{"uid":"cap_iow1yXxDrTnptVWk2-lBf","slug":"statistical-tests-normality-check-3f2ad65b","name":"Statistical Tests – Normality Check","description":"Normality screen for a sample: skewness, excess kurtosis, Jarque-Bera test with p-value, and the 68-95-99.7 rule check.","url":"https://stats-tests.x402tookit.com/normality-check?utm_source=zero.xyz","method":"GET","headers":{},"bodySchema":{"type":"object","$schema":"https://json-schema.org/draft/2020-12/schema","required":["input"],"properties":{"input":{"type":"object","required":["type","method"],"properties":{"type":{"type":"string","const":"http"},"method":{"enum":["GET"],"type":"string"},"queryParams":{"type":"object","required":["values"],"properties":{"values":{"type":"string","description":"Sample values (8 to 500)"}}}},"additionalProperties":false},"output":{"type":"object","required":["type"],"properties":{"type":{"type":"string"},"example":{"type":"object","properties":{"n":{"type":["null","number"]},"sd":{"type":["null","number"]},"asOf":{"type":["null","string"]},"mean":{"type":["null","number"]},"pValue":{"type":["null","number"]},"source":{"type":["null","string"]},"reasons":{"type":["array","null"],"items":{"type":"string"}},"summary":{"type":["null","string"]},"verdict":{"type":["null","string"]},"degraded":{"type":["boolean","null"]},"skewness":{"type":["null","number"]},"disclaimer":{"type":["null","string"]},"jarqueBera":{"type":["null","number"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"within1SdPct":{"type":["null","number"]},"within2SdPct":{"type":["null","number"]},"within3SdPct":{"type":["null","number"]},"excessKurtosis":{"type":["null","number"]},"significantAt5pct":{"type":["boolean","null"]}}}}}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.02","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.02/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_K96sk4T_BctHaM6E-3Q4F","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.02","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Screens a numeric sample for normality using skewness, excess kurtosis, Jarque-Bera test with p-value, and the 68-95-99.7 rule check.","exampleAgentPrompt":"Can you run a normality check on these values and tell me the skewness, excess kurtosis, Jarque-Bera statistic, p-value, and whether the data passes the 68-95-99.7 rule? The sample is: 12.3, 14.1, 13.8, 15.0, 12.9, 14.7, 13.2, 16.1, 11.8, 14.5, 13.9, 15.3, 12.6, 14.0, 13.5","exampleUseCases":[{"title":"Pre-test assumption check for t-test","prompt":"Before I run a two-sample t-test, I need to verify normality — can you run a normality screen on these 30 measurements and tell me the Jarque-Bera result and p-value? Values: 101, 98, 103, 97, 105, 99, 102, 100, 104, 96, 101, 103, 98, 100, 99, 102, 97, 104, 101, 98, 103, 100, 99, 102, 97, 105, 101, 100, 98, 103"},{"title":"Financial returns distribution screening","prompt":"I have daily portfolio returns for the past month and want to know if they're normally distributed — please check skewness, kurtosis, and give me the Jarque-Bera p-value for these values: 0.8, -0.3, 1.2, 0.5, -1.1, 2.4, 0.1, -0.7, 1.5, 0.3, -0.2, 0.9, 1.1, -0.5, 0.6, 0.4, -0.8, 1.3, 0.2, -0.4, 0.7, 0.0, -0.6, 1.0, 0.5, -0.9, 0.3, 1.4, -0.1, 0.8"},{"title":"Quality control sample normality audit","prompt":"We're auditing a manufacturing process and need to know if these 20 unit weight measurements follow a normal distribution — run the normality check with the 68-95-99.7 rule and tell me the verdict: 250.1, 249.8, 250.3, 250.0, 249.9, 250.2, 250.5, 249.7, 250.1, 250.4, 249.6, 250.2, 250.0, 249.8, 250.3, 250.1, 249.9, 250.2, 250.0, 250.1"}],"resultDescription":"Returns a JSON object containing: sample size (n), mean, standard deviation, skewness, excess kurtosis, Jarque-Bera statistic, p-value, significance flag at 5%, percentages of values within 1/2/3 standard deviations, a human-readable verdict and summary, list of reasons supporting the verdict, any checks not performed, and optional degraded/disclaimer flags.","failureModes":["Fewer than 8 or more than 500 values provided — returns error or degraded result","Non-numeric values in the sample — parsing failure","Missing required 'values' query parameter — validation error","Degenerate input (all identical values) — undefined skewness/kurtosis"],"whenToPreferThis":"Choose this endpoint when you need a quick, comprehensive normality screen combining moment-based metrics (skewness, kurtosis), an omnibus test (Jarque-Bera), and an empirical rule check in a single call. Ideal as a pre-flight check before parametric tests (t-test, ANOVA, regression) that assume normality. Prefer this over manual calculation or generic statistics libraries when you need a structured, verdict-ready JSON response with p-values. For very large samples or formal hypothesis testing workflows, complement with the sibling endpoints for specific tests.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-21T07:20:05.109Z","isFirstParty":false,"canonicalSlug":"statistical-tests-normality-check-3f2ad65b"}