1. What is the Chi-Square Statistic?

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 count
• \( E \) — Expected count
• \( \sum \) — Sum over all categories

Explanation: The formula calculates the sum of 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 is crucial for determining whether observed distributions differ from theoretical expectations, testing independence between variables, and assessing goodness-of-fit.

4. Using the Calculator

Tips: Enter observed and expected counts as comma-separated values. Both lists must have the same number of values. Expected counts should not 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 distributions or independence between variables.

Q2: What's a good chi-square value?
A: The interpretation depends on degrees of freedom and significance level. Higher values indicate greater divergence from expected.

Q3: What are the assumptions of chi-square tests?
A: Observations must be independent, categories mutually exclusive, and expected counts ≥5 for most cells.

Q4: What's the difference between chi-square and t-test?
A: Chi-square tests categorical data, while t-tests compare means of continuous data between groups.

Q5: Can I use chi-square for small sample sizes?
A: For small samples (expected counts <5), consider Fisher's exact test instead.