Probability & Statistics Lab
Advanced statistics in one tool: normal / binomial / Poisson distributions, descriptive stats, outlier detection, regression, correlation matrix, confidence intervals, z / t / chi-square tests, ANOVA and Monte Carlo simulation. Paste your CSV data and go — all exact, all in your browser.
How to Use
- Pick a tool. <strong>Distributions</strong> (normal, binomial, Poisson) take parameters; the <strong>data</strong> tools take numbers you paste — one value per line, or CSV/TSV with columns.
- For <strong>regression</strong> and the two-sample <strong>t-test</strong>, paste two columns (x and y, or the two groups). For the <strong>correlation matrix</strong> and <strong>ANOVA</strong>, each column is a variable / group. A header row is detected automatically.
- Every test reports the statistic, degrees of freedom, the exact <strong>p-value</strong>, and whether to reject H₀ at α = 0.05 — computed from the real distribution functions, not a lookup table.
- Distributions, histograms, scatter+fit lines and the Monte-Carlo convergence are drawn on the chart so you can <em>see</em> the result.
- The example for <strong>Monte Carlo</strong> estimates π from random points; raise the trials and re-run to watch it converge.
Chart
What it computes
About the Probability & Statistics Lab
Use the Probability & Statistics Lab — a free, easy tool for everyday maths and number work. Nothing is uploaded, and you do not need an account. Advanced statistics in one tool: normal / binomial / Poisson distributions, descriptive stats, outlier detection, regression, correlation matrix, confidence intervals, z / t / chi-square tests, ANOVA and Monte Carlo simulation. Paste your CSV data and go — all exact, all in your browser.
How it works
Put each value in its box and read the answer as you go. Because it recalculates live, you can play with the inputs to see how each one moves the result — handy for checking your own working or planning ahead. Everything happens on your device, so it is fast and private.
Want the deeper story? The Knowledge Base explains the ideas behind the tools in more detail.
Frequently Asked Questions
What can it actually do?
<strong>Distributions:</strong> normal (PDF, CDF, percentiles, z-scores), binomial and Poisson (PMF/CDF, mean, variance). <strong>Descriptive:</strong> mean, median, SD, variance, quartiles, IQR, skewness, kurtosis, and outlier detection (IQR fences and z-score). <strong>Relationships:</strong> linear regression (slope, intercept, r, R², significance) and a Pearson correlation matrix. <strong>Inference:</strong> confidence intervals, one- and two-sample t-tests, z-test, chi-square goodness-of-fit and independence, and one-way ANOVA. Plus Monte-Carlo simulation.
Where do the p-values come from?
They're computed directly from the distribution functions — the error function for the normal, the regularized incomplete gamma for chi-square, and the regularized incomplete beta for the t and F distributions — using the standard numerical algorithms. So a chi-square of 3.841 with 1 df returns p = 0.05 exactly, no table interpolation. The same routines give exact critical values for confidence intervals.
How do I choose a hypothesis test?
Comparing a sample mean to a known value → <strong>one-sample t-test</strong>. Comparing two group means → <strong>two-sample (Welch) t-test</strong>. Comparing three or more group means → <strong>one-way ANOVA</strong>. Checking whether counts match an expected distribution → <strong>chi-square goodness-of-fit</strong>; checking whether two categorical variables are related → <strong>chi-square independence</strong> on a contingency table.
What does the regression output mean?
It fits y = slope·x + intercept by least squares and reports r (correlation), R² (fraction of variance explained), the standard error and t-statistic of the slope with its p-value (is the relationship significant?), and the RMSE. The chart shows the data points with the fitted line.
What is Monte Carlo simulation good for?
Estimating probabilities or quantities by random sampling when an exact formula is hard. The built-in demo throws random darts at a square and uses the fraction landing in the quarter-circle to estimate π — the error shrinks like 1/√N, which you can watch on the convergence chart. The same idea powers risk modelling, integration and queueing analysis.
Is my data uploaded anywhere?
No. Parsing, every statistic and test, and the charts run entirely in your browser. Paste sensitive data freely — nothing leaves the page, and it works offline.
How do I use the Probability & Statistics Lab?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Do I need to install or sign up for anything?
Not at all — it runs in the browser with nothing to install and no account. After it loads once, it even works without an internet connection.
Is my information private?
Yes. Everything happens in your browser. Nothing you type is sent to a server or saved anywhere.
Common Use Cases
Research & data analysis
Run the right test, get the exact p-value, and see the effect.
A/B testing
Two-sample t-test or chi-square to judge whether a change really helped.
Quality control
Distributions, control limits, outlier detection and process capability.
Forecasting & modelling
Regression, correlation and Monte-Carlo risk simulation.
Stats coursework
Check distributions, CIs, t/chi-square/ANOVA with the working shown.
Engineering & science
Reliability (Poisson/binomial), measurement spread and comparisons.
Last updated: