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Statistics Calculators

Summarize numeric datasets and plan samples without hiding denominator choices, interpolation rules, or survey-design assumptions. Each calculator identifies the statistical boundary behind its answer and keeps a reproducible example beside the calculation.

200 statistics calculatorsDescriptive dataSampling and estimationConfidence intervalsHypothesis testsDistribution analysisTime seriesRobust and nonparametric methodsRegression and correlation

Descriptive data

Explore center, spread, order statistics, robust summaries, and dataset scale. Pages that depend on quartiles or percentiles identify their interpolation convention instead of presenting the result as universal across software.

Arithmetic Mean Calculator

Finds the arithmetic mean of a numeric dataset and keeps the count and total visible.

Median Calculator

Finds the middle of an ordered dataset, averaging the two central values when the count is even.

Mode Calculator

Identifies the most frequently occurring value or tied values in a numeric dataset.

Data Range Calculator

Measures the full span of a dataset from its smallest observation to its largest.

Sample Variance Calculator

Calculates sample variance with the n minus one denominator used to estimate population variance.

Population Variance Calculator

Calculates variance when the entered values constitute the complete population of interest.

Sample Standard Deviation Calculator

Calculates sample standard deviation in the original measurement unit.

Population Standard Deviation Calculator

Calculates the standard deviation of a complete population represented by the entered values.

Coefficient of Variation Calculator

Expresses sample standard deviation relative to the absolute arithmetic mean.

Standard Error of the Mean Calculator

Estimates the standard deviation of the sample-mean sampling distribution from one dataset.

Sum of Squared Deviations Calculator

Totals squared deviations from the arithmetic mean before any variance denominator is applied.

Root Mean Square Calculator

Calculates the quadratic mean by averaging squared observations and taking the square root.

Trimmed Mean Calculator

Removes an equal percentage of ordered observations from both tails before calculating the mean.

Winsorized Mean Calculator

Replaces extreme ordered observations with the nearest retained boundary values before averaging.

Range to Mean Ratio Calculator

Compares the dataset range with the absolute arithmetic mean as a percentage.

Interquartile Range Calculator

Measures the width of the middle half of an ordered dataset using linearly interpolated quartiles.

Dataset Quartiles Calculator

Returns the first quartile, median, and third quartile from an ordered numeric dataset.

Five Number Summary Calculator

Summarizes location and spread with the minimum, first quartile, median, third quartile, and maximum.

Dataset Percentile Calculator

Finds an entered percentile with type-7 linear interpolation between ordered observations.

Median Absolute Deviation Calculator

Calculates the median absolute deviation from the dataset median as a robust scale measure.

Sampling and estimation

Plan sample sizes, margins of error, finite-population adjustments, cluster effects, stratum allocations, and survey-weight effective sample size. These tools separate arithmetic precision from representativeness and study design.

Mean Estimate Sample Size Calculator

Estimates the sample size required to estimate a mean with known or planning standard deviation.

Proportion Estimate Sample Size Calculator

Estimates a simple-random-sample size for a proportion using an expected proportion and absolute margin.

Finite Population Sample Size Calculator

Applies the finite-population adjustment to an initial sample-size requirement.

Known Sigma Mean Margin of Error Calculator

Calculates a two-sided mean margin of error when the population standard deviation is treated as known.

Estimated Sigma Mean Margin of Error Calculator

Calculates a mean margin of error from a sample standard deviation and a supplied t critical value.

Proportion Margin of Error Calculator

Calculates the normal-approximation margin of error around an observed sample proportion.

Proportion Standard Error Calculator

Estimates the standard error of a sample proportion under independent Bernoulli sampling.

Difference in Proportions Standard Error Calculator

Calculates the unpooled standard error for a difference between two independent sample proportions.

Pooled Proportion Calculator

Combines successes and trials from two groups into one pooled proportion.

Cluster Design Effect Calculator

Estimates the variance inflation from equal-size cluster sampling using average cluster size and intracluster correlation.

