Statistics Tools
Browse all available statistics tools.
Available tools
- A/B Test Result Analyzer Compare two variant conversion rates with a two-proportion z-test.
- Arithmetic Geometric Mean Gap Two Values Tool Compute arithmetic geometric mean gap two values from explicit bounded inputs.
- Arithmetic Harmonic Mean Two Value Gap Tool Calculate arithmetic harmonic mean two value gap from explicit caller-supplied inputs.
- Arithmetic Mean Calculator Calculate the arithmetic average of a list of numbers.
- Asymmetric Absolute Deviation Totals Separate total absolute deviations below and above an explicit reference, retaining asymmetric loss evidence without estimating a distribution.
- Autocorrelation Calculator Compute sample autocorrelation coefficients for lags one through a maximum lag.
- Benford's Law First-Digit Checker Count leading nonzero decimal digits 1–9 in nonzero observations for comparison with Benford's logarithmic proportions. A small or range-restricted sample alone is not evidence of fraud.
- Benjamini-Hochberg FDR Calculator Adjust p-values with the Benjamini-Hochberg false discovery rate procedure.
- Bonferroni Correction Calculator Adjust a p-value for multiple comparisons using the Bonferroni correction.
- Bootstrap Confidence Interval Calculator Estimate a percentile bootstrap confidence interval for a sample mean or median with deterministic resampling.
- Bootstrap Standard Error Calculator Estimate the standard error of a sample statistic with bootstrap resampling.
- Centered Sum Observation Update Tool Compute centered sum observation update from explicit bounded inputs.
- Central Moment Standardization Term Tool Standardize a supplied central moment by its declared order; no bias correction or moment estimation.
- Chi-Square Goodness-of-Fit Calculator Test how well observed category counts fit an expected distribution.
- Chi-Square Independence Statistic Calculator Calculate Pearson's uncorrected independence statistic and expected counts for an RxC contingency table, without a p-value or small-sample validity claim.
- Coefficient of Determination Calculator Calculate R² from observed and predicted values.
- Coefficient of Range Calculator Calculate the range divided by the sum of maximum and minimum values.
- Coefficient of Range Practice Create reproducible practice for Coefficient of Range Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Coefficient of Variation Calculator Calculate population standard deviation as a percentage of the mean.
- Cohen's D Calculator Compute Cohen's d effect size between two independent samples using pooled standard deviation.
- Confidence Interval Asymmetric Margin Tool Split a supplied interval around an estimate into separate lower and upper margins; no confidence level is inferred.
- Confidence Interval for a Proportion Estimate a population proportion with a two-sided normal-approximation interval.
- Confidence Level Tail Allocation Tool Calculate confidence level tail allocation from explicit caller-supplied inputs.
- Correlation Attenuation Reliability Factor Tool Calculate correlation attenuation reliability factor from explicit caller-supplied inputs.
- Correlation Sign Rescale Policy Tool Correlation under nonzero linear rescaling; a collapsed variable returns an undefined flag and zero placeholder.
- Correlation Squared Sign Loss Label Tool Compute correlation squared sign loss label from explicit bounded inputs.
- Count Above Threshold Tool Count how many values in a list are strictly greater than a threshold.
- Covariance Denominator Convention Factor Tool Calculate covariance denominator convention factor from explicit caller-supplied inputs.
- Covariance One Pair Sign Contribution Tool Calculate covariance one pair sign contribution from explicit caller-supplied inputs.
- Cumulative Frequency Calculator Create sorted values with frequency and cumulative-frequency counts.
- Degrees Freedom Constraint Count Tool Subtract a caller-supplied count of independent linear constraints from the observation dimension; independence is assumed, not tested.
- Effect Size Signed Reference Change Reverse or preserve an explicitly signed contrast effect size without transforming an odds ratio or unsigned measure.
- Effective Sample Size Weight Split Tool Calculate effective sample size weight split from explicit caller-supplied inputs.
- Empirical Cdf One Tie Jump Tool Calculate empirical cdf one tie jump from explicit caller-supplied inputs.
- Empirical Cdf Single Observation Step Tool Compute empirical cdf single observation step from explicit bounded inputs.
- Explicit Robust Cutoff Classification Table Classify observations against explicitly supplied inclusive robust-screen cutoffs; does not estimate robust cutoffs or establish outliers, errors or diagnosis.
- Exponential Moving Average Calculator Compute an exponential moving average series seeded with the first observation.
