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

No annotations are provided, so the description carries the full burden. It does not state the return value, whether it's a two-tailed computation, or unit/format expectations, and the '5 free trial calls per signed wallet' note only describes billing, not tool behavior.

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 front-loads the purpose, followed by a short promotional clause. Nothing is padded, though the trial-call note is somewhat peripheral to correct invocation.

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 annotations, no output schema, zero required parameters and four undocumented string parameters, the description leaves an agent unable to determine how to construct a valid call. It should at minimum define each parameter's role and the shape of the result.

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 largely fails: 'a' and 'b' versus 'sample1' and 'sample2' are never mapped to means, variances, or raw samples. The brief mention of 'means and variances' hints at one interpretation but contradicts the sample-named parameters.

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 (Welch's t statistic) and the two-sample case, which clearly distinguishes it from siblings like x402-chi-square-stat or x402-zscore. However the claim that it works 'from their means and variances' conflicts with the parameter names (a, b, sample1, sample2), leaving the actual input model ambiguous.

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?

No guidance on when to use Welch's t statistic versus a pooled t-test or any sibling, and no context about prerequisites. It does not explain the relationship between the four parameters or which to supply.

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