1. What is a Chi-Square P-value?

The chi-square p-value represents the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. It helps determine the statistical significance of chi-square test results.

2. How Does the Calculator Work?

The calculator uses the chi-square distribution formula:

Where:

• \( \chi^2 \) — Chi-square test statistic
• \( \text{df} \) — Degrees of freedom
• \( \text{CDF} \) — Cumulative distribution function of the chi-square distribution

Explanation: The p-value is calculated by finding the area under the chi-square distribution curve to the right of the observed test statistic.

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 the chi-square statistic (must be ≥ 0) and degrees of freedom (must be ≥ 1). The calculator will compute the right-tailed p-value.

5. Frequently Asked Questions (FAQ)

Q1: What is a chi-square test used for?
A: Chi-square tests are used to examine relationships between categorical variables or test goodness-of-fit to distributions.

Q2: How do I determine degrees of freedom?
A: For contingency tables, df = (rows - 1) × (columns - 1). For goodness-of-fit, df = categories - 1 - parameters estimated.

Q3: What does p < 0.05 mean?
A: There's less than a 5% probability the observed results occurred by chance if the null hypothesis is true.

Q4: Can I get a two-tailed p-value?
A: Chi-square tests are inherently one-tailed (right-tailed) as the test statistic is always positive.

Q5: When is chi-square test not appropriate?
A: When expected frequencies are too low (typically <5 in any cell), consider Fisher's exact test instead.