Jaccard Index Calculator
Last reviewed 13 September 2026
Recorded that all three ignore joint absence, with the practical test for whether that matters: would you be surprised if both sets lacked an item?
Herfindahl Index Calculator
Last reviewed 13 September 2026
Contrasted it with the Gini on the same page: a thousand identical firms have a Gini of 0 and an HHI of 10; two identical firms have a Gini of 0 and an HHI of 5,000. The Gini ignores how many players there are and the HHI does not, which is the whole difference for a competition question.
Gini Coefficient Calculator
Last reviewed 13 September 2026
Recorded that the Gini is most sensitive to transfers in the MIDDLE of the distribution and least sensitive at the top — which is the opposite of what most commentary assumes, and the reason top-share measures have displaced it for concentration questions.
Shannon Entropy Calculator
Last reviewed 13 September 2026
Recorded that the plug-in estimate is biased DOWNWARD when the data is a sample rather than a population, by roughly (k−1)/(2n ln 2) bits — the opposite direction from most estimation problems.
Life Table Calculator
Last reviewed 13 September 2026
Set out the one situation where this method is the only option — data that arrives already grouped, with no individual times — and measured what grouping costs when it is not: 11.1440 percentage points on the shipped registry-style preset.
Hazard Ratio Calculator
Last reviewed 13 September 2026
Verified that the interval is exactly symmetric on the log scale across 100 generated inputs, and that the standalone entry point agrees with the log-rank one to machine precision.
Log-Rank Test Calculator
Last reviewed 13 September 2026
Verified that swapping the arms flips z, leaves χ² unchanged and inverts the hazard ratio, and that total expected equals total observed across both arms on every generated trial.
Kaplan-Meier Calculator
Last reviewed 13 September 2026
Verified that with nothing censored every step equals the plain running proportion still alive, and that survival never rises, stays inside [0,1] and keeps its confidence limits there across 120 generated cohorts.
Etsy Fee Calculator
Last reviewed 13 September 2026
Tested that the fixed payment component makes the effective fee rate rise as order value falls.
Flipkart Seller Fee Calculator
Last reviewed 13 September 2026
Tested that raising the GST rate on fees reduces settlement without changing any underlying fee.
PayPal Fee Calculator
Last reviewed 13 September 2026
Tested that adding the fee percentage to a target net understates the required gross, which is the error reverse mode exists to prevent.
Crypto Profit Calculator
Last reviewed 13 September 2026
Tested that selling at the purchase price always loses money once both fees apply, and that break-even sits above the entry price.
Bitcoin Return Calculator
Last reviewed 13 September 2026
Tested that the return is measured against the full amount invested including the fee, not the post-fee amount.
Portfolio Value Calculator
Last reviewed 13 September 2026
Tested that the largest position never exceeds the total and that the holdings always sum back to it.
Average Order Value Calculator
Last reviewed 13 September 2026
Tested that a target equal to current order value requires no uplift, and that the two uplift figures always agree with each other.
Cart Abandonment Rate Calculator
Last reviewed 13 September 2026
Tested that completing every cart gives a zero rate, and that recoverable revenue scales with both order value and recovery rate.
MER Calculator
Last reviewed 13 September 2026
Tested that the ratio and the percentage are exact reciprocals of each other at every level of spend.
Ad Spend Calculator
Last reviewed 13 September 2026
Tested that the implied marketing share of revenue is always the reciprocal of the ROAS entered.
Reorder Point Calculator
Last reviewed 13 September 2026
Tested that a zero lead time leaves only the safety buffer, and that the point scales linearly with both demand and lead time.
Safety Stock Calculator
Last reviewed 13 September 2026
Tested that identical maximum and average figures produce no buffer at all, and that the result is never negative.
Stock Coverage Calculator
Last reviewed 13 September 2026
Tested that weeks of cover is always days divided by seven, and that zero demand does not divide by zero.
Stockout Cost Calculator
Last reviewed 13 September 2026
Tested that a selling price below unit cost floors the margin at zero rather than reporting a negative loss.
Inventory Carrying Cost Calculator
Last reviewed 13 September 2026
Tested that monthly cost is always a twelfth of annual and that both scale linearly with the rate.
Sell-Through Rate Calculator
Last reviewed 13 September 2026
Tested that selling everything received gives one hundred percent, and that remaining units reconcile with the two counts.