- F-Statistic Calculator Calculate an F statistic as the ratio of two variances.
- F-Statistic Practice Create reproducible practice for F-Statistic Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Finite Population Variance Sampling Factor Tool Calculate finite population variance sampling factor from explicit caller-supplied inputs.
- Finite Value Sign Counts Count sign classes of explicitly finite observations, treating signed zero as zero and rejecting nonfinite values rather than dropping them.
- Fisher Z Correlation Domain Gap Tool Calculate fisher z correlation domain gap from explicit caller-supplied inputs.
- Fisher Z-Transformation Calculator Transform a correlation coefficient with the Fisher inverse hyperbolic tangent.
- Fisher Z-Transformation Practice Create reproducible practice for Fisher Z-Transformation Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Fisher's Exact Test Compute the two-sided Fisher exact p-value for a 2×2 contingency table with fixed margins. Tables above 10,000 total observations are rejected to bound exact enumeration.
- Frequency Table Generator Count numeric values and return a deterministic ascending frequency table.
- Gaussian Kernel Density Estimator Evaluate a univariate equally weighted Gaussian kernel density estimate at supplied points using an explicit absolute bandwidth, without automatic bandwidth selection or boundary correction.
- Geometric Mean Calculator Calculate the geometric mean of nonnegative numbers.
- Geometric Mean Log Deletion Term Tool Calculate geometric mean log deletion term from explicit caller-supplied inputs.
- Gini Coefficient Calculator Calculate the 0–1 Gini inequality coefficient for nonnegative observations using the sorted-sum formula. An all-zero sample is undefined, not perfectly equal.
- Group Mean Centered Values Center each observation by its explicit group’s sample mean, retaining group-center evidence and original order; no between-group inference.
- Group Median Centered Values Center each observation by its explicit group’s sample median, retaining group-center evidence and original order; no between-group inference.
- Harmonic Mean Calculator Calculate the harmonic mean of positive numbers, such as rates or ratios.
- Histogram Bin Boundary Roundoff Policy Tool Compute histogram bin boundary roundoff policy from explicit bounded inputs.
- Holm-Bonferroni Calculator Adjust a family of p-values with the step-down Holm-Bonferroni procedure.
- Huber Residual Loss Slope Return Huber residual loss and its signed derivative at a positive explicit transition delta; slope adds behavior beyond existing scalar Huber loss.
- Inclusive Quartiles Calculator Calculate Q1, Q2, and Q3 by including the median in both halves of an odd-sized dataset.
- Interquartile Mean Calculator Calculate the mean of the values between the inclusive first and third quartiles, ignoring outside extremes.
- Interquartile Range Calculator Calculate the difference between Q3 and Q1 of a dataset.
- Jackknife Bias Calculator Estimate the bias of a sample statistic with leave-one-out jackknife resampling.
- Kaplan-Meier Survival Estimator Estimate survival over time with the product-limit estimator from right-censored durations.
- Kendall Tau-b Rank Correlation Calculator Calculate tie-adjusted Kendall tau-b and disjoint concordant, discordant, and tied pair counts, without a p-value approximation.
- Kruskal-Wallis Test Calculator Calculate the tie-corrected Kruskal-Wallis H statistic for independent groups.
- Kurtosis Excess Reference Shift Tool Calculate kurtosis excess reference shift from explicit caller-supplied inputs.
- Log Mean Exp Two Value Stability Tool Compute log mean exp two value stability from explicit bounded inputs.
- Mann-Whitney U Test Calculator Calculate the Mann-Whitney U statistic for two independent samples.
- Margin of Error Calculator Calculate a normal-approximation margin of error for a mean.
- Margin of Error Practice Create reproducible practice for Margin of Error Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Maximum Value Calculator Return the largest value in a finite numeric list.
- Mean Absolute Deviation Calculator Calculate mean absolute deviation around the arithmetic mean.
- Mean Absolute Deviation from Reference Compute mean absolute deviation about a caller-supplied reference; existing mean-absolute-deviation centers on the sample mean instead.
- Mean Absolute Deviation from the Median Automatically find the sample median and average its absolute deviations, without confusing this mean aggregation with the median absolute deviation statistic.
- Mean Calculator Calculate the arithmetic mean of a finite numeric list.
- Mean of Paired Ratios Compute the mean of explicit paired finite ratios, rejecting any zero denominator rather than silently omitting undefined pairs; no ratio-of-sums substitution.
