1. What is Chi-Square P Value?

The Chi-Square P Value represents the probability of observing a test statistic at least as extreme as the one calculated, assuming the null hypothesis is true. It's used in chi-square tests of independence and goodness-of-fit tests.

2. How Does the Calculator Work?

The calculator uses the chi-square distribution:

Where:

• \( \chi^2 \) — Calculated chi-square statistic
• \( k \) — Degrees of freedom
• \( \Gamma \) — Gamma function

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

3. Importance of P Value

Details: The p-value helps determine statistical significance in hypothesis testing. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis.

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 corresponding p-value.

5. Frequently Asked Questions (FAQ)

Q1: What does a p-value of 0.05 mean?
A: A p-value of 0.05 means there's a 5% probability of observing the results if the null hypothesis is true. This is commonly used as the threshold for statistical significance.

Q2: How are degrees of freedom determined?
A: For a contingency table, df = (rows - 1) × (columns - 1). For goodness-of-fit, df = number of categories - 1 - number of estimated parameters.

Q3: What's the relationship between χ² and p-value?
A: Higher χ² values (with the same df) result in smaller p-values. The exact relationship depends on the degrees of freedom.

Q4: When is the chi-square test appropriate?
A: When testing independence between categorical variables or goodness-of-fit, with expected frequencies ≥5 in most cells.

Q5: What are alternatives for small expected frequencies?
A: Fisher's exact test or likelihood ratio test may be more appropriate when expected frequencies are small.