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 is a key concept in statistical hypothesis testing.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( p \) — P-value (dimensionless)
• \( stat \) — Test statistic (dimensionless)
• \( \text{cdf} \) — Cumulative distribution function

Explanation: The calculator computes the area under the probability distribution curve beyond the observed test statistic.

3. Importance of P-value Calculation

Details: P-values help determine statistical significance in hypothesis testing. A smaller p-value provides stronger evidence against the null hypothesis.

4. Using the Calculator

Tips: Enter the test statistic, select the appropriate distribution (Normal, t, or Chi-square), specify degrees of freedom (if applicable), and choose the tail type.

5. Frequently Asked Questions (FAQ)

Q1: What is a statistically significant p-value?
A: Typically, p-values ≤ 0.05 are considered statistically significant, but the threshold depends on the field of study and specific research context.

Q2: What's the difference between one-tailed and two-tailed tests?
A: One-tailed tests look for an effect in one direction, while two-tailed tests look for an effect in either direction.

Q3: When should I use the t-distribution vs normal?
A: Use t-distribution for small sample sizes (typically n < 30) or when population standard deviation is unknown.

Q4: What does degrees of freedom mean?
A: Degrees of freedom represent the number of independent values that can vary in the calculation.

Q5: Can p-values prove a hypothesis?
A: No, p-values only provide evidence against the null hypothesis. They don't prove the alternative hypothesis is true.