- Mean Update Finite Precision Residual Tool Calculate mean update finite precision residual from explicit caller-supplied inputs.
- Median Absolute Deviation Calculator Automatically find the sample median and the unscaled median of its absolute deviations, without a normal-consistency correction.
- Median Absolute Deviation from Reference Compute median absolute deviation about an explicitly supplied reference, not automatically the sample median and not normal-consistency scaled.
- Median Calculator Calculate the median of a list of numbers.
- Median Even Middle Pair Policy Tool Resolve an even-sample median from its ordered middle pair under an explicit lower, upper, or average convention.
- Median Tie Middle Gap Tool Calculate median tie middle gap from explicit caller-supplied inputs.
- Midhinge Calculator Calculate the midpoint of the inclusive first and third quartiles of a dataset.
- Midrange Calculator Calculate the midpoint between a dataset's minimum and maximum.
- Minimum Value Calculator Return the smallest value in a finite numeric list.
- Mode Calculator Return every most-frequent value in a finite numeric list, sorted ascending.
- Most Common Value Count Tool Count how many times the most frequent value appears in a list of numbers.
- Moving Average Smooth a series into arithmetic means over overlapping fixed-size windows.
- Normal Score One Observation Leverage Tool Compute normal score one observation leverage from explicit bounded inputs.
- Number Needed to Treat Calculator Calculate number needed to treat from treatment and control event rates.
- Odds Ratio Calculator Calculate an odds ratio from a two-by-two contingency table.
- One-Sample T-Score Calculator Calculate a one-sample t score for a hypothesized population mean.
- One-Way ANOVA F-Ratio Calculator Compare the variation between two or more independent groups with a one-way ANOVA F-ratio.
- Outlier Count IQR Tool Count values outside the Tukey fences of one and a half interquartile ranges.
- Paired Difference Reference Sign Return an explicitly oriented paired difference without estimating a sample mean or testing a hypothesis.
- Paired T-Test Calculator Calculate the paired-samples t statistic from two matched numeric series.
- Pairwise Absolute Difference Sum Sum absolute differences over every unordered observation pair exactly once; no normalization into Gini or dispersion estimators.
- Pairwise Complete Count Tool Count jointly observed rows for one supplied variable pair without imputing missing values.
- Partial Autocorrelation Calculator Compute partial autocorrelations with the Durbin-Levinson recursion over the sample autocorrelation sequence (the classical Yule-Walker-style estimator).
- Pearson Correlation Calculator Calculate Pearson’s linear correlation coefficient for two paired numeric series.
- Percentage Trim One Tail Count Tool Calculate percentage trim one tail count from explicit caller-supplied inputs.
- Percentile Position Tie Label Tool Describe lower, upper and midrank percentile positions for an explicitly supplied tie block, with strict-less and equal counts.
- Percentile Value Calculator Calculate the value at a percentile of a dataset using linear interpolation between closest ranks.
- Permutation Test Calculator Exact two-sided permutation test on the difference of two group means; all C(nA+nB, nA) group assignments of the pooled sample (each sample capped at 8 values) are enumerated deterministically.
- Pooled Standard Deviation Calculator Calculate pooled sample standard deviation from two sample variances and sizes.
- Pooled Standard Deviation Practice Create reproducible practice for Pooled Standard Deviation Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Pooled Variance Calculator Calculate pooled sample variance from two sample variances and sizes.
- Pooled Variance One Stratum Numerator Tool Calculate pooled variance one stratum numerator from explicit caller-supplied inputs.
- Pooled Variance Practice Create reproducible practice for Pooled Variance Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Pooled Within Group Sum Squares Tool Pool supplied unbiased sample variances with n−1 degrees-of-freedom weights.
- Population Covariance Calculator Calculate population covariance for paired numeric observations.
- Population Summary Calculator Calculate the count, mean, population variance, and population standard deviation of a dataset.
- Population Variance Calculator Calculate the population variance of a dataset.
- Positive Negative Sum Balance Report positive and negative signed totals with net and magnitude-normalized balance; all-zero observations have unknown/null balance.
- Principal Component Analysis (PCA) Compute centered, unstandardized sample-covariance PCA through the existing thin Jacobi SVD, with projected scores, sample explained variances and deterministic component signs; degenerate subspaces remain nonunique.
- Proportion Confidence Interval Calculator Estimate a population proportion with a two-sided normal-approximation confidence interval.
