About the StatBench Statistics Calculator
StatBench is a free set of statistics tools for coursework, theses, survey analysis and business reports — no installation needed. Your data never leaves your device; everything is computed in the browser.
Features
- Descriptive statistics — mean, median, mode, sample/population SD and variance, quartiles (4 methods), IQR, skewness, kurtosis, outliers, histogram and box plot
- Normal distribution — z-scores, cumulative, interval and two-tailed probabilities, inverse lookup, shaded curve
- Confidence intervals — mean (t or z) and proportion (Wilson, Clopper–Pearson, Wald) side by side
- Sample size — survey sample size from margin of error and confidence level, finite population correction, response rate, reverse margin of error
- t-tests — one-sample, independent (Welch/Student), paired; one- and two-tailed p-values, CI, Cohen's d, equal-variance F-test
- Chi-square tests — goodness of fit and independence on tables up to 8×8, expected counts, Cramér's V, Yates correction
- Correlation & regression — Pearson r and Spearman ρ with p-values, coefficients with SE and CI, prediction intervals, scatter plot
- Combinatorics & probability — exact nCr, nPr, repetition variants and factorials; binomial and Poisson probabilities
- Tables & guides — z, t, chi-square and F tables plus concept guides built around worked examples
How to use
- Pick a calculator from the numbered tabs at the top.
- Copy a column from Excel or Google Sheets and paste it into the data box, or enter summary values such as mean and SD.
- Results update as you type. Change the confidence level, alternative hypothesis or α to compare.
- “Copy results” copies a tab-separated table you can paste into a spreadsheet or document.
Accuracy
All probability distributions are implemented from scratch without external libraries: the Lanczos approximation for log-gamma, series and continued fractions (Lentz's algorithm) for the regularized incomplete gamma and beta functions, Wichura's AS241 algorithm for normal quantiles, and bisection for t, chi-square and F quantiles. Tail probabilities are computed directly rather than as 1 minus a CDF, so even tiny p-values keep their significant digits.
As of 2026-09-23 the functions were checked against about 900 reference values from SciPy 1.13.1 and about 120 values computed with mpmath at 50-digit precision: every distribution function agrees to a relative error below 1e-10 (mostly below 1e-12). Descriptive statistics, t-tests, chi-square tests and correlation/regression match SciPy and NumPy. Results are usually shown with 6–8 significant digits.
Privacy
Your data is processed only in your browser and is never sent to or stored on any server. Only your light/dark theme choice is saved in the browser.
Frequently asked questions
Should I use the sample or the population standard deviation?
If your data is a sample drawn from a larger group, use the sample SD, which divides by n−1 (Excel STDEV.S). If you measured every member of the group you care about, use the population SD, which divides by n (STDEV.P). Most research and survey data are samples.
My quartiles differ from Excel or another calculator.
There are several ways to compute quartiles. The default matches Excel QUARTILE.INC (R type 7); you can switch to QUARTILE.EXC (SPSS, Minitab), Tukey hinges or the TI-calculator method. Choose the same method as the tool you compare with.
Welch or Student for an independent t-test?
Unless you are confident that the variances are equal, use Welch's test. It loses almost nothing when variances are equal and keeps the error rate accurate when they are not. Welch is the default.
The p-value shows '< 1e-300'.
The p-value is smaller than the smallest number double-precision floating point can represent. It is effectively 0; report it as p < 0.001.
What expected proportion should I enter for a survey sample size?
Use 50% if you have no prior information. p(1−p) is largest at p = 0.5, so it gives the safest sample size that keeps the margin of error on target whatever the result.
I get a warning that expected counts are below 5.
With many small expected counts the chi-square approximation becomes inaccurate. Merge categories, or for a 2×2 table consider Fisher's exact test.
Is my data stored or sent anywhere?
No. All calculations run in JavaScript inside your browser and the data is never sent to a server. Closing the page discards your input.
Can I paste data copied from Excel?
Yes. A single column is separated by line breaks and multiple columns by tabs, and both are recognized. In the correlation calculator you can paste two columns into the X box and they are split into X and Y.