Introduction
A p value tells you how likely it is to get results at least as extreme as yours if the null hypothesis is true.1 In statistics, p values help you judge how well your data fit that hypothesis.1 A small p value (usually less than 0.05) means your data would be unusual if the null hypothesis were true.1 A large p value means there isn't enough proof to say something meaningful happened.
This p value calculator makes it easy to find your p value without doing the hard math by hand. Just enter your test statistic, pick your test type, and the calculator does the rest. This tool checks whether your results are statistically significant for a z-test, t-test, or chi-square test.
How to Use Our p Value Calculator
Enter your test statistic and select your test type to quickly find the p value for your hypothesis test.
Test Statistic: Type in the test statistic (such as a z-score or t-value) that you got from your statistical test. This is a number that shows how far your result is from the null hypothesis.
Degrees of Freedom: Enter the degrees of freedom for your test. This number depends on your sample size and the type of test you are running. For a z-test, you can leave this blank. For a t-test, it is usually your sample size minus one.
Test Type: Choose whether you are running a one-tailed (left), one-tailed (right), or two-tailed test. A one-tailed test checks for an effect in only one direction, while a two-tailed test checks for an effect in both directions.
Distribution Type: Select the distribution your test uses. Common choices are the z-distribution (normal distribution) for large samples or the t-distribution for smaller samples.
Significance: The result is labelled significant when p is less than 0.05, the most common significance level.2 If you use a different level, such as 0.01, compare your p value with it yourself.
Once you hit calculate, the tool will return your p value and tell you whether it is below 0.05.
What Is a P-Value?
A p-value (probability value) is a number between 0 and 1 that tells you how likely it is to get your test results (or something more extreme) if the null hypothesis is true.1 The null hypothesis is the default assumption that there is no real effect or no real difference in your data. A small p-value means your results are unlikely under that assumption, which gives you a reason to reject it.
How Do You Interpret a P-Value?
In most fields, researchers compare the p-value to a threshold called the significance level (α), which is usually set at 0.05.2 Here is how to read the result:
- p < 0.05: The result is statistically significant, and you reject the null hypothesis.
- p ≥ 0.05: The result is not statistically significant. You do not have enough evidence to reject the null hypothesis.
Keep in mind that a p-value does not tell you the size of an effect or how important a finding is.1 It only tells you how unusual your data would be if the null hypothesis were true.1
Test Statistics and Distributions
To get a p-value, you first calculate a test statistic from your data. The type of test statistic depends on the kind of analysis you are doing. This calculator supports five common types:
- Z-score: Used when you know the population standard deviation or have a large sample size. It follows the standard normal distribution.
- t-statistic: Used when the sample size is small and the population standard deviation is unknown. It follows the Student's t-distribution, which requires degrees of freedom (df).3
- Chi-square (χ²): Used in tests of independence or goodness-of-fit for categorical data. It follows the chi-square distribution and requires degrees of freedom.
- F-statistic: Used in ANOVA and regression analysis to compare variances between groups. It follows the F-distribution and requires two degrees of freedom values: one for the numerator (df₁) and one for the denominator (df₂).
- Pearson r: The correlation coefficient that measures the linear relationship between two variables. It ranges from −1 to 1. The calculator converts r into a t-statistic using the formula t = r × √(df / (1 − r²)), then finds the p-value from the t-distribution.4
Tail Types Explained
The tail type refers to the direction of your hypothesis test. It affects how the p-value is calculated from the test statistic:
- Left-tailed: Tests whether the true value is less than the hypothesized value. The p-value is the area under the curve to the left of the test statistic.
- Right-tailed: Tests whether the true value is greater than the hypothesized value. The p-value is the area under the curve to the right of the test statistic.
- Two-tailed: Tests whether the true value is different from the hypothesized value in either direction. The p-value is the combined area in both tails beyond the test statistic.4 This is the most commonly used option.
What Are Degrees of Freedom?
Degrees of freedom (df) represent the number of independent values in your data that are free to vary. For a t-test, df is usually the sample size minus 1 (n − 1).3 For a Pearson r correlation, df equals n − 2.4 For a chi-square test, df depends on the number of categories. Degrees of freedom shape the probability distribution and directly affect the p-value. A smaller df means heavier tails and a larger p-value for the same test statistic.3