Learn
Calculating a p-value is the easy part. These guides cover the harder part — what the number means, what it cannot tell you, and how to report it so nobody draws the wrong conclusion.
7 min read
What is a p-value?
A clear, honest explanation of what a p-value measures, what it cannot tell you, and why the most natural interpretation of it is the wrong one.
9 min read
How to interpret p-values correctly
The five most common p-value misinterpretations, why each is wrong, and what to say instead — with worked examples of significant and non-significant results.
6 min read
One-tailed vs two-tailed tests
When a one-tailed test is legitimate, when it is p-hacking, and why two-tailed is the right default for almost all research and A/B testing.
6 min read
Significance level (α) explained
What alpha really controls, why 0.05 is a convention rather than a law, and how to choose a threshold that fits the cost of being wrong.
8 min read
What "p < 0.05" actually means
Your p-value came out under 0.05. Here is what that does and does not establish, what to do next, and why the threshold is 0.05 in the first place.
9 min read
How to find a p-value in Excel
The Excel formulas that produce a p-value, which one fits your test, and the four mistakes that quietly give you the wrong answer.
7 min read
How to report p-values in APA style
APA 7 rules for reporting p-values, test statistics, effect sizes and confidence intervals — with worked examples for t, F, chi-square and correlation.
8 min read
How to find a p-value in R
Every way R gives you a p-value: pt, pnorm, pchisq and pf for a statistic you already have, and t.test, chisq.test and cor.test for raw data.
8 min read
How to find a p-value in Python
Every SciPy function that returns a p-value, from norm.sf and t.sf to ttest_ind and chi2_contingency — and why sf beats 1 - cdf every time.
7 min read
How to find the p-value in SPSS
Where the p-value hides in SPSS output, why it is labelled Sig., what the ".000" really means, and which row of a t-test table to read.
6 min read
How to find a p-value on a TI-84
Using normalcdf, tcdf and STAT TESTS on a TI-84 to get a p-value, including the 1E99 trick for an infinite bound and the classic sign mistake.
7 min read
Degrees of freedom, explained
What degrees of freedom actually count, why it is usually n minus 1, the formula for every common test, and what happens to your p-value when df is small.
7 min read
What is the null hypothesis?
What the null hypothesis is, how to state it for any test, why you can only reject or fail to reject it, and why every p-value is computed assuming it is true.
Reference
P-value tables
Z, t, chi-square, F and correlation tables, generated from this site’s own SciPy-validated engine rather than transcribed.