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 helps determine the statistical significance of results in hypothesis testing.

2. How Does the Calculator Work?

The calculator uses the t-distribution to calculate p-values:

Where:

• \( t \) — t-statistic from your test
• \( df \) — Degrees of freedom
• \( t\_cdf \) — Cumulative distribution function for the t-distribution

Explanation: For a two-tailed test, we calculate the probability in both tails beyond the observed t-value. For one-tailed tests, we only consider one tail.

3. Interpretation of p-values

Details: A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, while a large p-value suggests weak evidence against it.

4. Using the Calculator

Tips: Enter your t-statistic (can be positive or negative), degrees of freedom, and select whether you're conducting a one-tailed or two-tailed test.

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 degrees of freedom?
A: Degrees of freedom typically equal your sample size minus the number of parameters estimated (e.g., n-1 for a one-sample t-test).

Q3: What p-value threshold should I use?
A: 0.05 is common, but the appropriate threshold depends on your field and the consequences of Type I errors.

Q4: Can I get exact p-values for very small values?
A: This calculator provides approximations. For extremely small p-values, specialized statistical software may be needed.

Q5: Does this work for other distributions?
A: This calculator specifically uses the t-distribution, which is appropriate for small samples or when population variance is unknown.