- Proportion Confidence Interval Practice Create reproducible practice for Proportion Confidence Interval Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Proportion Observation Denominator Type Qualify an explicit proportion denominator type by source without selecting a statistical estimand.
- Proportion Within Range Calculator Calculate the fraction of values inside an inclusive lower and upper bound.
- Quantile Interpolation Rank Fraction Tool Return zero-based Type-7 linear quantile indexes and interpolation fraction.
- Quartile Coefficient of Dispersion Calculator Calculate quartile dispersion from first and third quartiles.
- Quartile Coefficient of Dispersion Practice Create reproducible practice for Quartile Coefficient of Dispersion Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Quartile Deviation Calculator Calculate the semi-interquartile range, half the distance between the inclusive third and first quartiles.
- Quartile Rule Midpoint Index Tool Half-sample membership indices for median-of-halves quartiles, with explicit odd-median inclusion.
- Quartiles Calculator Calculate Q1, the median (Q2), and Q3 of a dataset.
- Range Calculator Calculate the minimum, maximum, and range of a finite numeric list.
- Rank Distance Tie Gap Tool Compare two explicit tied-rank intervals using midpoint, minimum and maximum distances.
- Rank Tie Correction Factor Compute the exact-tie cubic correction factor 1-sum(t^3-t)/(n^3-n) for n>=2; does not itself correct a named test statistic.
- Rank Tie Cubic Sum Sum t^3-t over exact numeric rank tie blocks for finite observations; no rank-test p-value or independence inference.
- Ratio of Sums Compute ratio of paired sums, retaining signed denominator totals and null at zero; differs from the mean of individual ratios.
- Relative Risk Calculator Calculate relative risk from event and total counts in two groups.
- Relative Standard Error Calculator Calculate standard error as a percentage of an estimate's magnitude.
- Relative Standard Error Practice Create reproducible practice for Relative Standard Error Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Residual Studentization Scale Label Preserve explicit residual studentization scale wording without estimating residual variance.
- Risk Difference Calculator Calculate treatment risk minus control risk from event and total counts.
- Root Mean Square Calculator Calculate the quadratic mean, or root mean square, of a list of numbers.
- Sample Covariance Calculator Calculate unbiased sample covariance for paired numeric observations.
- Sample Kurtosis Calculator Calculate Pearson and Fisher excess kurtosis from sample central moments, with optional finite-sample bias correction and no normality-test claim.
- Sample Leverage Complement Tool Compute one simple-regression diagonal leverage and its complement from supplied centered predictor data with an intercept.
- Sample Median Two Middle Average Range Tool Calculate sample median two middle average range from explicit caller-supplied inputs.
- Sample Proportion Continuity Correction Term Tool Calculate sample proportion continuity correction term from explicit caller-supplied inputs.
- Sample Quantile Index Fraction Component Tool Compute sample quantile index fraction component from explicit bounded inputs.
- Sample Size for Mean Calculator Two-sided sample size for estimating a population mean: n = (z*sigma/E)^2 with z defaulting to 1.96.
- Sample Size for Mean Practice Create reproducible practice for Sample Size for Mean Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Sample Size for Proportion Calculator Two-sided sample size for estimating a proportion: n = p*(1-p)*(z/E)^2 with z defaulting to 1.96.
- Sample Size Missingness Denominator Tool Resolve the observed sample count and missing fraction from explicit total and missing counts.
- Sample Size Rounding Achieved Margin Tool Calculate sample size rounding achieved margin from explicit caller-supplied inputs.
- Sample Variance Calculator Calculate unbiased sample variance using the n−1 denominator.
- Sample Variance Denominator Residual Tool Calculate sample variance denominator residual from explicit caller-supplied inputs.
- Sample Variance Deviation Term Tool Return one observation's squared-deviation contribution to sample variance using the supplied mean and n-1 denominator.
- Sample Variance One Point Deletion Term Tool Compute sample variance one point deletion term from explicit bounded inputs.
- Skewness Calculate the sample skewness of a list of numbers.
- Skewness Standardization Scale Factor Tool Calculate skewness standardization scale factor from explicit caller-supplied inputs.
- Spearman Rank Correlation Calculator Calculate Spearman correlation using one-based average ranks and the existing Pearson calculation's numeric precision, returning both rank vectors without a p-value.
- Standard Deviation Calculator Calculate the population standard deviation of a dataset.
