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 quantifies the evidence against the null hypothesis in statistical hypothesis testing.

2. How P Values are Calculated

The calculation depends on the test statistic and its sampling distribution:

Where:

• \( T \) — Test statistic under null hypothesis
• \( t \) — Observed test statistic value
• \( H_0 \) — Null hypothesis

Explanation: The p-value is calculated using the cumulative distribution function (CDF) of the appropriate statistical distribution (normal, t, chi-square, or F).

3. Statistical Significance

Details: A p-value below a predetermined significance level (often 0.05) suggests rejecting the null hypothesis. However, p-values should be interpreted in context with effect sizes and confidence intervals.

4. Using the Calculator

Tips: Enter your test statistic value, select the appropriate distribution, specify degrees of freedom if needed, and choose the tail type (left, right, or two-tailed).

5. Frequently Asked Questions (FAQ)

Q1: What does p < 0.05 mean?
A: There's less than 5% probability of observing the data if the null hypothesis were true, suggesting statistically significant evidence against H₀.

Q2: Can p-value prove the null hypothesis?
A: No, p-values can only provide evidence against the null hypothesis, not prove it true.

Q3: Why use different distributions?
A: Different tests (t-test, ANOVA, chi-square) have different sampling distributions for their test statistics.

Q4: 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.

Q5: Are p-values the only way to interpret results?
A: No, effect sizes and confidence intervals provide complementary information about the magnitude and precision of effects.