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Statistics & Data Calculators

Probability, statistical significance, confidence intervals and data analysis calculators for coursework and real analysis.

101 calculatorsProbability, distributions & data analysis

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Confidence IntervalCalculate the confidence interval for a sample mean.T-Score CalculatorCalculate the one-sample t-statistic for testing whether a sample mean differs from a hypothesized population mean.Binomial ProbabilityCalculate the probability of getting exactly k successes in n independent trials, using the binomial distribution.Two-Sample T-TestCalculate the t-statistic for comparing the means of two independent samples (Welch's t-test).

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Sample Size CalculatorCalculate the minimum sample size needed for a survey or study at a given confidence level and margin of error.
Margin of Error CalculatorCalculate the margin of error for a survey result given sample size and confidence level.
Correlation Coefficient CalculatorCalculate the Pearson correlation coefficient between two paired sets of numbers.
Percentile Rank CalculatorFind what percentile a value falls at within a dataset.
Coefficient of Variation CalculatorCalculate the coefficient of variation - a standardized measure of data spread relative to the mean.
Normal Distribution Probability CalculatorCalculate the probability of a value falling below, above, or between points on a normal distribution.
Empirical Rule (68-95-99.7) CalculatorCalculate the value ranges covering 68%, 95%, and 99.7% of a normal distribution.
Skewness CalculatorCalculate the sample skewness of a dataset to measure the asymmetry of its distribution.
Interquartile Range (IQR) CalculatorCalculate the first quartile, third quartile, interquartile range, and outlier bounds for a dataset.
Kurtosis CalculatorCalculate the sample excess kurtosis of a dataset to measure how heavy-tailed its distribution is.
Standard Error of the Mean CalculatorCalculate the standard error of the mean from a sample's standard deviation and size.
Covariance CalculatorCalculate the sample covariance between two paired sets of numbers.
Poisson Probability CalculatorCalculate the probability of a given number of events occurring in a fixed interval, using the Poisson distribution.
Geometric Mean CalculatorCalculate the geometric mean of a set of numbers - the standard way to average growth rates or investment returns.
Harmonic Mean CalculatorCalculate the harmonic mean of a set of numbers - the standard way to average rates like speed.
Relative Risk & Odds Ratio CalculatorCalculate relative risk and odds ratio from a 2x2 exposure/outcome contingency table.
Chi-Square Goodness of Fit CalculatorCalculate the chi-square statistic to test how well observed data fits expected frequencies.
Cohen's d Effect Size CalculatorCalculate Cohen's d - a standardized measure of the size of the difference between two group means.
Two-Proportion Z-Test CalculatorCalculate the z-statistic for comparing two independent sample proportions.
Bayes' Theorem CalculatorCalculate the probability of a hypothesis given new evidence, using Bayes' Theorem.
Inverse Normal Distribution CalculatorFind the z-score and value corresponding to a given percentile or cumulative probability.
F-Test (Variance Ratio) CalculatorCalculate the F-statistic to compare the variances of two samples.
Linear Regression CalculatorCalculate the least-squares regression line, slope, intercept, and R² for a set of paired data points.
Median Absolute Deviation (MAD) CalculatorCalculate the median absolute deviation - a robust measure of spread that resists distortion from outliers.
Histogram Bin CalculatorCalculate the recommended number of histogram bins and bin width for a dataset, using Sturges' Rule.
Exponential Distribution Probability CalculatorCalculate the probability of waiting a given time or less for an event, using the exponential distribution.
Uniform Distribution Probability CalculatorCalculate the probability of a value falling within a range, for a continuous uniform distribution.
Hypergeometric Distribution CalculatorCalculate the probability of drawing a specific number of successes when sampling without replacement.
Confidence Interval for a Proportion CalculatorCalculate the confidence interval for a population proportion from sample data.
Weighted Standard Deviation CalculatorCalculate the standard deviation of a dataset where each value has a different weight or importance.
