Eight distributions
Normal, Student’s t, chi-square, F, exponential, uniform, binomial and Poisson, each with its own parameters.
TOOL 07 / STATISTICS
Probabilities and hypothesis tests, with the picture to match.
Find a probability or a critical value from eight distributions, or run a hypothesis test on your data. Each answer comes with the curve it was read from.
No account required · Right in your browser · Works offline once opened
SLIDE RULE / StatisticsSCREENSHOT
WHAT IT DOES
The statistics tables, replaced.
Everything you would look up at the back of a statistics textbook, calculated for the exact numbers in front of you.
Any probability
P(X ≤ a), P(X ≥ a) or P(a ≤ X ≤ b), with the matching area shaded on the curve, plus the mean, variance and standard deviation of the distribution.
Critical values
Go the other way with Find x: give a probability and get the value it belongs to, for a critical value or a percentile.
Eight hypothesis tests
One-sample, two-sample (Welch or pooled) and paired t-tests, tests of one or two proportions, and chi-square tests of goodness of fit and independence.
A full result
The test statistic, degrees of freedom, p-value and confidence interval, a plain-language conclusion at your chosen α, and an effect size where one applies: Cohen’s d for the t-tests, Cramér’s V for independence.
Your data, from where it is
Type or paste a sample, or fill it from a column of the table on the grapher’s Data tab. Send the result to a worksheet when you are done.
A WORKED TEST
From eight measurements to a conclusion.
Is the mean of 5.1 4.9 5.3 5.6 5.0 4.8 5.2 5.4 different from 5? Choose the one-sample t-test, enter the sample and the reference value, and pick the alternative: ≠, < or >.
The answer: t = 1.7219 with 7 degrees of freedom, p = 0.1288, and a 95% confidence interval of [4.9393, 5.3857]. At α = 0.05, do not reject H₀. Cohen’s d is 0.609.
The plot under the result shows the test statistic on its distribution, so you can see how far into the tail it falls.
SLIDE RULE / StatisticsSCREENSHOT
WHAT IS COVERED
Pick the test that fits the question.
Each test asks its question in plain words before it asks for numbers.
- TESTUSE IT FORYOU PROVIDE
One-sample tA mean against a reference valueOne sample and the reference value.Two-sample t (Welch)Two means, variances not assumed equalTwo independent samples.Two-sample t (pooled)Two means, equal variances assumedTwo independent samples.Paired tBefore and after on the same subjectsTwo samples of the same length.One proportionA proportion against a reference valueSuccesses and the number of trials.Two proportionsTwo proportions against each otherSuccesses and trials for each group.χ² goodness of fitCounts against expected countsObserved and expected counts.χ² independenceWhether two factors are relatedA table of counts.
QUESTIONS
Before you open it.
Can it replace a z-table or t-table?
Yes. Choose the distribution, enter the value and read the probability, or use Find x to go from a probability back to a critical value. It works for any mean, standard deviation or degrees of freedom, not only the ones a printed table lists.
Does it give confidence intervals?
Yes. The t-tests and proportion tests report a confidence interval at the level set by your α, alongside the p-value.
Where are means, standard deviations and regression?
On the grapher’s Data tab, which gives summary statistics for each column of a table and fits curves with standard errors and R².
Is it free?
Yes. Every distribution and test is in the free plan, with no account needed. Saving a plot as an image is part of Pro.
One of eight tools that work together.
A value from one goes straight into another- CalculatorScientific and symbolic, with the steps behind each answer.
- Unit converterEvery unit of a quantity at once, and compound units.
- ReferenceConstants, materials, steam tables and section properties.
- FormulasOver 200 formulas, each solvable for any quantity.
- Graph2D curves, 3D surfaces and curve fitting to data.
- SolversMatrices and systems with working, and differential equations.
- WorksheetA whole problem on one sheet, with units and live results.
- The whole toolkit →See how the eight tools fit together, and what is free.
No more reading along a z-table.
Open the statistics tool — Free ↗No account required. Free for every tool; Pro adds unlimited worksheets and exports.