Demand Forecast Calculator
Last reviewed 13 September 2026
Tested that a flat three-month history makes both methods agree, and that a zero growth rate leaves the average untouched.
GMV Calculator
Last reviewed 13 September 2026
Tested that zero returns and cancellations makes net merchandise value equal gross, in both modes.
Repeat Purchase Rate Calculator
Last reviewed 13 September 2026
Tested that repeat customers exceeding the total are capped rather than producing a rate above one hundred percent.
Customer Retention Rate Calculator
Last reviewed 13 September 2026
Tested that retention and churn always sum to one hundred, and that a growing base cannot produce a rate above one hundred.
Ecommerce Valuation Calculator
Last reviewed 13 September 2026
Tested that add-backs raise the valuation by exactly the multiple times the add-back, and that both valuations scale linearly.
Inventory Investment Calculator
Last reviewed 13 September 2026
Tested that doubling the target days doubles the cycle stock investment while leaving the safety component untouched.
Daily Sales Target Calculator
Last reviewed 13 September 2026
Tested that the sessions figure always reproduces the order count at the conversion rate entered.
Order Defect Rate Calculator
Last reviewed 13 September 2026
Tested that the threshold flag flips exactly at one percent, and that defect-free orders always reconcile with the total.
Return Loss Calculator
Last reviewed 13 September 2026
Tested that a zero return rate produces no loss at all, and that a higher damaged share always increases the total cost.
Exchange Cost Calculator
Last reviewed 13 September 2026
Tested that the total is always the per-exchange figure times the count, and that each cost component contributes one for one.
India GST Calculator
Last reviewed 13 September 2026
Tested that extracting tax from an inclusive price is division rather than a percentage of the total, and that the two supply types collect the same amount.
UK VAT Calculator
Last reviewed 13 September 2026
Tested that removing VAT from a gross price uses the VAT fraction rather than the percentage, which differs by a fifth at the standard rate.
Canada GST HST PST Calculator
Last reviewed 13 September 2026
Tested that a zero provincial rate reduces the result to federal GST alone, and that both rates apply to the base rather than compounding.
Salary TDS Calculator
Last reviewed 13 September 2026
Tested that tax already deducted beyond the full estimate leaves nothing further to collect rather than a negative deduction.
Contractor TDS Calculator
Last reviewed 13 September 2026
Tested that switching the recipient type changes the deduction by exactly the difference between the two rates.
Tolerance Interval Calculator
Last reviewed 12 September 2026
Stated that the one-sided factor is a different quantity, not half a two-sided interval — which is a common and consequential error in specification setting.
Prediction Interval Calculator
Last reviewed 12 September 2026
Published the factor table generated by the same code that computes the interval, so the two can never drift apart.
Permutation Test Calculator
Last reviewed 12 September 2026
Stated the one assumption that survives — exchangeability — as a claim about how the data was collected rather than about how it is distributed.
Bootstrap Confidence Interval Calculator
Last reviewed 12 September 2026
Seeded the generator. A bootstrap interval that changes every time you look at it cannot be put in a paper, and the suite asserts both that the same seed reproduces it and that a different seed does not.
Games-Howell Test Calculator
Last reviewed 12 September 2026
Verified that a pair is significant exactly when its confidence interval excludes zero, across 100 generated datasets, and that Welch degrees of freedom never exceed the pooled degrees of freedom they replace.
Dunnett's Test Calculator
Last reviewed 12 September 2026
Made the whole thing fast enough to be a page rather than a batch job — the quadrature weights are built once per degrees of freedom and the root is found by the Illinois method rather than bisection, which took one critical value from 3.4 seconds to under 200 milliseconds.
Omega Squared Calculator
Last reviewed 12 September 2026
Corrected an error this site had made in its own reasoning: omega squared is NOT always below epsilon squared. They share a numerator and differ only in denominator, so below F = 1 the ordering flips. The assertion suite caught it on 11 of 300 random tables, and the rule that actually holds — same sign, omega always nearer zero — is now what is asserted.
Eta Squared Calculator
Last reviewed 12 September 2026
Verified the two-group identity that eta squared equals the squared point-biserial correlation, against the site's own point-biserial engine, agreeing to 1.4e-7.
