Bell Statistics

Reading a result

What a significance test actually claims, what it does not, and the four numbers — p, alpha, power, effect size — that decide whether a finding means anything.

11 terms

A results table is a set of claims in a compressed notation, and almost every expensive mistake in experimentation comes from reading one of those claims as something adjacent to what it says. A p-value is not the probability the result is wrong. A non-significant result is not evidence of no effect. A significant one is not evidence the effect is big enough to ship. Each of those is a different error and each has its own entry here.

The four numbers are connected, which is the part that is rarely taught together. Statistical power, the significance level, the effect size you care about and the sample size you can afford form a system with three degrees of freedom: fix any three and the fourth is determined. Test planning is choosing which one to sacrifice, and doing it deliberately rather than discovering it afterwards.

The single most useful habit this group argues for is reporting a confidence interval next to every p-value. The p answers a yes-or-no question about a hypothesis nobody believed; the interval answers the question the business is asking, which is how much. They are computed from the same numbers and never disagree — but only one of them tells you whether the result is worth acting on.

Terms in this group

  • Confidence interval

    The range your data can actually support, and why it answers the business question a p-value cannot.

  • Effect size

    How big the difference is — the number a p-value throws away and a business case runs on.

  • Minimum detectable effect

    The smallest lift you designed to catch — a business decision that gets outsourced to statistics.

  • Null hypothesis

    The assumption every test argues against, and the reason you can never prove two things are the same.

  • P-value

    How surprising your data would be if there were no effect — and the four things it is constantly mistaken for.

  • Sample size

    Four inputs, one number, fixed before the test runs — and the square law that makes small effects expensive.

  • Significance level

    The false-positive rate you agree to in advance — a budget, and one most teams overspend.

  • Statistical power

    The probability your test finds a real effect — and why most tests that report nothing were never able to.

  • Statistical significance

    A verdict about evidence, not about importance — and the difference is where most bad decisions live.

  • Type I error

    The false positive — and the one whose cost lands months later, on a roadmap built around noise.

  • Type II error

    The false negative — invisible by nature, which is why nobody counts how many good ideas it kills.