1. What is the Chi-Square Test Statistic?

The Chi-Square test statistic (χ²) is used to determine whether there is a significant difference between observed and expected frequencies in one or more categories. It's commonly used in hypothesis testing to assess goodness of fit or independence.

2. How Does the Calculator Work?

The calculator uses the Chi-Square formula:

Where:

• \( O \) — Observed frequency
• \( E \) — Expected frequency
• \( \sum \) — Summation over all categories

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

3. Importance of Chi-Square Test

Details: The Chi-Square test is essential for categorical data analysis, helping researchers determine if observed distributions differ significantly from expected distributions under the null hypothesis.

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 should not be zero to avoid division errors.

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 leading to rejection of the null hypothesis.

Q2: What are the assumptions of the chi-square test?
A: The test assumes independence of observations, adequate sample size, and expected frequencies of at least 5 in each category.

Q3: When should I use a chi-square test?
A: Use it when you have categorical data and want to test hypotheses about distributions or associations between variables.

Q4: What is the degrees of freedom for chi-square?
A: For goodness-of-fit tests, df = number of categories - 1. For contingency tables, df = (rows-1) × (columns-1).

Q5: How do I interpret the p-value from chi-square?
A: A p-value less than your significance level (typically 0.05) indicates that the observed differences are statistically significant.