1. What is the Chi Square Test Statistic?

The chi-square (χ²) test statistic measures the difference between observed and expected frequencies in categorical data. It's used to test hypotheses about distributions and associations between variables in contingency tables.

2. How Does the Calculator Work?

The calculator uses the chi-square formula:

Where:

• \( O \) — Observed frequency (unitless)
• \( E \) — Expected frequency (unitless)
• \( \chi^2 \) — Chi square statistic (unitless)

Explanation: The formula sums the squared differences between observed and expected values, divided by expected values across all categories.

3. Importance of Chi Square Calculation

Details: Chi-square tests are essential for determining whether observed data significantly deviates from expected distributions, testing independence between variables, and validating statistical models.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What does a high chi-square value indicate?
A: A high chi-square value suggests a significant difference between observed and expected frequencies, potentially rejecting the null hypothesis.

Q2: When should I use a chi-square test?
A: Use chi-square tests for categorical data analysis, goodness-of-fit tests, and tests of independence in contingency tables.

Q3: What are the assumptions of chi-square tests?
A: Assumptions include independent observations, adequate sample size, and expected frequencies ≥5 in most cells.

Q4: How do I interpret the p-value from chi-square?
A: A p-value < 0.05 typically indicates statistical significance, suggesting the observed differences are unlikely due to chance alone.

Q5: Can chi-square be used for small sample sizes?
A: For small samples, Fisher's exact test is often preferred as chi-square may not be accurate when expected frequencies are too low.