stats.eta_squared

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

Annotations already cover read-only/idempotent/closed-world, so the bar is lower, and the description still adds real value: the exact formula (SS_between / SS_total), output precision (6 significant digits for effect size and F, 10 decimal places for p), and a statistical caveat about small-sample bias.

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?

Four dense sentences, front-loaded with what is computed before input format, output precision, and the interpretation caveat. No filler, though the formula and precision sentences could be condensed slightly.

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?

An output schema exists, so return structure need not be spelled out; the description nonetheless pins down precision and the returned statistics. Input format, constraints, and a usage caveat are all present, leaving nothing an agent needs to call 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?

Schema coverage is 0%, so the description must compensate, and it does: groups is a per-group list of Decimal strings, with at least 2 groups and at least 2 values per group. This fully specifies format and cardinality constraints for the single nested-array parameter.

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 computation: one-way ANOVA effect sizes eta^2 (biased) and omega^2 (bias-corrected), plus F, p, and df. It clearly differs in substance from stats.anova_oneway and stats.cohens_d, but never names a sibling to reinforce the distinction.

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?

Input constraints (2+ groups, 2+ values each) and an interpretation note ('with small samples eta^2 is inflated, so look at omega^2 too') are given, which implies the usage context. However, there is no explicit when-to-use/when-not guidance versus stats.anova_oneway or stats.cohens_d.

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