In a significance test the arithmetic is the easy part and the interpretation is where it goes wrong. A t-test will hand you a p-value whether or not your observations were independent, whether or not the difference is large enough to be worth acting on, and whether or not you decided which tail you cared about before you looked at the data. The number arrives with the same confident face either way, which is what makes a wrong one dangerous: nobody who reads it downstream can tell. So every page here shows the working rather than only the verdict, and says what its result does not mean as plainly as what it does. Underneath, the distribution functions are the whole job — there is no closed form for these tail probabilities, so they are approximated, and an approximation that is quietly wrong looks exactly like one that is right. Ours are checked against all 2300 entries of the NIST/SEMATECH critical-value tables, and each test reproduces the worked example printed in the handbook section it is built from — including four cells where the handbook's own tables turned out to be the thing that was off.
Tools in this category
Standard Deviation Calculator
Paste a list of numbers for the mean, variance and standard deviation — sample and population side by side, so the n − 1 you need is the one you get.
Confidence Interval Calculator
Turn a mean, a standard deviation and a sample size into a margin of error and an interval, with the Student t value the sample size actually calls for.
Z-Score Calculator
Turn a value, a mean and a standard deviation into a z-score, then into the share of a normal distribution below it, above it and outside it either way.
T-Test Calculator
Run a one-sample, two-sample or paired t-test on numbers you paste in: the t statistic, its degrees of freedom, the p-value and the size of the difference.
Chi-Square Test Calculator
Paste a contingency table of counts and get the chi-square statistic, its degrees of freedom, the p-value, the critical value and the smallest expected count.
One-Way ANOVA Calculator
Paste one group of readings per line and get the whole one-way ANOVA table: sums of squares, mean squares, the F ratio, its degrees of freedom and the p-value.
Normal Distribution Calculator
Turn a z-score into the area under the standard normal curve below, above, outside and between — or turn an area back into the z-score that cuts it off.
Sample Size and Power Calculator
How many observations a test of a mean needs to detect the shift you care about, at the significance level and power you pick.
Suggest a tool
Tell us what is missing and where its numbers should come from.
What should it convert, calculate or generate, and where would the authoritative numbers come from? A link to the standard or publication that defines them is the most useful thing you can send.
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How these tools are built
Every tool in this category runs entirely in your browser: there is no upload, no account and no request to a server once the page has loaded. The numbers behind them are transcribed from the organisation that defines them — NIST for units, the W3C for web formats, the WHO for health measures — and each page names its source next to the formula. A tool whose reference values stop reproducing fails the build and does not ship, which is the whole reason the catalogue grows slowly.