P-Value Calculator
Calculate the probability of your test results based on Z-Score
Two-tailed
Left-tailed (P[Z < z])
Right-tailed (P[Z > z])
Calculated P-Value:
0.0000
What is a P-Value?
In statistics, the p-value (probability value) is a number that describes how likely you are to have found a particular set of observations if the null hypothesis were true. It is a critical metric used in hypothesis testing to help determine the statistical significance of your findings.
A p-value doesn't tell you the probability that the null hypothesis is true; rather, it tells you the probability of seeing data as extreme as yours if the null hypothesis is already assumed to be true.
How to Calculate P-Value
Calculating a p-value typically involves three main steps:
- Define the Null Hypothesis (Hâ‚€): Assume there is no effect or no difference between the groups.
- Calculate the Test Statistic: Depending on your data, you calculate a Z-score, T-score, or F-statistic. This measures how many standard deviations your observed data is from the null hypothesis mean.
- Find the Probability: Use a probability distribution table (like the Normal Distribution or T-Distribution) to find the area under the curve corresponding to your test statistic.
Example Calculation:
Suppose you have a Z-score of 2.0 and you are conducting a two-tailed test.
Suppose you have a Z-score of 2.0 and you are conducting a two-tailed test.
- The area to the right of Z=2.0 is approximately 0.0228.
- Since it is a two-tailed test, you multiply by 2.
- P-Value = 0.0228 × 2 = 0.0456.
- If your significance level (alpha) is 0.05, you would reject the null hypothesis because 0.0456 < 0.05.
Interpreting the Results
- P ≤ 0.05: Statistically significant. There is strong evidence against the null hypothesis; you reject the null hypothesis.
- P > 0.05: Not statistically significant. There is weak evidence against the null hypothesis; you fail to reject the null hypothesis.
- P ≈ 0.01: Very strong evidence against the null hypothesis.
One-Tailed vs. Two-Tailed Tests
A two-tailed test is used when you want to see if there is any difference between the groups (increase or decrease). A one-tailed test is used when you are specifically looking for an effect in one direction (e.g., only checking if a new drug is better than the old one, not worse).