Correlation Significance Test CalculatorTest whether a correlation coefficient is statistically significant, using a t-test.
Confidence Interval for Difference of Two MeansCalculate the confidence interval for the difference between two independent sample means.
Grubbs' Outlier Test CalculatorTest whether the most extreme value in a dataset is a statistical outlier, using Grubbs' Test.
Cohen's Kappa (Interrater Agreement) CalculatorCalculate Cohen's Kappa to measure agreement between two raters, correcting for chance agreement.
Trimmed Mean CalculatorCalculate a trimmed mean - a robust average that removes a percentage of extreme values from each end before averaging.
Standard Deviation Range Estimate CalculatorQuickly estimate a dataset's standard deviation from its range, using the range rule of thumb.
A/B Test Sample Size CalculatorCalculate the sample size needed per variant to reliably detect a minimum effect size in an A/B test.
Percentile Value CalculatorFind the value at a given percentile within a dataset.
Relative Frequency CalculatorCalculate the relative frequency (proportion) of each category from raw counts.
Standard Score Comparison CalculatorCompare two raw scores from different distributions by converting both to z-scores.
Frequency Table Class Width CalculatorCalculate the class width needed to build a frequency table with a chosen number of classes.
Cumulative Frequency CalculatorCalculate the cumulative frequency and cumulative percentage from a table of category counts.
Z-Score Range Coverage CalculatorCalculate what percentage of a normal distribution falls within any chosen number of standard deviations of the mean.
Simple Random Sample Selection ProbabilityCalculate the probability that a specific individual is included in a simple random sample.
Stratified Sample Allocation CalculatorCalculate how to proportionally allocate a total sample size across population strata (subgroups).
One-Way ANOVA CalculatorCalculate the F-statistic for a one-way ANOVA comparing the means of three independent groups.
Paired T-Test CalculatorCalculate the t-statistic for comparing two sets of matched or before/after measurements.
One-Sample Z-Test CalculatorCalculate the z-statistic and p-value for testing a sample mean against a known population mean and standard deviation.
P-Value from Z-Score CalculatorConvert a z-score into a one-tailed or two-tailed p-value.
P-Value from T-Score CalculatorApproximate the p-value for a t-statistic and its degrees of freedom.
Statistical Power CalculatorEstimate the statistical power of a two-sample test given effect size, sample size per group, and significance level.
Chi-Square Test of Independence CalculatorTest whether two categorical variables are independent, using a 2x2 contingency table.
McNemar's Test CalculatorTest for a significant change in paired categorical data, such as before/after survey responses.
Fisher's Exact Test CalculatorCalculate the exact p-value for a 2x2 contingency table, ideal for small sample sizes.
Wilson Score Interval CalculatorCalculate a confidence interval for a proportion using the Wilson score method, more reliable than the normal approximation for small samples.
Confidence Interval for Variance CalculatorCalculate the confidence interval for a population variance and standard deviation from sample data.
Confidence Interval for a Poisson Rate CalculatorCalculate an exact confidence interval for a Poisson rate or count, using the chi-square relationship.
Incidence Rate Ratio CalculatorCalculate the incidence rate ratio and its confidence interval between two groups, using person-time data.
Number Needed to Treat (NNT) CalculatorCalculate the number needed to treat from control and treatment group event rates.
Diagnostic Test Accuracy CalculatorCalculate sensitivity, specificity, predictive values, and likelihood ratios from a diagnostic test's confusion matrix.
Log-Normal Distribution Probability CalculatorCalculate the probability of a value on a log-normal distribution, given the mean and standard deviation of its logarithm.
Negative Binomial Probability CalculatorCalculate the probability of needing a specific number of failures before reaching a target number of successes.
Geometric Distribution Probability CalculatorCalculate the probability that the first success occurs on a specific trial.
Multinomial Probability CalculatorCalculate the probability of a specific set of outcome counts across more than two categories.
Cramer's V CalculatorCalculate Cramer's V, a measure of association strength between two categorical variables, from a chi-square statistic.