Design Effect Effective Sample Size Calculator

Translates an actual sample count into an approximate simple-random-sample equivalent using design effect.

Nonresponse Adjusted Sample Size Calculator

Inflates a completed-sample target for an expected nonresponse percentage.

Participants per Cluster Calculator

Allocates a design-effect-adjusted total sample evenly across a chosen number of clusters.

Proportional Stratum Allocation Calculator

Allocates a total sample to one stratum in proportion to that stratum’s population share.

Two-Stratum Neyman Allocation Calculator

Splits a fixed sample between two strata in proportion to population size times within-stratum standard deviation.

Sampling Fraction Calculator

Reports the sampled share of a finite population as a percentage.

Finite Population Correction Calculator

Calculates the finite-population correction for sampling without replacement.

Kish Effective Sample Size Calculator

Estimates effective sample size from unequal positive analysis weights using Kish’s approximation.

Relative Standard Error Calculator

Expresses a standard error relative to the absolute magnitude of its estimate.

Sample Size for a New Margin of Error Calculator

Scales an existing sample size to a tighter or wider target margin under the inverse-square relationship.

Confidence intervals

Estimate uncertainty for means, proportions, rates, ratios, correlations, regression quantities, predictions, and normal-theory variability. Each page states the interval convention and exposes any critical value supplied by the user.

Known Sigma Mean Difference Interval Calculator

Builds a two-sided interval for the difference between independent means when both population standard deviations are treated as known.

Welch Mean Difference Interval Calculator

Estimates an independent-means difference without assuming equal population variances and reports Welch–Satterthwaite degrees of freedom.

Paired Mean Difference Interval Calculator

Forms a t interval from within-pair differences rather than treating the two measurements as independent samples.

Wald Proportion Interval Calculator

Computes the familiar symmetric normal-approximation interval around an observed proportion.

Wilson Score Interval Calculator

Calculates Wilson score limits, which recenter and widen the interval according to sample size.

Agresti Coull Interval Calculator

Uses an adjusted count and adjusted sample size before applying a symmetric proportion interval.

One-Sided Proportion Upper Bound Calculator

Finds a one-sided Wilson upper confidence bound for a binomial proportion.

One-Sided Proportion Lower Bound Calculator

Finds a one-sided Wilson lower confidence bound for a binomial proportion.

Difference in Proportions Interval Calculator

Constructs an unpooled normal interval for the difference between two independent proportions.

Risk Ratio Confidence Interval Calculator

Calculates a log-scale confidence interval for the ratio of two independent risks.

Odds Ratio Confidence Interval Calculator

Computes an odds ratio and a large-sample interval from a complete 2×2 table.

Poisson Rate Confidence Interval Calculator

Estimates a Poisson event rate and two-sided limits using Byar’s chi-square approximation.

Variance Confidence Interval Calculator

Applies chi-square quantiles to estimate a normal population variance.

Standard Deviation Confidence Interval Calculator

Takes square roots of chi-square variance limits to estimate a normal population standard deviation.

Correlation Confidence Interval Calculator

Uses Fisher’s z transformation to form an approximate interval for a Pearson correlation.

Regression Slope Confidence Interval Calculator

Forms a confidence interval around a fitted regression slope using its model-based standard error.

Regression Intercept Confidence Interval Calculator

Forms a confidence interval for the fitted response where all predictors equal zero.

Mean Response Confidence Interval Calculator

Calculates uncertainty around the expected response at a specified predictor setting.

Individual Prediction Interval Calculator

Calculates a prediction interval for one future response at a stated predictor setting.

Normal Tolerance Interval Calculator

Applies a supplied normal-theory tolerance factor to a sample mean and standard deviation.

Hypothesis tests

Evaluate mean, proportion, contingency-table, variance, rank, sequence, and outlier questions. Results include the statistic, reference degrees of freedom where applicable, and a two-sided or upper-tail p-value labeled by method.

One Sample T Test Calculator

Tests a sample mean against a stated null value with an estimated standard deviation.

Paired T Test Calculator

Tests whether the population mean of paired differences is zero.

