AP Stats P-Value Calculator

Find the two-tailed p-value for a z statistic or a t statistic. Enter your test statistic, choose z or t, and add degrees of freedom for a t-test. The calculator gives you the p-value and tells you whether it is below common alpha levels.

What Is a P-Value?

A p-value is the probability of getting results at least as extreme as the ones you observed, if the null hypothesis were true. A small p-value, usually below 0.05, is evidence against the null hypothesis, because your results would be surprising if the null were true. A large p-value is not proof that the null is true, it only means your data do not give strong evidence against it.

How to Use This Calculator

1) Type your test statistic, keeping its sign or using its absolute value; the two-tailed calculation uses the absolute value. 2) Choose z if the population standard deviation is known, or t if you used a sample standard deviation. 3) For t, type the degrees of freedom, usually n - 1 for a one-sample test. 4) Press Calculate P-Value and compare the result with your alpha level, usually 0.05.

How to Calculate a P-Value

For a two-tailed test, the p-value is the probability of getting a test statistic at least as extreme as yours, in either direction, if the null hypothesis were true. For z, that is p = 2 × (1 - normal CDF(|z|)). For t, the same idea uses the t-distribution with your degrees of freedom.

Worked example: t = 2.50 with df = 24. The two-tailed p-value is about 0.020. Because 0.020 is less than 0.05, you would reject the null hypothesis at the 0.05 level, but not at the 0.01 level.

Tips and Common Mistakes

• Do not confuse a one-tailed and a two-tailed p-value. This calculator gives a two-tailed p-value; a one-tailed p-value is half of it, when the direction matches your alternative.
• A p-value is not the probability that the null hypothesis is true. It is the probability of data this extreme, assuming the null is true.
• For a t-test, entering the wrong degrees of freedom changes the p-value, especially for small samples.
• Always state your alpha level before you look at the p-value, so you do not move the goalposts after seeing the result.

Frequently Asked Questions

What does a p-value of 0.03 mean?

If the null hypothesis were true, you would see a result at least this extreme about 3% of the time. At alpha = 0.05, that is statistically significant.

Is a smaller p-value always better?

A smaller p-value is stronger evidence against the null, but it does not by itself prove a large or important effect. Report the effect size and confidence interval too.

What is the difference between a z p-value and a t p-value?

A z p-value uses the normal distribution. A t p-value uses the t-distribution, which has heavier tails for small samples and approaches the normal distribution as degrees of freedom grow.

Why does my p-value change when degrees of freedom change?

With fewer degrees of freedom, the t-distribution is wider, so the same test statistic is less surprising and the p-value is larger.

What do I do if my p-value is 0.06?

At alpha = 0.05, you fail to reject the null hypothesis. That does not prove the null is true; it means the evidence is not strong enough at that level.

Can a p-value be greater than 1?

No. A p-value is a probability, so it is always between 0 and 1.

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