Eta-Squared CalculatorCalculate eta-squared, the proportion of total variance explained by group membership in an ANOVA.
Cohen's h CalculatorCalculate Cohen's h, a standardized effect size for comparing two proportions.
Process Capability (Cpk) CalculatorCalculate Cp and Cpk to assess how well a process fits within its specification limits.
Control Chart Limits (X-bar and R) CalculatorCalculate upper and lower control limits for X-bar and R control charts, using standard SPC constants.
DPMO and Sigma Level CalculatorCalculate defects per million opportunities (DPMO) and the approximate Six Sigma level for a process.
Spearman's Rank Correlation CalculatorCalculate Spearman's rank correlation coefficient to measure the monotonic relationship between two variables.
Fleiss' Kappa CalculatorCalculate Fleiss' Kappa to measure agreement among three or more raters classifying items into two categories.
Cronbach's Alpha CalculatorCalculate Cronbach's alpha to measure the internal consistency reliability of a multi-item scale or test.
Benford's Law Deviation CalculatorCompare observed leading-digit frequencies to Benford's Law to check for anomalies in a dataset.
Runs Test for Randomness CalculatorTest whether a binary sequence shows statistically significant patterns, using the Wald-Wolfowitz runs test.
Finite Population Correction Factor CalculatorCalculate the finite population correction factor used to adjust standard error when sampling a large fraction of a small population.
Systematic Sampling Interval CalculatorCalculate the sampling interval for systematic sampling from a population list.
Cluster Sampling Design Effect CalculatorCalculate the design effect and effective sample size for a cluster sample, given the intraclass correlation.
Survey Response Rate CalculatorCalculate the response rate for a survey from completed responses and total attempted contacts.
Signal-to-Noise Ratio CalculatorCalculate the signal-to-noise ratio (SNR) as a plain ratio and in decibels.
Standardized Residual CalculatorCalculate the standardized residual for an observed value against a predicted value, and flag potential outliers.
Two-Sample Z-Test CalculatorCalculate the z-statistic for comparing two independent sample means when population standard deviations are known.
Confidence Interval for Difference of Two ProportionsCalculate the confidence interval for the difference between two independent sample proportions.
Sample Size for Mean Estimation CalculatorCalculate the minimum sample size needed to estimate a population mean within a target margin of error.
Pooled Standard Deviation CalculatorCalculate the pooled standard deviation from two independent samples, assuming equal population variances.
Modified Z-Score Outlier DetectorDetect outliers using the modified z-score method, based on median absolute deviation instead of the mean.
Gini Coefficient CalculatorCalculate the Gini coefficient to measure inequality within a set of values, such as income or wealth.
Shannon Entropy CalculatorCalculate the Shannon entropy of a set of category counts, measuring the unpredictability or diversity of the distribution.
Lag-1 Autocorrelation CalculatorCalculate the lag-1 autocorrelation of a time series, measuring how strongly each value relates to the one before it.
Moving Average CalculatorCalculate the simple moving average of a data series across a chosen window size.
Exponential Smoothing Forecast CalculatorForecast the next value in a time series using simple exponential smoothing.
Confidence Interval for the Median CalculatorCalculate a nonparametric confidence interval for a dataset's median, based on order statistics.
Relative Standard Error CalculatorCalculate the relative standard error (RSE) of an estimate, expressed as a percentage of the estimate itself.
Index of Dispersion CalculatorCalculate the variance-to-mean ratio to test whether count data is more clustered or more uniform than random.
Youden's J Index CalculatorCalculate Youden's J statistic to summarize a diagnostic test's overall discriminative ability.
Mann-Whitney U Test CalculatorCalculate the Mann-Whitney U statistic, a nonparametric alternative to the two-sample t-test.
Adjusted R-Squared CalculatorCalculate adjusted R-squared from a regression's R-squared, sample size, and number of predictors.

About Statistics & Data Calculators

Standard deviation by hand is tedious and error-prone one input at a time - these calculators run the actual statistical formulas (not approximations) for probability, significance testing, and distribution analysis, showing the work so you can verify it, not just trust it.