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IBM

MCP Math Server

by IBM

sample_size_mean

Calculate required sample size per group for comparing means using power analysis. Determine how many observations are needed to detect a specified effect size with statistical significance.

Instructions

Calculate required sample size per group for comparing means (power analysis) (Domain: statistics, Category: inference)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
effect_sizeYes
alphaNo
powerNo
alternativeNotwo-sided
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 calculation (power analysis), implying it's a read-only operation, but doesn't clarify output format (e.g., returns an integer sample size), assumptions (e.g., normal distribution, equal variances), or limitations (e.g., large effect sizes may yield small samples). For a statistical tool with no annotation coverage, this leaves significant gaps in understanding its behavior.

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 extremely concise and front-loaded: a single sentence that directly states the tool's purpose, followed by domain/category tags. There is zero wasted verbiage, and every element (calculation, sample size, means comparison, power analysis) earns its place by contributing essential context. The structure is clear and efficient.

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 tool's complexity (statistical power analysis with 4 parameters), lack of annotations, 0% schema description coverage, and no output schema, the description is incomplete. It identifies the tool's domain and high-level purpose but omits critical details: parameter meanings, behavioral assumptions, output format, and usage context. For a tool that requires precise statistical inputs, this leaves too much undefined.

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

Parameters1/5

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

The schema description coverage is 0%, meaning none of the 4 parameters (effect_size, alpha, power, alternative) are documented in the schema. The description adds no parameter semantics—it doesn't explain what 'effect_size' represents (e.g., Cohen's d), the meaning of 'alpha' (significance level), 'power' (probability of detecting an effect), or valid values for 'alternative' (e.g., 'two-sided', 'greater', 'lesser'). This forces the agent to guess parameter meanings, which is inadequate.

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: 'Calculate required sample size per group for comparing means (power analysis)'. It specifies the verb ('calculate'), resource ('sample size per group'), and context ('comparing means', 'power analysis'), with domain/category tags adding precision. However, it doesn't explicitly differentiate from sibling tools like 'power_analysis' or 't_test_two_sample', which might handle related statistical tasks.

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 no guidance on when to use this tool versus alternatives. It mentions 'power analysis' and 'comparing means', but doesn't specify prerequisites, scenarios (e.g., experimental design, hypothesis testing), or contrast with siblings like 'power_analysis' (general) or 't_test_two_sample' (which might compute test statistics). Without such context, an agent must infer usage from the tool name and parameters alone.

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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