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

With no annotations provided, the description carries the whole burden. It discloses the trial-call pricing, which is genuinely useful, but says nothing about return shape, how unequal group sizes or zero variance are handled, or whether the call is a read-only computation. It also says the inputs are 'arrays' while the schema declares plain strings, leaving the actual input contract unresolved.

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?

It is short and front-loaded, with the definition first and the input hint second. However the 'Cohens D:' prefix merely restates the tool name and the emoji-laden trial line is promotional, so a portion of the text does not help an agent invoke the tool.

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?

A four-parameter statistical tool with no annotations, no output schema, and zero schema descriptions needs a much fuller description. As written, an agent cannot tell what a and b do, nor whether groups should be strings or arrays, which is a blocking ambiguity for correct invocation.

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 0% across four parameters, so the description must compensate and only partly does: it names group1 and group2 and calls them arrays, but never mentions the a and b parameters at all. For half the parameters the agent has no guidance, and the array-versus-string type mismatch actively misleads.

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?

The description gives a specific verb and resource: 'Calculate Cohen's d effect size between two groups', then clarifies the semantics ('how far two means differ in standard deviations'). That is enough to separate it from most siblings such as x402-t-statistic or x402-correlation, though it never explicitly distinguishes itself from x402-effect-size, which sounds near-identical.

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?

There is no when-to-use or when-not-to-use guidance, no mention of alternatives like x402-effect-size or x402-pooled-std, and no prerequisites. The only contextual note is the free-trial quota, which is billing information rather than selection guidance.

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