1. What Is Chi-Square Critical Value?

The chi-square critical value is the threshold value in a chi-square distribution at a given significance level and degrees of freedom. It is used to determine statistical significance in hypothesis testing.

2. How Does The Calculator Work?

The calculator uses the chi-square critical value formula:

Where:

• \( \alpha \) — Significance level (dimensionless)
• \( \text{df} \) — Degrees of freedom (integer)

Explanation: The formula calculates the inverse of the chi-square cumulative distribution function at the specified significance level and degrees of freedom.

3. Importance Of Chi-Square Critical Value

Details: The chi-square critical value is essential for determining whether to reject the null hypothesis in chi-square tests, including goodness-of-fit tests and tests of independence.

4. Using The Calculator

Tips: Enter the significance level (α) between 0 and 1, and degrees of freedom as a positive integer. All values must be valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance level (α)?
A: The significance level represents the probability of rejecting the null hypothesis when it is true, typically set at 0.05 or 0.01.

Q2: What are degrees of freedom in chi-square tests?
A: Degrees of freedom depend on the test type. For a contingency table, it's (rows-1) × (columns-1).

Q3: How is the critical value used in hypothesis testing?
A: If the test statistic exceeds the critical value, the null hypothesis is rejected.

Q4: What's the relationship between α and the critical value?
A: Lower α values result in higher critical values, making it harder to reject the null hypothesis.

Q5: Can this calculator be used for one-tailed tests?
A: Chi-square tests are typically right-tailed, so this calculator is designed for standard chi-square testing.