Welch Two Sample T Test Calculator

Tests independent means without imposing equal variances.

Pooled Two Sample T Test Calculator

Tests independent means with a common variance estimated by pooling both sample variances.

One Proportion Z Test Calculator

Tests an observed binomial proportion against a null proportion using the null standard error.

Two Proportion Z Test Calculator

Tests equality of two independent proportions with a pooled null standard error.

Chi Square Goodness of Fit Calculator

Compares observed category counts with a fully specified expected count pattern.

Chi Square Independence Test Calculator

Tests association in a 2×2 table by comparing observed cells with margins-based expected counts.

Fisher Exact Test Calculator

Calculates the two-sided Fisher exact p-value for a 2×2 table with fixed margins.

McNemar Test Calculator

Tests marginal symmetry in paired binary data from the two discordant cell counts.

One Way ANOVA Calculator

Partitions variation into between-group and within-group components for three independent samples.

F Test for Two Variances Calculator

Compares two normal-population variances using their sample variance ratio.

Levene Test Calculator

Tests equality of group variances by applying ANOVA to absolute deviations from each group mean.

Bartlett Test Calculator

Tests homogeneity of several normal-population variances using a corrected log-variance statistic.

Mann Whitney U Test Calculator

Compares two independent groups through pooled ranks and reports a tie-corrected normal approximation.

Wilcoxon Signed Rank Test Calculator

Ranks absolute nonzero paired differences and compares the positive and negative rank sums.

Kruskal Wallis Test Calculator

Compares three independent groups with pooled ranks and a tie-corrected chi-square reference.

One Sample Sign Test Calculator

Counts observations above and below a hypothesized median and applies an exact two-sided binomial test.

Runs Test for Randomness Calculator

Checks whether a binary sequence has unusually few or many runs relative to its counts of zeros and ones.

Grubbs Outlier Test Calculator

Tests the most extreme standardized deviation in an approximately normal sample.

Regression and correlation

Measure paired association, fit simple regression quantities, inspect explained variation and collinearity, and convert between common model scales. Pages distinguish arithmetic identities from claims about causation or model adequacy.

Pearson Correlation Calculator

Measures the strength and direction of a linear association between two paired numeric variables.

Spearman Rank Correlation Calculator

Calculates a monotonic association from the ranks of paired observations.

Kendall Tau Correlation Calculator

Compares concordant and discordant pairs to measure ordinal association.

Sample Covariance Calculator

Calculates covariance for paired observations using the sample denominator.

Population Covariance Calculator

Calculates covariance when the entered paired values are the complete population of interest.

Simple Regression Slope Calculator

Fits the least-squares slope for a simple linear regression with one predictor.

Simple Regression Intercept Calculator

Calculates the least-squares intercept from paired predictor and response values.

Regression Predicted Value Calculator

Evaluates a supplied simple-regression line at a chosen predictor value.

Regression Residual Calculator

Calculates the vertical residual left after a regression prediction.

Coefficient of Determination Calculator

Reports the fraction of response variation accounted for by a fitted prediction relative to a mean-only baseline.

Adjusted R Squared Calculator

Adjusts R² for sample size and the number of fitted predictors.

Regression Standard Error Calculator

Estimates the residual spread of a regression after accounting for fitted predictors.

Regression F Statistic Calculator

Tests whether a multiple regression explains more variation than an intercept-only model.

Variance Inflation Factor Calculator

Translates an auxiliary regression R² into the variance inflation associated with predictor collinearity.

Partial Correlation Calculator

Removes the linear association with one control variable from a pairwise correlation.

Standardized Regression Coefficient Calculator

Converts a simple-regression slope into standard-deviation units for comparing predictors on different scales.

Logit to Probability Calculator

Converts a log-odds value into a probability between zero and one.

Probability to Logit Calculator

Converts a probability into the log-odds scale used by logistic models.

Exponential Regression Prediction Calculator

Evaluates an exponential regression curve at a selected predictor value.

Power Regression Prediction Calculator

Evaluates a power-law regression curve for a positive predictor value.

