1. What Is Chi-Square?

The chi-square (χ²) statistic is a measure of the difference between observed and expected frequencies in categorical data. It's widely used in hypothesis testing to determine whether observed data differs significantly from expected results.

2. How Does the Calculator Work?

The calculator uses the chi-square formula:

Where:

• \( o \) — Observed value (dimensionless)
• \( e \) — Expected value (dimensionless)
• \( \sum \) — Sum over all categories

Explanation: For each category, the calculator squares the difference between observed and expected values, divides by the expected value, and sums these values across all categories.

3. Importance of Chi-Square

Details: Chi-square tests are fundamental in statistics for testing independence between categorical variables and goodness-of-fit tests. They help determine whether observed deviations from expectations are statistically significant.

4. Using the Calculator

Tips: Enter comma-separated observed and expected values. Both lists must have the same number of values. Expected values cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: When should I use a chi-square test?
A: Use it when you have categorical data and want to test hypotheses about frequency distributions or associations between variables.

Q2: What does a high chi-square value mean?
A: Higher values indicate greater discrepancy between observed and expected results, potentially leading to rejection of the null hypothesis.

Q3: What are the assumptions of chi-square tests?
A: The test assumes random sampling, independence of observations, and that expected frequencies are sufficiently large (typically ≥5 per category).

Q4: Can chi-square be used for continuous data?
A: No, chi-square is for categorical data. Continuous data must be binned into categories first.

Q5: How do I interpret the p-value from chi-square?
A: A p-value below your significance level (often 0.05) suggests the observed differences are statistically significant.