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

Annotations already declare readOnly, idempotent and closed-world, so the safety profile is covered. The description adds real value beyond them by disclosing what the tool returns: critical values and significance determination at the 0.05 and 0.01 thresholds, which is not captured anywhere else since there is no output schema.

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?

Two tight sentences with the core transformation front-loaded and the threshold details second; nothing is wasted. The appended web page URL is extraneous but negligible.

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 five-parameter, all-optional tool with no output schema, the description covers the operation, supported distributions, tails and return highlights adequately. The remaining gap is the per-distribution relevance of df1/df2, which an agent must guess.

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?

Schema description coverage is 100%, so the baseline is 3. The description adds distribution and tail vocabulary that matches the enums, but it does not clarify the non-obvious mapping of df1 vs df2 to the F distribution or that df is irrelevant for z, leaving the one genuinely ambiguous parameter relationship undocumented.

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?

States a specific verb and resource: converting a z, t, chi-square or F statistic into a p-value. It also enumerates the exact outputs (tail-specific p-value, critical values, significance flags), which clearly separates it from sibling z_score_calculator and confidence_interval_calculator.

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?

Usage is implied rather than stated: an agent can infer this is for hypothesis-testing significance, and the description lists supported distributions and tails. But there is no explicit when-to-use vs alternatives (e.g. z_score_calculator, confidence_interval_calculator) and no exclusions or prerequisites.

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