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 uses the t-distribution to calculate p-values:

Where:

• \( t \) — t-statistic value
• \( df \) — Degrees of freedom
• \( tails \) — 1 for one-tailed test, 2 for two-tailed test

Explanation: The t-distribution is used when sample sizes are small and population standard deviation is unknown.

3. Importance of P-value Calculation

Details: P-values help determine statistical significance in hypothesis testing. Lower p-values provide stronger evidence against the null hypothesis.

4. Using the Calculator

Tips: Enter the t-value from your test, degrees of freedom (typically n-1), and select whether you need a one-tailed or two-tailed 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: What is considered a statistically significant p-value?
A: Typically p < 0.05 is considered significant, but this threshold depends on your field and study design.

Q3: How do I determine degrees of freedom?
A: For a simple t-test, df = n-1 where n is sample size. Different tests have different df calculations.

Q4: When should I use t-distribution vs normal distribution?
A: Use t-distribution when sample sizes are small (<30) or population standard deviation is unknown.

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