1. What is Chi-square Goodness Of Fit?

The Chi-square goodness of fit test determines whether sample data matches a population distribution. It compares observed counts with expected counts to see if differences are statistically significant.

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 test measures how much the observed data deviates from what was expected under the null hypothesis.

3. Importance of Chi-square Test

Details: This test is widely used in research to determine if categorical data fits an expected distribution, such as genetic ratios, survey results, or quality control.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions of this test?
A: The test assumes random sampling, independence of observations, and that expected counts are at least 5 in each category.

Q2: How do I interpret the chi-square value?
A: Compare your result to a chi-square distribution table with appropriate degrees of freedom (categories - 1).

Q3: What's the difference between goodness of fit and test of independence?
A: Goodness of fit compares one categorical variable to a distribution, while test of independence examines relationship between two categorical variables.

Q4: When should I use Fisher's exact test instead?
A: When sample size is small (expected counts < 5), Fisher's exact test is more appropriate.

Q5: Can I use this for continuous data?
A: No, the chi-square test is for categorical data. For continuous data, consider Kolmogorov-Smirnov test.