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

Annotations already declare readOnlyHint=true, idempotentHint=true, and openWorldHint=false. The description adds useful behavioral context by identifying the test type and the sample-ratio-mismatch diagnostic; the output schema reduces the need to explain return values.

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

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

One compact sentence states the test and lists the outputs, followed by a reference URL. There is no redundant or buried information.

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

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

For a low-complexity calculator with full schema coverage, clear annotations, and an output schema, the description supplies sufficient domain context (test type and diagnostic checks) for an agent to invoke it correctly.

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

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

All five parameters have schema descriptions at 100% coverage, including confidence_pct's allowed values and default. The description does not add parameter semantics beyond what the schema already provides, so the baseline of 3 is appropriate.

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

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

Names a specific statistical procedure and target (two-proportion test of an A/B result) and enumerates the outputs, making it clearly distinguishable from sibling calculators such as ARR, churn, NPS, and rule-of-40.

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

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

Provides no explicit when-to-use, prerequisites, or alternative-selection guidance. The A/B-result framing implies the intended use case, but an agent must infer it from the purpose statement rather than being routed by the description.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.