Stat Tools

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Twenty-eight tools for what a set of numbers says

What a list of numbers is centred on and how far it spreads, with both divisors side by side because that is the commonest mistake in the subject. Where any one value sits in it, under all six definitions of a percentile, because a spreadsheet has already chosen one of them for you and they disagree. What falls outside, by both published rules. What shape it has, as a table of classes or as a histogram or as a box plot.

Then what a sample says about the thing it came from: the interval a mean or a proportion is known to, how many people a survey of a given precision needs, and whether the difference between two variants of a page is more than noise. Then whether a difference is real at all — a t-test in its three forms and a chi-squared test over a table of counts — and how two variables relate, with the scatter plot that tells a correlation of nothing from a perfect curve.

And the probability half: two events combined, a sum of dice counted rather than simulated, the odds of a draw at every prize tier, the birthday problem, every notation a bookmaker uses, and the binomial, normal and Poisson distributions. Each of them says what it assumes, because a p-value and a confidence interval are the two most misread numbers there are and neither means what it is usually taken to mean.

Describing data

Z-score
How far from the mean a value is, and what share is beyond it.

Box plot
The middle half of one group or several, with what lies outside.

Outliers
The values a list would rather not have, by both published rules.

Moving average
The three kinds side by side, and what each of them lags by.

From a sample

Sample size
How many are needed for an answer that narrow.

Testing a difference

T-test
One sample, two samples or a set of pairs, against a claim.

Two variables

Correlation
How far two variables move together, twice, with the picture.

Linear regression
The line of best fit, its equation and how far each point misses it.

Probability

Dice probability
The whole distribution of a total, counted rather than simulated.

Lottery odds
The chance of matching a draw, at every prize tier.

Distributions

Choosing

Random sample
A sample from a list, reproducibly, from a seed you choose.

Elo rating
The expected score between two ratings, and what a result changes.

Questions

Should I divide by n or by n − 1?
By n − 1 when the list is a sample of something larger, and by n when it is everything there is. Dividing by n on a sample underestimates the spread of what it came from, which is what Bessel's correction fixes. On a handful of values the two answers differ by a tenth, so every tool here that computes a spread shows both and says which it used.
Why do two people get different percentiles from the same numbers?
Because a percentile is six definitions and they only agree on a long list. On nine values the ninetieth percentile is 8.2 under a spreadsheet's PERCENTILE, 9 under its PERCENTILE.EXC, and 9 again under the plain-language "the value below which ninety per cent fall". The percentile tool prints all six side by side.
What does a confidence interval actually mean?
It is a property of the method, not of your one answer. Intervals built this way cover the true value ninety-five per cent of the time; this particular one either does or it does not, and nothing in your data says which. That is the second most misread number in the subject, after the p-value.
Is anything I type uploaded?
No. The tools are compiled to WebAssembly and run inside the browser tab. Nothing you type is sent to a server, and you can watch your browser's network panel while you use one to see that nothing leaves the page. That is worth more here than elsewhere: these are experiments, survey answers and measurements taken from people.