1. What is Chi-Square Critical Value?

The chi-square critical value is the threshold value from the chi-square distribution that separates likely from unlikely outcomes for a given significance level and degrees of freedom. It's used in hypothesis testing and confidence interval construction.

2. How Does the Calculator Work?

The calculator uses the inverse chi-square distribution function:

Where:

• \( \alpha \) — Significance level (probability threshold)
• \( df \) — Degrees of freedom
• \( \chi^2 \) — Chi-square distribution

Explanation: The function calculates the value where the cumulative probability equals 1-α for the given degrees of freedom.

3. Importance of Critical Value

Details: Critical values are essential for determining statistical significance in chi-square tests, including tests of independence, goodness-of-fit tests, and variance tests.

4. Using the Calculator

Tips: Enter significance level (typically 0.05 for 5% significance) and degrees of freedom. Values must be valid (0 < α < 1, df ≥ 1).

5. Frequently Asked Questions (FAQ)

Q1: What is a typical significance level?
A: Common values are 0.10, 0.05, and 0.01, with 0.05 being most common in many fields.

Q2: How do I determine degrees of freedom?
A: For contingency tables, df = (rows - 1) × (columns - 1). For variance tests, df = n - 1.

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

Q4: Are there limitations to chi-square tests?
A: Chi-square tests require sufficiently large expected cell counts (typically ≥5) and independent observations.

Q5: Can I use this for one-tailed tests?
A: Chi-square tests are inherently right-tailed. For left-tailed tests, use 1-α as your significance level.