- Standard Deviation Rounding Interval Envelope Tool Calculate standard deviation rounding interval envelope from explicit caller-supplied inputs.
- Standard Error Calculator Calculate standard error from standard deviation and sample size.
- Standard Error Cluster Weight Reference Tool Calculate standard error cluster weight reference from explicit caller-supplied inputs.
- Student T Statistic Zero Effect Point Tool Calculate student t statistic zero effect point from explicit caller-supplied inputs.
- Studentized Residual Known Leverage Factor Tool Calculate studentized residual known leverage factor from explicit caller-supplied inputs.
- Success Count Complement Table Compute bounded observed success-count complements and rates, with null for zero-trial evidence; no inference of failure mechanisms or confidence intervals.
- Sum of Squares Calculator Calculate the sum of squared deviations from the sample mean.
- T-Interval Calculator Calculate a two-sided Student's t confidence interval for a population mean with unknown sigma.
- Third Central Moment Single Deviation Tool Calculate third central moment single deviation from explicit caller-supplied inputs.
- Trim Explicit Cutoffs Trim observations strictly outside supplied numeric cutoffs, preserving original order and removal provenance; no quantile estimation.
- Trim Fixed Count per Tail Apply fixed-count-per-tail sorted trimming with a nonempty retained center; exact equal values use stable numeric order.
- Two-Sample T-Test Calculator Calculate Welch's or pooled two-sample t statistic for independent samples.
- Unbiased Covariance Centering Correction Tool Compute unbiased covariance centering correction from explicit bounded inputs.
- Unique Count Tool Count the distinct numeric values in a list.
- Variance Denominator Rescale Tool Calculate variance denominator rescale from explicit caller-supplied inputs.
- Variance Negative Roundoff Tolerance Tool Compute variance negative roundoff tolerance from explicit bounded inputs.
- Weight Rescale Standard Error Invariance Check Tool Compute weight rescale standard error invariance check from explicit bounded inputs.
- Weighted Denominator Coverage Report nonnegative weight coverage with explicitly known denominator evidence; unknown denominators are not silently treated as zeros or included in ratios.
- Weighted Mean Calculator Calculate an arithmetic mean using nonnegative observation weights.
- Weighted Mean Centering Term Tool Calculate weighted mean centering term from explicit caller-supplied inputs.
- Weighted Mean Missing Weight Budget Tool Calculate weighted mean missing weight budget from explicit caller-supplied inputs.
- Weighted Mean One Observation Deletion Term Tool Calculate weighted mean one observation deletion term from explicit caller-supplied inputs.
- Weighted Mean One Weight Sensitivity Tool Compute weighted mean one weight sensitivity from explicit bounded inputs.
- Weighted Mean Weight Normalizer Tool Normalize nonnegative observation weights to sum one for a weighted mean; positive finite total weight is required.
- Weighted Quantile Atom Boundary Tool Weighted empirical inverse using an explicit >= versus > atom-boundary convention, clamped at probability one.
- Weighted Quantile Cumulative Boundary Choice Tool Calculate weighted quantile cumulative boundary choice from explicit caller-supplied inputs.
- Weighted Sample Degrees of Freedom Constraint Tool Compute weighted sample degrees of freedom constraint from explicit bounded inputs.
- Weighted Second Moment Contribution Calculate one explicit weight-normalized squared-distance contribution about a supplied origin without estimating variance degrees of freedom.
- Weighted Variance One Weight Derivative Tool Differentiate population weighted variance with respect to one observation weight, accounting for the moving weighted mean.
- Wilcoxon Signed-Rank Test Calculator Calculate a two-sided Wilcoxon signed-rank statistic for matched samples.
- Winsorize Explicit Cutoffs Winsorize finite observations at explicit inclusive numeric cutoffs, retaining original changed indexes; does not estimate population tail cutoffs.
- Winsorize Fixed Count per Tail Apply fixed-count-per-tail winsorization retaining original observation order with a nonempty retained center; exact equal values use stable numeric order.
- Z Confidence Interval Calculator Calculate a two-sided z confidence interval for a population mean.
- Z Confidence Interval Calculator Calculate a two-sided confidence interval for a population mean when the population standard deviation is known.
- Z-Score Calculator Calculate how many standard deviations a value lies from a mean.
- Zscore Zero Spread Policy Tool Apply a supplied center and spread to one z-score, with an explicit zero-spread policy. When undefined, the numeric zero is a sentinel identified by defined=false.