1. What is the Chi-square Test Statistic?

The chi-square (χ²) statistic is a measure of how observed counts differ from expected counts in categorical data analysis. It's used in tests of independence and goodness-of-fit tests.

2. How Does the Calculator Work?

The calculator uses the chi-square formula:

Where:

• \( O \) — Observed counts
• \( E \) — Expected counts
• \( \sum \) — Sum over all categories

Explanation: The statistic sums the squared differences between observed and expected counts, divided by the expected counts for each category.

3. Importance of Chi-square Test

Details: The chi-square test helps determine whether observed frequency counts differ significantly from expected counts, indicating potential relationships between categorical variables.

4. Using the Calculator

Tips: Enter comma-separated observed and expected counts. Both lists must be the same length and contain positive numbers (expected counts cannot be zero).

5. Frequently Asked Questions (FAQ)

Q1: When should I use a chi-square test?
A: When you have categorical data and want to test for independence between variables or goodness-of-fit to a distribution.

Q2: What's a significant chi-square value?
A: Compare your statistic to the chi-square distribution with appropriate degrees of freedom (typically p < 0.05 indicates significance).

Q3: What are the assumptions?
A: Independent observations, expected counts ≥5 in most cells (some allow ≥1 with corrections), and categorical data.

Q4: What if my expected counts are small?
A: Consider Fisher's exact test or combine categories to increase expected counts.

Q5: Can I use this for continuous data?
A: No, the chi-square test is for categorical data. For continuous data, consider other tests like t-tests or ANOVA.