P Value Calculator Statistics

P-value Calculation:

\[ P = P(T \geq |t|) \text{ for two-tailed test} \] \[ P = P(T \geq t) \text{ for right-tailed test} \] \[ P = P(T \leq t) \text{ for left-tailed test} \]

Test Statistic (t/z):

Test Type:

Tail Type:

Degrees of Freedom:

P-value:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is a P-value?

The p-value is the probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is true. It's a key concept in statistical hypothesis testing.

2. How Does the Calculator Work?

The calculator computes p-values based on either the standard normal distribution (Z-test) or Student's t-distribution (T-test):

\[ P = P(T \geq |t|) \text{ (two-tailed)} \] \[ P = P(T \geq t) \text{ (right-tailed)} \] \[ P = P(T \leq t) \text{ (left-tailed)} \]

Where:

\( T \) — Test statistic distribution (Z or T)
\( t \) — Observed test statistic value
\( P \) — Calculated p-value

Explanation: The calculator determines the probability of observing a test statistic as or more extreme than the one calculated from your sample data.

3. Interpreting P-values

Guidelines:

p ≤ 0.01: Very strong evidence against null hypothesis
0.01 < p ≤ 0.05: Strong evidence against null hypothesis
0.05 < p ≤ 0.10: Weak evidence against null hypothesis
p > 0.10: Little or no evidence against null hypothesis

4. Using the Calculator

Steps:

Enter your test statistic (t or z score)
Select whether it's from a Z-test or T-test
Choose the appropriate tail type for your hypothesis
For T-tests, enter degrees of freedom
Click "Calculate" to get your p-value

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between one-tailed and two-tailed tests?
A: One-tailed tests look for an effect in one direction only, while two-tailed tests consider both directions.

Q2: When should I use a Z-test vs T-test?
A: Use Z-test when population standard deviation is known and sample size is large (>30). Use T-test for small samples or when population SD is unknown.

Q3: What does a p-value of 0.05 mean?
A: There's a 5% probability of seeing your results (or more extreme) if the null hypothesis were true.

Q4: Can p-value prove the null hypothesis?
A: No, it can only fail to reject it. Absence of evidence is not evidence of absence.

Q5: Why is my p-value different from statistical software?
A: This calculator uses approximations. For exact values, use specialized statistical software.