Bell Statistics

Data and distributions

The statistical foundations everything else is built on: spread, the normal curve, why sample means behave, and what one extreme value can do to a test.

6 terms

These are the terms the rest of the glossary quietly assumes. Every significance test, every confidence interval and every sample-size calculation on this site is built from a notion of spread and a claim about how sample means are distributed, and the entries here are those two things stated properly rather than taken on trust.

The load-bearing idea is the central limit theorem, and it is more useful than it is usually made to sound. It is not the claim that data are normally distributed — revenue per user emphatically is not — but that the average of enough draws is, whatever the shape underneath. That is what lets a t-test work on data that looks nothing like a bell curve, and knowing it is what tells you when the test stops being safe.

The practical entry in this group is outlier. One customer who spent forty thousand pounds can move a revenue metric further than the experiment did, and the decision about what to do with them has to be made before the data are seen or it is simply a choice about which result to get. Spread is where that shows up: variance is what a single extreme value inflates, and variance is what sample size is spent on.

Terms in this group

  • Central limit theorem

    Why averages go bell-shaped even when the data do not — the result that makes ordinary tests work.

  • Normal distribution

    The bell curve — and why your skewed revenue data usually does not break the test anyway.

  • Outlier

    The extreme value that decides your result — and why the rule for handling it must precede the data.

  • Standard deviation

    How spread out the data are, in the data's own units — and the reason some metrics need vastly more sample.

  • Standard error

    How much your estimate would move if you ran the study again — precision, not spread.

  • Variance

    Spread in squared units — awkward to read, and the quantity every sample-size formula is built on.