1. What is 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 helps determine the statistical significance of results in hypothesis testing.

2. How Does the Calculator Work?

The calculator computes p-values using either the normal distribution (Z-test) or t-distribution (T-test):

Where:

• \( z \) — Z-score (standard normal deviate)
• \( t \) — T-score
• \( df \) — Degrees of freedom (for T-test)
• \( \text{norm\_cdf} \) — Standard normal cumulative distribution function
• \( \text{t\_cdf} \) — Student's t-distribution cumulative distribution function

Explanation: The calculator adjusts the p-value based on whether you're conducting a one-tailed (left or right) or two-tailed test.

3. Importance of P Value

Details: P-values help researchers determine whether to reject the null hypothesis. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis.

4. Using the Calculator

Tips: Select the appropriate test type (Z or T), enter your test statistic, and for T-tests, provide degrees of freedom. Choose the tail type based on your hypothesis.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between Z-test and T-test?
A: Z-test is used when population parameters (mean and variance) are known, while T-test is used with small samples or when population variance is unknown.

Q2: What is a good p-value?
A: Typically, p ≤ 0.05 is considered statistically significant, but the threshold depends on your field and study design.

Q3: How do I interpret a two-tailed p-value?
A: A two-tailed p-value tests for the possibility of the effect in both directions (greater than or less than).

Q4: Why do I need degrees of freedom for T-test?
A: Degrees of freedom affect the shape of the t-distribution, which becomes more normal as df increases.

Q5: Can p-value prove the null hypothesis?
A: No, p-value can only provide evidence against the null hypothesis, not prove it true.