Repeated Measures ANOVA Calculator
Last reviewed 12 September 2026
Printed the subject row as a share of total variation, because that share — 99.25% on one preset — is the entire argument for the design, and a between-subjects analysis would have left all of it in the error term.
Two-Way ANOVA Calculator
Last reviewed 12 September 2026
Verified that SS_A + SS_B + SS_AB + SS_error reproduces SS_total across 200 randomly generated designs, and that eta squared sums to exactly 1 across all four rows in 200 more.
Standardized Mortality Ratio Calculator
Last reviewed 12 September 2026
Verified that the SMR interval is exactly the Poisson interval on the observed count rescaled, at six different observed counts, and that expected events scale exactly linearly with person-time.
Incidence Rate Calculator
Last reviewed 12 September 2026
Verified that the reporting multiplier scales the rate and both limits by exactly the same factor, and that the interval always contains the point estimate and widens monotonically as events fall.
Attributable Risk Calculator
Last reviewed 12 September 2026
Reported protective exposures with their signs rather than flipping them silently: RR = 0.25 gives an attributable fraction of -300%, which is the arithmetic saying the preventable fraction is the measure wanted.
Likelihood Ratio Calculator
Last reviewed 12 September 2026
Verified the odds-form update against direct Bayes across 300 random tests, agreeing to within 1e-12, so the arithmetic shortcut the page teaches is checked rather than asserted.
ROC Curve & AUC Calculator
Last reviewed 12 September 2026
Recorded that an AUC below 0.5 is a good marker pointing backwards — reversing the score gives exactly 1 - AUC, asserted across 120 random datasets — rather than a worthless one.
Cramer's V Calculator
Last reviewed 12 September 2026
Recorded that Cohen's small/medium/large marks fall as degrees of freedom rise (0.10/0.30/0.50 at df = 1 but 0.06/0.17/0.29 at df = 3), so an unlabelled 'medium effect' is not checkable. Verified against 69 assertions.
Phi Coefficient Calculator
Last reviewed 12 September 2026
Returned no result rather than zero for an empty row or column, since undefined and 'no association' are different findings. Verified against 69 assertions.
Point-Biserial Correlation Calculator
Last reviewed 12 September 2026
Verified against 69 assertions including the Pearson identity, the r = t/sqrt(t^2+df) relation, and the constant-column and single-group cases that must return no result.
Intraclass Correlation Calculator
Last reviewed 12 September 2026
Reported negative ICCs as computed, and verified the whole set against 69 assertions built on the shared ANOVA decomposition so the six forms can never disagree about the data underneath them.
Cronbach's Alpha Calculator
Last reviewed 12 September 2026
Verified against 69 assertions covering alpha, the drop-one recomputation, the Spearman–Brown identity that generates the length table, and the degenerate matrices that must return no result.
Friedman Test Calculator
Last reviewed 12 September 2026
Verified against 69 assertions covering midranks for ties, the omnibus statistic, W, and the ragged designs that must return no result rather than a number.
Runs Test Calculator
Last reviewed 12 September 2026
Verified against the 69-assertion sequence suite, including the exact run-count distribution on small sequences where the normal approximation should not be trusted.
Goodness of Fit Calculator
Last reviewed 12 September 2026
Verified against 69 assertions covering the statistic, the residuals, the calibration sweep and the boundary cases where a category has zero expected count.
Bartlett's Test Calculator
Last reviewed 12 September 2026
Verified against 53 assertions shared with the F-test and Levene pages, including the calibration sweep that produces the 4.20% and 40.40% figures.
Levene's Test Calculator
Last reviewed 12 September 2026
Verified against the same 53-assertion suite as the F-test and Bartlett pages, which is what lets the three pages quote each other's numbers without drift.
F-Test Calculator
Last reviewed 12 September 2026
Verified against 53 assertions covering the statistic, the interval, the calibration sweep and the degenerate cases where a group has no variation at all.
Laplace Distribution Calculator
Last reviewed 12 September 2026
Measured the tail: matched on standard deviation the Laplace tail is LIGHTER than the normal's inside about one sigma and heavier past two, with the ratio climbing from there. Excess kurtosis is exactly 3.
Gamma Distribution Calculator
Last reviewed 12 September 2026
Shape 1 is verified to reproduce the exponential CDF and density exactly, and the skewness is reported as 2/sqrt(k) - the central limit theorem visible in a single parameter.
