What Is P Value With Steps?
A p-value is the probability of getting a test statistic at least as extreme as yours, assuming the null hypothesis is true. A small p-value means the data would be surprising under the null hypothesis.
To find it, take the area under the curve beyond your statistic. For a right-tailed test that is the right tail. For a two-tailed z or t test it is double the smaller tail.
Choose the distribution, enter the statistic and degrees of freedom, and pick the tail. The calculator shows the cumulative area, the p-value, the critical value and whether to reject.
How to Use the P Value With Steps Calculator
- Pick the distribution of your statistic.
- Enter the value, the degrees of freedom and the tail.
- Follow the steps from the cumulative area to the p-value and the decision.
P Value With Steps Formula
Right-tailed
Two-tailed (symmetric)
P Value With Steps Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| z, t, χ², F | The test statistic | Choose the matching distribution |
| df | Degrees of freedom | Two values for F |
| α | Significance level | Commonly 0.05 |
| p | The p-value | Reject H₀ if p ≤ α |
P Value With Steps Worked Example
With the example values loaded in the calculator above, the steps are:
- The test statistic is t = 2.1 with 15 degrees of freedom.
- Find the cumulative area to the left of 2.1: 0.973472. The area to the right is 1 − 0.973472 = 0.0265276.
- Two-tailed: p = 2 × the smaller tail = 2 × 0.0265276 = 0.053055.
- Compare p = 0.053055 with α = 0.05: p > α, so fail to reject H₀.
Result: Two-tailed p-value = 0.053055; Decision = Fail to reject H₀ at α = 0.05.
Worked example: t = 2.1, df = 15, two-tailed
The area to the right of 2.1 with 15 degrees of freedom is 0.0265. Doubling for a two-tailed test gives p = 0.053.
At α = 0.05 this is just above the cutoff, so you fail to reject H₀. A result this close to alpha is best reported with its exact p-value.
Which tail for which test
z and t tests can be left, right or two-tailed. Chi-square and F tests are normally right-tailed because large values mean a bigger departure from the null hypothesis.
Where P Value With Steps Is Used
Finishing a hypothesis test
Turn a computed statistic into a p-value.
Replacing tables
Get the exact p-value instead of a bound.
Checking software output
Confirm a p-value from a statistic and its degrees of freedom.
Common P Value With Steps Mistakes to Avoid
- Report the exact p-value, not just whether it is below 0.05.
- Make sure the degrees of freedom match your test.
P Value With Steps Terms and Definitions
- p-value
- The probability of a statistic at least as extreme as the one observed, assuming the null hypothesis is true.
P Value With Steps FAQs
How do you calculate a p-value from a test statistic?
Find the area under the distribution curve beyond the statistic, in one tail or both tails, using the cumulative distribution function.
How do I find a 2 tailed p-value?
Double the area in the smaller tail, or use both tails beyond the absolute value of a symmetric statistic.
What is a small p-value?
One at or below your chosen alpha, often 0.05. It means the data are unlikely under the null hypothesis.
Is the p-value the probability the null is true?
No. It assumes the null is true and measures how extreme the data are.
Can I use a table instead?
Tables give only bounds on the p-value. This calculator gives the exact value.
What are the degrees of freedom?
For a one-sample t test, n − 1. For chi-square goodness of fit, categories − 1. For F, the numerator and denominator values from your test.