1. What is Chi-square Critical Value?

The chi-square critical value is the point on the chi-square distribution that corresponds to a specified significance level (α) and degrees of freedom (df). It's used in hypothesis testing to determine the threshold for rejecting the null hypothesis.

2. How Does the Calculator Work?

The calculator determines the critical value for a given significance level and degrees of freedom:

Where:

• \( \alpha \) — Significance level (probability of Type I error)
• \( df \) — Degrees of freedom
• \( \chi^2 \) — Chi-square critical value

Explanation: The critical value separates the rejection region from the non-rejection region in a chi-square test.

3. Importance of Chi-square Critical Value

Details: Critical values are essential for conducting chi-square tests of independence, goodness-of-fit tests, and other statistical analyses that use the chi-square distribution.

4. Using the Calculator

Tips: Enter the significance level (typically 0.05, 0.01, or 0.10) and degrees of freedom (≥1). The calculator will return the critical value.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between α and the critical value?
A: As α decreases (more stringent test), the critical value increases, making it harder to reject the null hypothesis.

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

Q3: What if my test statistic exceeds the critical value?
A: You reject the null hypothesis at the specified significance level.

Q4: Can I calculate critical values for one-tailed tests?
A: Chi-square tests are typically right-tailed, so the same approach applies.

Q5: Where can I find chi-square distribution tables?
A: Most statistics textbooks include these tables, or you can use this calculator instead.