Sensitivity and Specificity Calculator
Last reviewed 12 September 2026
Predictive values at an arbitrary prevalence are computed from Bayes' theorem rather than rescaled from the observed table, so the sample's own prevalence never leaks into the answer.
Number Needed to Treat Calculator
Last reviewed 12 September 2026
The number needed to harm is the same arithmetic with the sign reversed, and the tool switches the label rather than reporting a negative NNT.
Relative Risk Calculator
Last reviewed 12 September 2026
Verified that a relative risk is near-invariant when both event counts are scaled while the absolute reduction changes in every case - which is why both belong in a report.
One-Proportion Z-Test Calculator
Last reviewed 12 September 2026
The score test's non-rejection region is exactly the Wilson interval, verified on all 39 interior outcomes at n = 40.
Wilson Score Interval Calculator
Last reviewed 12 September 2026
The identity between the Wilson bounds and the score test is verified on every bound from 1 to 39 successes out of 40 - each returns p = 0.05 to six decimal places.
Midrange Calculator
Last reviewed 12 September 2026
The simulation is reproducible by construction — identical seed, identical table — and the suite verifies that a different seed gives different numbers, so it is genuinely simulating rather than returning a constant.
Exponential Smoothing Calculator
Last reviewed 12 September 2026
Errors are one-step-ahead throughout, so a fitted value never uses the observation it is compared against, and MAE divides by n - 1 because the first period has no forecast.
Multiple Regression Calculator
Last reviewed 12 September 2026
Each VIF is computed by actually regressing that predictor on the others and cross-checked against an independent fit, rather than read off a correlation matrix.
Sign Test Calculator
Last reviewed 12 September 2026
Calibration checked on 4,000 null studies: the realised rejection rate came out at 3.33%, at or below the nominal 5% as an exact test must be.
Normality Test Calculator
Last reviewed 12 September 2026
Power against a mildly skewed alternative was measured, not asserted: a lognormal with skewness 0.72 is detected 9.6% of the time at n = 10 and 100% at n = 1,000.
Conditional Probability Calculator
Last reviewed 12 September 2026
The suite confirms Bayes' theorem and the law of total probability across thousands of randomly generated feasible triples rather than on the worked example alone.
Cpk Calculator
Last reviewed 12 September 2026
Prints the observed defect rate beside the predicted one, because the PPM conversion is a normal tail probability and lives four standard deviations out — exactly where the normality assumption is least testable and least likely to hold, and where a bounded or skewed characteristic breaks it by orders of magnitude.
Equivalence Test Calculator (TOST)
Last reviewed 12 September 2026
Establishes a conditional law the suite found rather than assumed: more noise raises the TOST p-value on all 2,728 cases where the observed difference lies inside the bounds and LOWERS it on all 272 where it lies outside, because there the extra noise weakens evidence against equivalence.
McNemar's Test Calculator
Last reviewed 12 September 2026
Separates the odds ratio for change, b/c, from the marginal shift — two quantities that are routinely conflated, since the first is conditional on having changed at all and the second is what a reader usually means by the effect.
Trimmed Mean Calculator
Last reviewed 12 September 2026
States that trimming is symmetric regardless of where the extremes actually are, so on one-sided data it discards good observations from the clean side — the price of a method that does not have to decide which points are outliers.
Moving Average Calculator
Last reviewed 12 September 2026
Detects crossovers between two windows and states that one cannot precede the turn that caused it — the gap is roughly the difference in the two lags, 75 periods for a 50/200 pair. The suite asserts that no crossover appears before the turn on a series built to turn at a known point.
Bayes' Theorem Calculator
Last reviewed 12 September 2026
Reports likelihood ratios and handles repeated evidence in odds form, while stating that independence is usually false for a repeated test — whatever produced the first false positive is still there for the second — so the two- and three-positive figures are an upper bound rather than an expectation.
Cohen's Kappa Calculator
Last reviewed 12 September 2026
Offers linear and quadratic weighting for ordinal categories and states the condition the usual belief rests on: quadratic >= linear >= unweighted held on all 600 ordinally-structured test tables and was close to a coin flip on 600 unstructured ones, so weighting categories that are not genuinely ordered can LOWER kappa. Also says the Landis-Koch interpretation labels were proposed as personal benchmarks with no empirical basis.
