1. What is Chi-Square Goodness of Fit Test?

The Chi-Square Goodness of Fit test determines whether observed sample data matches an expected theoretical distribution. It compares observed frequencies with expected frequencies to test hypotheses about distributions.

2. How Does the Calculator Work?

The calculator uses the Chi-Square formula:

Where:

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

Explanation: The test measures how much the observed data deviates from what was expected. Larger χ² values indicate greater deviation from the expected distribution.

3. When to Use This Test

Details: Use this test when you have categorical data and want to compare observed frequencies with expected frequencies based on a theoretical distribution. Common applications include genetics, marketing research, and quality control.

4. Using the Calculator

Tips: Enter observed and expected values for each category. Add or remove categories as needed. All values must be non-negative numbers. Expected values should not 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 frequencies are at least 5 for each category.

Q2: How do I interpret the χ² value?
A: Compare your χ² value to a critical value from the Chi-Square distribution table based on your degrees of freedom (categories - 1) and significance level.

Q3: What if my expected values are less than 5?
A: Consider combining categories or using Fisher's exact test if you have many small expected frequencies.

Q4: Can I use this for continuous data?
A: You must first bin continuous data into categories before applying this test.

Q5: What's the difference between goodness of fit and test of independence?
A: Goodness of fit compares one variable to a theoretical distribution, while test of independence examines the relationship between two categorical variables.