Distribution analysis

Work with Bernoulli, binomial, Poisson, uniform, exponential, Weibull, lognormal, gamma, beta, F, and normal quantities, then summarize skewness, kurtosis, and count dispersion with their parameter conventions visible.

Bernoulli Mean and Variance Calculator

Calculates the mean and variance of a Bernoulli indicator with one trial.

Binomial Expected Count and Deviation Calculator

Calculates the expected number and standard deviation of successes in independent identical Bernoulli trials.

Poisson Expected Count and Deviation Calculator

Calculates the mean and standard deviation of a Poisson event count.

Uniform Mean and Variance Calculator

Calculates moments of a continuous uniform distribution on a finite interval.

Exponential Mean and Half Life Calculator

Calculates the mean waiting time and median-like half-life for an exponential waiting-time model.

Weibull Reliability Calculator

Calculates the probability that a Weibull lifetime exceeds a chosen time.

Weibull Quantile Calculator

Finds the Weibull time by which an entered cumulative fraction of lifetimes has occurred.

Lognormal Mean Median and Mode Calculator

Calculates the three central summaries of a lognormal variable from its log-scale parameters.

Lognormal Parameter Conversion Calculator

Converts an arithmetic mean and standard deviation into the normal parameters of a lognormal model.

Gamma Mean and Variance Calculator

Calculates the first two moments of a gamma distribution from shape and scale.

Beta Mean and Variance Calculator

Calculates the mean and variance of a beta distribution on the unit interval.

F Ratio Statistic Calculator

Forms the ratio of two positive variances for comparison with an F reference distribution.

Normal Interval Expected Frequency Calculator

Calculates the expected fraction and count inside an interval under a normal model.

Percentile to Normal Quantile Calculator

Finds a normal-distribution quantile from a mean, standard deviation, and cumulative percentile.

Distribution Skewness Calculator

Calculates the moment coefficient of skewness for a numeric dataset.

Distribution Excess Kurtosis Calculator

Calculates excess kurtosis relative to the normal distribution’s value of zero.

Normal Method of Moments Calculator

Maps the first two moments of a normal model to its location and spread parameters.

Gamma Method of Moments Calculator

Estimates gamma shape and scale by matching the first two observed moments.

Count Data Dispersion Index Calculator

Compares count variance with its mean to screen for underdispersion, equidispersion, or overdispersion relative to Poisson behavior.

Zero Event Probability Calculator

Calculates the probability of observing no events in a Poisson interval.

Robust and nonparametric methods

Use resistant centers, pairwise differences, ranks, empirical probabilities, and robust fences when a mean-and-variance summary is not enough. Each tool names its order-statistic convention and screening limits.

Median of Pairwise Slopes Calculator

Calculates the Theil–Sen median of nonvertical pairwise slopes for paired data.

Hodges Lehmann Location Calculator

Calculates the one-sample Hodges–Lehmann pseudomedian from all self-inclusive pairwise averages.

Median Polish Center Calculator

Provides a robust center for a flattened two-way table before row and column effects are examined separately.

Robust Z Score Calculator

Standardizes one value using the sample median and a normal-consistency-scaled median absolute deviation.

Modified Z Score Calculator

Calculates the common MAD-based modified z score for a selected observation.

Median Absolute Pairwise Difference Calculator

Summarizes pairwise separation with the median of all absolute differences.

Sn Robust Scale Calculator

Calculates the Rousseeuw–Croux Sn robust scale estimator.

Qn Robust Scale Calculator

Calculates the Rousseeuw–Croux Qn scale from the first quartile of pairwise distances.

Interdecile Range Calculator

Measures the width of the central 80% using type-7 percentile interpolation.

Interpercentile Range Calculator

Calculates the width between two user-selected interpolated percentiles.

Bowley Skewness Calculator

Measures quartile-based skewness using the median and the two quartiles.

Moors Kurtosis Calculator

Uses octiles to describe tail weight relative to the interquartile range.