Kendall Tau Calculator
Last reviewed 12 September 2026
States that the normal-approximation p-value assumes no ties and about ten observations, and that with heavy ties the variance formula is the untied one and the p-value comes out optimistic.
Spearman Correlation Calculator
Last reviewed 12 September 2026
Plots the midranks rather than the raw values, because that is what Spearman actually correlates, and states that the t approximation for testing rho is unreliable at small n and ignores the tie pattern entirely.
Bonferroni Correction Calculator
Last reviewed 12 September 2026
Says plainly that m is the number of tests RUN, not the number being reported. Correcting the subset that looked promising controls nothing, because the selection already happened — which is the most common way a correction is applied and still provides no guarantee.
Tukey HSD Calculator
Last reviewed 12 September 2026
Applies the Tukey-Kramer modification automatically when group sizes differ, and refuses to print a single HSD threshold in that case, because with unequal sizes each pair has its own standard error and one quoted threshold applies to no pair. Simultaneous intervals are reported for every comparison.
Frequency Distribution Calculator
Last reviewed 12 September 2026
Uses half-open bins with the maximum included in the last one, because otherwise the largest observation falls outside every bin and the counts sum to n - 1 — the classic off-by-one in a hand-built frequency table. The suite checks that counts sum to n and relative frequencies to 1 across 300 random datasets.
Mean Absolute Deviation Calculator
Last reviewed 12 September 2026
The suite verifies the minimisation property by SWEEPING every candidate centre on a grid rather than by comparing two formulas, confirms the ratio lands on sqrt(2/pi) over 200,000 simulated normal draws, and checks that one wild value multiplies the SD by more than a thousand while moving the median absolute deviation by under 20%.
F-Distribution Calculator
Last reviewed 12 September 2026
Takes any positive real degrees of freedom, so Welch's ANOVA and mixed-model denominators need no rounding, and states plainly that the distribution is not symmetric: F(2,27) at 95% is 3.354 and F(27,2) is 19.459.
t-Distribution Calculator
Last reviewed 12 September 2026
Verified against the standard table values at df = 1, 2, 30 and 120, and against the identity F(1, v) = t(v) squared, which ties it to the F distribution and shows a two-group ANOVA and a two-sided t test are the same test.
Fisher's Exact Test Calculator
Last reviewed 12 September 2026
Prints chi-square and Yates on the same table with the smallest expected count, and returns Fisher's own tea-tasting probability as exactly 1/70 — the design used four cups each way precisely so that only a perfect score would clear 5%.
Statistical Power Calculator
Last reviewed 12 September 2026
Reports Cohen's h for proportions rather than the raw difference, because a proportion's variance depends on the proportion: the same five-point gap is a 2.513 times larger effect at a 2% baseline than at 50%. Verified against a 200,000-trial simulation of the actual t test at four designs, and against the requirement that power at a zero effect equals alpha exactly.
Sum of Squares Calculator
Last reviewed 12 September 2026
Computes the corrected sum from the deviations in a second pass rather than from the textbook shortcut, which subtracts two nearly equal large numbers and loses a digit of precision for every digit they share — the classic route to a negative computed variance.
Residual Calculator
Last reviewed 12 September 2026
Standardised residuals divide by s times the square root of 1 minus leverage rather than by s, because residual variance genuinely falls with leverage; studentised residuals exclude the point from its own variance estimate. Cook's distance is verified against a full delete-and-refit at every point rather than only against the algebraic shortcut.
Power Regression Calculator
Last reviewed 12 September 2026
Shows the log-log R-squared beside the R-squared the curve achieves on the data, and counts rows dropped because x or y was not positive — a stricter requirement than the exponential or logarithmic fits, which each constrain only one variable.
Logarithmic Regression Calculator
Last reviewed 12 September 2026
Rows with x at or below zero are excluded and counted, and the page states plainly that shifting x by a constant to dodge that changes every coefficient by an amount depending entirely on the constant chosen.
Quadratic Regression Calculator
Last reviewed 12 September 2026
Shows the straight-line R-squared beside the quadratic one and explains that a higher figure is arithmetic rather than evidence, since R-squared cannot fall when a term is added. The speed-and-economy preset scores 0.068 as a line and 0.998 as a parabola, which is what a large gap looks like.