1. What is the Chi-Square Test Statistic?

The chi-square (χ²) test statistic measures how observed counts differ from expected counts under a null hypothesis. It's widely used in tests of independence and goodness-of-fit in categorical data analysis.

2. How Does the Calculator Work?

The calculator uses the chi-square formula:

Where:

• \( \chi^2 \) — Chi-square test statistic
• \( O \) — Observed count in each category
• \( E \) — Expected count in each category
• \( \sum \) — Sum over all categories

Explanation: For each category, we calculate the squared difference between observed and expected counts, divided by the expected count. These values are summed across all categories to get the final chi-square statistic.

3. Importance of Chi-Square Test

Details: The chi-square test is fundamental in statistics for testing relationships between categorical variables and assessing goodness-of-fit for distributions. It helps determine whether observed deviations from expectations are likely due to chance.

4. Using the Calculator

Tips: Enter observed and expected values as numbers separated by commas or spaces. Both lists must be the same length. Expected values cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a good chi-square value?
A: A "good" value depends on degrees of freedom and significance level. Lower values indicate better fit to expected distribution.

Q2: When is chi-square test appropriate?
A: When testing independence in contingency tables or goodness-of-fit with categorical data and sufficient sample size (expected counts ≥5).

Q3: What are degrees of freedom in chi-square?
A: For a test of independence, df = (rows-1)*(columns-1). For goodness-of-fit, df = categories-1-parameters estimated.

Q4: What if my expected counts are small?
A: With expected counts <5, consider Fisher's exact test or combine categories.

Q5: Can chi-square be negative?
A: No, since all terms are squared, the chi-square statistic is always ≥0.