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

Annotations already declare readOnly/idempotent/non-destructive/closed-world, so the safety profile is covered. The description adds behavior beyond that: default tail=two-sided, default alpha=0.05, and that the result includes a plain-language interpretation with assumptions.

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 dense but front-loaded sentences where nearly every clause maps a test name to its arguments. It is efficient for 17 parameters, though the inline enumeration reads like a compressed spec rather than prose.

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?

With no output schema, the description correctly states what comes back (statistic, p-value, interpretation). Assumptions handling is mentioned. The only real gap is documentation of the table argument's structure and error behavior.

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 coverage is 0% across 17 parameters, so the description carries the load and does so well, mapping each test to its inputs (data/mu0, data1/data2, successes/n/p0, successes1/n1/successes2/n2, observed/expected, table). It stops short of specifying the shape of `table` for chi2-independence or when `expected` may be omitted in chi2-gof.

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+resource ('Run a significance test') and even names the outputs (statistic, p-value, plain-language interpretation). It does not explicitly position itself against siblings like confidence_interval or descriptive_stats, but the scope is unmistakable.

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?

It tells the agent exactly how to select a variant by enumerating each value of `test` with its required argument set, plus the optional tail and alpha defaults. What it lacks is when to reach for this tool versus confidence_interval or bayes_update.

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