Methodology

No calculator on this site is written from memory. Each one starts from a documented methodology source, a formula or algorithm derived from that source, and a set of independently calculated test cases checked against a trusted reference implementation (such as R, SciPy, or statsmodels) before the corresponding page ships. Where two reputable references disagree on a convention, this site picks one explicitly and states which convention it used rather than leaving the choice ambiguous.

Numerical conventions

• Full internal precision is retained throughout every calculation. Results are displayed to 3 significant decimals for statistics and 3 decimal places for p-values, with "p < .001" used only as display notation once a p-value is that small.
• Default alpha is .05 and default confidence level is 95%, always visibly editable.
• Missing values are never silently dropped. The default policy is to stop and explain: show the count and location of missing entries, and offer an explicit complete-case option only when that deletion is statistically coherent for the method involved.
• Nonfinite values, malformed tables, impossible probabilities, and negative counts or weights are rejected with an explanation, not silently corrected.

Assumption audit

Every engine explicitly separates three categories, even when one is brief: what is calculated directly from your data (sample size, missingness, zero variance, ties), what is evidence to review (a diagnostic plot, a skew statistic, a variance ratio) without being treated as proof, and what only you can verify (independence, sampling design, measurement validity, whether a causal claim is appropriate). A diagnostic test not rejecting an assumption is described as evidence, never as proof that the assumption holds.

Interpretation conventions

• Statistical significance and practical importance are never treated as the same thing. Where relevant, a result's magnitude and uncertainty are shown alongside, or instead of, a bare significance flag.
• A p-value is never described as the probability that the null hypothesis is true, and a result at or above alpha is described as inconclusive, never as proof that no effect exists.
• Correlation, regression, and association results are never described in causal language.
• A frequentist confidence interval is described as a repeated-sampling procedure, not as a probability statement about a fixed parameter falling inside one realized interval.
• Effect-size labels (small, medium, large) are stated as named conventions, not universal practical-importance thresholds.

Locked method-specific conventions

A number of choices that would otherwise be ambiguous are locked in explicitly rather than left to silent default, and every affected result names which convention was used:

• Independent-group mean comparisons use Welch's t-test by default (unequal variance not assumed); the classic equal-variance pooled test is available as an explicitly labeled comparison, never the default interpretation.
• Proportion confidence intervals use the Wilson score method by default, not the older Wald interval.
• Sample-versus-population denominator (n versus n minus 1) is always a visible, user-set choice, never guessed from the shape of your data.

What this site does not do

It does not run your data through a server. Every calculation happens in your browser, and nothing you enter is transmitted or stored (see Privacy). It does not treat a single online calculator as a source of truth: methodology sources are textbooks, package documentation, and peer-reviewed or authoritative reference material. And it does not use generative AI to produce interpretation text at the time you use a calculator. Every explanation you see is deterministic, written and tested in advance for the specific result you got, not generated on the fly.