), assumptions (e.g., symmetric differences), or limitations (e.g., sample size requirements). This leaves significant gaps for a statistical inference tool.

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, efficient sentence that front-loads the key information: the test name, type, and purpose. There's no wasted text, and it's appropriately sized for a tool with a clear statistical function.

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 no annotations, 0% schema coverage, no output schema, and a statistical test with behavioral complexity, the description is incomplete. It lacks details on parameters, output format, assumptions, and usage nuances, making it inadequate for reliable tool invocation without external knowledge.

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%, so the description must compensate. It doesn't explain the parameters at all—'before' and 'after' arrays or 'alpha' significance level—leaving their meaning and format undocumented. The description adds no parameter semantics beyond what's inferred from the test name.

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 performs a Wilcoxon signed-rank test, specifying it's a non-parametric paired test for determining significant differences between paired samples. It distinguishes itself from other statistical tests by naming the specific test, though it doesn't explicitly differentiate from sibling tools like 'paired_t_test' or 't_test_two_sample' beyond mentioning it's non-parametric.

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 description implies usage context by stating it's for 'paired samples' and 'non-parametric' testing, which suggests when to use it versus parametric alternatives. However, it doesn't provide explicit guidance on when to choose this over other non-parametric tests or when not to use it, and doesn't mention alternatives by 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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