Rank Sum Calculator

Sums the pooled ranks assigned to one independent group.

Signed Rank Sum Calculator

Calculates the signed rank sum after removing zero paired differences and ranking absolute differences.

Empirical Cumulative Probability Calculator

Reports the observed fraction of sample values at or below a selected value.

Empirical Survival Probability Calculator

Reports the observed fraction strictly above a selected value.

Quantile Rank Calculator

Places a selected value within the observed sample as a cumulative percentage.

Tukey Outlier Fences Calculator

Calculates inner Tukey fences from interpolated quartiles and identifies observations outside them.

Adjusted Boxplot Fences Calculator

Uses a Bowley-skewness adjustment to make upper and lower boxplot fences respond differently to asymmetric central data.

Winsorized Variance Calculator

Replaces equal-tail observations at retained boundaries before calculating sample variance.

Time series

Smooth ordered observations, measure serial dependence, evaluate forecast errors, estimate seasonal factors, and project trends while keeping window placement and forecast conventions explicit.

Simple Moving Average Calculator

Calculates the trailing simple moving average for the final time-series window.

Weighted Moving Average Calculator

Calculates a weighted average of the supplied recent observations.

Exponential Smoothing Calculator

Applies single exponential smoothing and returns the final smoothed level.

Double Exponential Smoothing Calculator

Uses Holt’s level-and-trend recursion to return a one-step forecast after the final observation.

Cumulative Moving Average Calculator

Returns the cumulative average at the final time point.

Rolling Standard Deviation Calculator

Calculates sample standard deviation over the final rolling window.

Rolling Z Score Calculator

Standardizes the final observation against the preceding rolling window including that observation.

Lag One Autocorrelation Calculator

Measures linear association between adjacent observations one period apart.

Autocovariance Calculator

Calculates the autocovariance at a selected lag using the full-series mean.

Mean Absolute Scaled Error Calculator

Scales forecast absolute error by the in-sample naive forecast error.

Mean Absolute Percentage Error Calculator

Calculates average absolute forecast error as a percentage of the actual values.

Symmetric Mean Absolute Percentage Error Calculator

Calculates a denominator-symmetric percentage error for paired actual and forecast values.

Root Mean Squared Forecast Error Calculator

Calculates the square-root mean squared error of a forecast sequence.

Mean Forecast Error Calculator

Calculates signed average forecast error to reveal directional bias.

Tracking Signal Calculator

Divides cumulative signed forecast error by mean absolute deviation to flag persistent bias.

Seasonal Index Calculator

Estimates each seasonal position’s mean relative to the overall series mean.

Deseasonalized Value Calculator

Removes a multiplicative seasonal factor from one observed value.

Compound Trend Projection Calculator

Projects a starting value with a constant compound growth rate.

Linear Trend Projection Calculator

Projects a value by extending a constant additive trend.

Naive Forecast Interval Calculator

Forms a simple interval around the last-observation naive forecast using a supplied forecast-error spread.

Experimental design and power

Plan sample sizes, compare standardized effects, count factorial runs, and make design assumptions visible before collecting data.

One Sample Mean Test Power Calculator

Estimates approximate two-sided power for a one-sample mean test.

Two Sample Mean Test Power Calculator

Estimates approximate power for a two-group mean comparison.

Paired Mean Test Power Calculator

Estimates power for a paired-mean design from the expected within-pair difference.

One Proportion Test Power Calculator

Estimates approximate power for a one-proportion test.

Two Proportion Test Power Calculator

Estimates approximate power for comparing two independent proportions.

Correlation Test Power Calculator

Estimates approximate power for detecting a nonzero correlation.

ANOVA Effect Size Calculator

Converts an ANOVA eta-squared value to Cohen’s f.

Cohen D Effect Size Calculator

Calculates Cohen’s d for a standardized difference between two means.

Hedges G Effect Size Calculator

Applies a small-sample correction to Cohen’s d.

Glass Delta Effect Size Calculator

Calculates Glass’s delta using the control-group standard deviation.

