calc.engineer

p value

p_value

Calculate the p-value for a z-score or t-statistic. Supports one-tailed (left or right) and two-tailed hypothesis tests using either the standard normal distribution or the Student's t-distribution when degrees of freedom are specified. Returns significance flags at the 0.01, 0.05, and 0.10 alpha levels. Essential for interpreting results from t-tests, z-tests, ANOVA post-hoc comparisons, and regression coefficients. Uses the Abramowitz & Stegun normal CDF approximation and regularized incomplete beta function for the t-distribution.

Input Schema

TableJSON Schema

Name	Required	Description	Default
`test_type`	No	Tail type: one_tail_left (p from left), one_tail_right (p from right), or two_tail (both tails combined).	two_tail
`test_statistic`	Yes	The z-score or t-statistic from your hypothesis test. Positive values indicate the observed value is above the null hypothesis mean.
`degrees_of_freedom`	No	Degrees of freedom for the t-distribution. Omit to use the standard normal (z) distribution.

Output Schema

TableJSON Schema

Name	Required	Description
`p_value`	Yes	The computed p-value representing the probability of observing a result at least as extreme as the test statistic under the null hypothesis.
`test_type`	Yes	The tail type used for this calculation.
`significant_at_01`	Yes	Whether the result is statistically significant at the 0.01 (1%) level.
`significant_at_05`	Yes	Whether the result is statistically significant at the 0.05 (5%) level.
`significant_at_10`	Yes	Whether the result is statistically significant at the 0.10 (10%) level.

TDQS

A4.5/5.0

Behavior5/5

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

No annotations are provided, so the description fully bears the burden of behavioral transparency. It discloses the specific approximation methods (Abramowitz & Stegun normal CDF, regularized incomplete beta function) and that it returns significance flags at three alpha levels. No contradictions.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is concise and well-structured, front-loading the main purpose and then adding details. Every sentence adds value without redundancy.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the complexity of a statistical tool, the description adequately covers purpose, methods, parameters, and output (significance flags). The presence of an output schema means return values need not be detailed. The description is complete for effective use.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

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 some context about distribution choice via degrees_of_freedom and lists applications, but does not add significant parameter-specific meaning beyond the schema.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool calculates p-values for z-scores or t-statistics, specifying support for one-tailed and two-tailed tests. It distinguishes itself from sibling tools (engineering calculators) by its statistical focus.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description provides clear usage context: it is essential for interpreting results from t-tests, z-tests, ANOVA post-hoc comparisons, and regression coefficients. It does not explicitly state when not to use or suggest alternatives, but the context sufficiently guides appropriate use.

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

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TDQS

A3.9/5.0

Disambiguation4/5

Despite 89 tools, each has a clearly distinct purpose with detailed descriptions that often reference related tools. Overlap exists (e.g., multiple LoRa/RF tools), but the descriptions are sufficient to distinguish them. Some confusion possible among similar-sounding tools like attenuator_pi and attenuator_tee, but the descriptions explicitly compare them.

Naming Consistency4/5

Consistent underscore-separated lowercase naming. Most tools follow a verb_noun pattern (e.g., capacitor_charge, wire_gauge) or noun_noun (power_cost). Minor inconsistencies such as 'bmi_calculator' vs 'solar_sizing' but overall predictable.

Tool Count2/5

89 tools is far too many for a single MCP server. This scope is more appropriate for multiple specialized servers. The sheer number will slow agent selection and increase cognitive load, reducing coherence.

Completeness3/5

Covers many domains (RF, solar, PCB, networking, math, etc.) but lacks depth in some areas (e.g., no three-phase power, no airflow calculations). Some domains have comprehensive coverage (LoRa/Meshtastic), but others feel incomplete for the tool count.

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