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Statistics & Data Science · pattern F, Dataset

A p-value from a test statistic.

Enter a z score to get one-tailed and two-tailed p-values, with the standard significance thresholds alongside — and a plain statement of what the number does not mean.

Inputs

The formula used

p = 2 × P(Z > |z|) for a two-tailed test

Based on the standard normal distribution. For a t statistic on a small sample the p-value is slightly larger, so treat this as an approximation below about thirty observations.

Two-tailed p-value

0.03235

One-tailed p
0.01618
Area to the left of z
0.98382
Significant at your α?
yes, p < α
Critical z at α = 0.05, two-tailed
1.96
Critical z at α = 0.01, two-tailed
2.576
Confidence level equivalent
95.0 %

A p-value is the probability of data at least this extreme if the null hypothesis were true. It is not the probability that the null is true, and it is not a measure of effect size.

What a p-value is not.

It is not the probability the null hypothesis is true, not the probability your result was chance, and not a measure of how large or important the effect is. A tiny p-value on a huge sample can accompany an effect too small to matter. Report the effect size and a confidence interval alongside it — most journals now require this precisely because p-values alone were being over-read.

Questions about p value

What does p < 0.05 mean?
That data at least this extreme would occur less than one time in twenty if the null hypothesis were true. It is a statement about the data under an assumption, not about the truth of the hypothesis.
One-tailed or two-tailed?
Two-tailed unless you predicted the direction in advance and can justify it. Switching to one-tailed after seeing the data halves the p-value illegitimately.
Why do people criticise p-values?
Because they are widely misread as effect size or as probability of truth, and because selecting analyses until p drops below 0.05 produces literatures that do not replicate.

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Statistical output here is for coursework and learning. Reported p-values and intervals assume the conditions stated on the page; nothing here checks whether those conditions hold for your data.