Cohen H Effect Size Calculator

Calculates Cohen’s h for a difference between two proportions.

Cramer V Effect Size Calculator

Calculates Cramer’s V from a contingency-table chi-square statistic.

Eta Squared Calculator

Calculates eta squared as the share of total variation associated with group differences.

Partial Eta Squared Calculator

Calculates partial eta squared for an effect relative to that effect’s error term.

Omega Squared Calculator

Calculates a less biased ANOVA omega-squared estimate.

Balanced Factorial Run Count Calculator

Counts observations in a balanced two-factor design.

Full Factorial Treatment Count Calculator

Counts treatment combinations in a full factorial.

Fractional Factorial Run Count Calculator

Counts runs in a simple two-level fractional factorial.

Replication Requirement Calculator

Estimates per-group replication for a two-mean target effect.

Randomization Block Size Calculator

Calculates the number of assignments in a balanced randomization block.

Categorical and diagnostic rates

Translate two-by-two counts and population denominators into sensitivity, risk, prevalence, likelihood, and agreement measures with their conditioning rules stated.

Sensitivity Calculator

Calculates sensitivity, the share of diseased cases detected by a test.

Specificity Calculator

Calculates specificity, the share of non-diseased cases correctly ruled out.

Positive Predictive Value Calculator

Calculates the chance that a positive test result is a true positive.

Negative Predictive Value Calculator

Calculates the chance that a negative test result is a true negative.

Diagnostic Accuracy Calculator

Calculates the proportion of all reference outcomes classified correctly.

False Positive Rate Calculator

Calculates the false-positive rate among non-diseased cases.

False Negative Rate Calculator

Calculates the false-negative rate among diseased cases.

Positive Likelihood Ratio Calculator

Calculates the positive likelihood ratio for a diagnostic result.

Negative Likelihood Ratio Calculator

Calculates the negative likelihood ratio for a diagnostic result.

Diagnostic Odds Ratio Calculator

Calculates the diagnostic odds ratio from a two-by-two table.

Prevalence Calculator

Calculates the proportion of a population with an existing condition at a stated time.

Incidence Proportion Calculator

Calculates cumulative incidence, also called incidence proportion, over a stated interval.

Incidence Rate Calculator

Calculates an incidence rate using accumulated person-time.

Risk Difference Calculator

Calculates the absolute difference in risks between two groups.

Relative Risk Calculator

Calculates the ratio of risks between two groups.

Attributable Fraction Among Exposed Calculator

Calculates the fraction of exposed-group risk attributable to the exposure under a causal interpretation.

Population Attributable Fraction Calculator

Calculates the population attributable fraction from exposure prevalence and relative risk.

Number Needed to Treat Calculator

Calculates the number needed to treat from an absolute risk reduction.

Number Needed to Harm Calculator

Calculates the number needed to harm from an absolute risk increase.

Cohen Kappa Agreement Calculator

Calculates Cohen’s kappa beyond chance agreement.

Choosing a descriptive summary

The arithmetic mean uses every observation, while the median and trimmed or winsorized means respond differently to long tails and extreme values. Spread measures also answer different questions: standard deviation follows deviations from the mean, the interquartile range describes the middle half, and range uses only the two endpoints.

Sample and population denominators

Variance and standard deviation pages distinguish a complete population from a sample used to estimate a larger population. That choice changes the denominator and should be made from the study boundary, not selected because one numerical answer looks preferable.

Percentiles and software conventions

Quantiles can differ across programs because several interpolation rules are legitimate. The dataset percentile and quartile pages in this category state that they use type-7 linear interpolation, making comparison and reproduction possible.

Planning a sample

Sample-size formulas begin with a confidence level, expected variability, and desired precision. Finite populations, nonresponse, clustering, unequal weights, and stratum allocation can then change how many records must be approached or observed.

What a larger sample cannot repair

Increasing the count generally reduces sampling error under the assumed design. It does not repair a biased frame, a poor measurement, systematic nonresponse, dependence ignored by the formula, or a mismatch between the sampled population and the population named in the conclusion.