Hypothesis testing · Tail areas
p-value & Critical-Value Calculator
Turn a test statistic into a p-value (z, t, χ², or F), or find the critical value for a given α — with a shaded picture of the tail, and a clear note on what the number does and doesn't tell you.
χ² and F tests are upper-tailed by convention.
Result
In plain English
This converts between a test statistic and a p-value — the two currencies of hypothesis testing. The whole game is measuring how surprising your result would be if “nothing is really going on.”
- test statistic
- A single number summarising how far your data sit from the “nothing happening” baseline.
- p-value
- The chance of a result at least this extreme if the null hypothesis (no effect) were true. It is not the chance that the hypothesis is wrong.
- critical value
- The threshold your statistic has to beat to count as “significant” at your chosen α.
- α (alpha)
- The false-alarm rate you're willing to accept — conventionally 0.05, i.e. a 1-in-20 chance of crying wolf.
- one- vs two-tailed
- Whether you care about a difference in one specific direction, or in either direction.
Frequently asked
What does a p-value actually mean?
It's the probability of a result at least this extreme if the null hypothesis were true. It is not the probability that the null is true, nor the probability your result is “due to chance,” nor a measure of effect size.
Is p < 0.05 the same as “important”?
No. With a large enough sample even a trivial difference can be “significant,” and a real effect can miss the cut in a small one. Significance is about detectability, not magnitude — always pair it with an effect size and interval.
One-tailed or two-tailed?
Use two-tailed unless you have a genuine, pre-registered reason to test a single direction. Switching to one-tailed after seeing the data to scrape under 0.05 is a form of p-hacking.
What is the difference between a p-value and a confidence interval?
They are two views of the same evidence. The p-value is a single number answering “how surprising is this data if nothing is going on?”; the confidence interval shows the whole range of effect sizes the data are compatible with. The interval is usually the more informative of the two — it conveys both significance (does it exclude zero?) and magnitude (how big could the effect plausibly be?), which a lone p-value hides entirely.