Why a receipt
Roughly half of published psychology papers that use significance testing contain at least one reported p-value inconsistent with its own test statistic and degrees of freedom (Nuijten et al., 2016 — linked under Methodology below) — not fraud, mostly transcription: results computed in one place, retyped in another. The workbench removes that step. The paragraph and the receipt are generated from the same computation record as the numbers on screen, so they cannot disagree with each other.
The receipt also records what usually goes unrecorded: the assumption checks that passed, the conventions the engine committed to before seeing your data, and a fingerprint of exactly the numbers analysed. Handing it over turns a claim into something a colleague can check in two minutes.
This page analyses data you already have. If you are still planning the study and need to know how many observations to collect, start with the sample size calculator
Methodology and sources
Every procedure on this page is implemented from its published formula and pinned by an automated test suite against expected values computed by two independent reference implementations — R 4.6.0 and SciPy 1.18.0 — on identical inputs. The pinned quantities agree across all three implementations to within one part in a billion, and most to machine precision. The suite runs on every change to this site; a disagreement fails the build.
Conventions are stated, not silent.Welch is the pre-specified two-sample default rather than a choice made after seeing Levene's result. Levene is median-centred (the Brown-Forsythe form). Rank tests use midranks with the tie-corrected variance and continuity correction. Chi-square carries no continuity correction, and Cramér's V is the classic form — some packages default to the bias-corrected variant, which is systematically smaller. Hedges' g uses the exact gamma-ratio correction. Upper-tail probabilities are computed directly rather than as 1 − CDF, which is why a p-value of 10⁻²⁵ on this page keeps its digits instead of collapsing to zero.
All arithmetic runs in your browser. Nothing you enter is transmitted, stored, or logged — the page makes no network request to produce a result.
Two limits worth stating plainly. These procedures assume the observations are independent — no test on this page can detect clustered, paired or time-ordered data pretending otherwise. And an assumption check is a screen, not a verdict: with small samples, Shapiro-Wilk has little power to detect non-normality, which is one more reason the rank-based companion is always computed alongside the primary test.
Primary sources
Behavior Research Methods (Springer)
Nuijten et al. (2016) — The prevalence of statistical reporting errors in psychology (1985–2013)The study behind the “roughly half of papers” figure above: across 250,000+ reported p-values, about half of papers using significance testing contained at least one p-value inconsistent with its own test statistic and degrees of freedom.
NIST/SEMATECH
e-Handbook of Statistical MethodsThe federal working reference for the procedures on this page — two-sample tests, correlation, contingency tables and one-way ANOVA, with their assumptions and worked interpretations.
The R Project
R: A language and environment for statistical computingOne of the two independent reference implementations this engine is pinned against: every shipped statistic is covered by tests whose expected values were computed with R 4.6.0 on identical inputs.
SciPy
SciPy: fundamental algorithms for scientific computing in PythonThe second independent reference implementation. R and SciPy disagree with each other and with this engine by less than one part in a billion on every pinned quantity.
Links go to the publishing agency, so you always read the current figure rather than a copy of it. This page embeds no agency data of its own.
Common questions
Which tests does the workbench run?
The four that cover the large majority of published analyses: Welch's independent-samples t-test (with Mann-Whitney U as a rank-based companion), Pearson correlation with a Fisher-z interval, the chi-square test of independence with Cramér's V, and one-way ANOVA (with Kruskal-Wallis as companion) with η² and ω². Assumption checks — Shapiro-Wilk and median-centred Levene — run automatically with every analysis.
Why Welch and not Student’s t-test?
Student’s t assumes the two groups have equal variances; Welch’s does not, costs almost nothing when variances happen to be equal, and avoids a documented error pattern — choosing the test after peeking at Levene’s result. The workbench runs Welch as its pre-specified default and says so on the receipt, so the choice is never data-dependent.
Is my data uploaded anywhere?
No. Every computation runs in your browser in JavaScript. The page makes no network request to produce a result, which you can confirm in your browser’s network tab. The receipt’s fingerprint is a SHA-256 hash computed locally — the data itself never leaves your machine, and we could not see it if we wanted to.
What is the receipt for?
It records the exact test, every assumption check including the ones that passed, the effect sizes, the convention choices, the engine version, and a SHA-256 fingerprint of exactly the numbers analysed. Anyone you hand it to — a co-author, a reviewer, a client — can paste the same data into this page and confirm every digit. It turns “trust me” into “check me”.
Why do my numbers differ slightly from another package?
Almost always a convention difference, not an error. Packages legitimately differ on things like Welch versus Student as the default, mean- versus median-centred Levene, corrected versus uncorrected Cramér’s V, and how ties are handled in rank tests. The receipt states every convention this engine uses, so the comparison is checkable line by line.
What is deliberately not here?
Post-hoc pairwise comparisons, paired designs, Spearman correlation, and Fisher’s exact test are not in this version — the page says so where it matters instead of silently substituting something else. Power and sample-size planning live in their own calculator on this site.
This page does the arithmetic. We check the numbers you put into it.
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Other calculators
These calculators are provided for general business analysis and are independent informational research — not investment, financial, legal, or tax advice. The arithmetic is standard and openly documented on this page; the assumptions you enter are yours, and the conclusions drawn from them are too.