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

The Chi-square goodness of fit test is a statistical hypothesis test used to determine whether a sample data matches a population with a specific distribution. It compares observed counts with expected counts to assess how well a theoretical distribution fits the empirical data.

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 counts deviate from the expected counts. A large chi-square value indicates poor fit between observed and expected distributions.

3. Importance of Chi-square Test

Details: The test is widely used in research to check if sample data fits theoretical expectations, test genetic ratios, examine survey responses, and validate statistical models.

4. Using the Calculator

Tips: Enter observed and expected counts as comma-separated values. Both lists must have the same number of values. All expected counts should be ≥5 for reliable results.

5. Frequently Asked Questions (FAQ)

Q1: When should I use this test?
A: Use when you have categorical data and want to test if observed frequencies match expected frequencies based on a theoretical distribution.

Q2: What are the assumptions of the test?
A: The test assumes random sampling, independence of observations, and that expected frequencies are sufficiently large (typically ≥5).

Q3: How do I interpret the chi-square value?
A: Compare your calculated χ² value to critical values from chi-square distribution tables with appropriate degrees of freedom (categories - 1).

Q4: What if my expected counts are less than 5?
A: Consider combining categories or using exact tests like Fisher's exact test for small sample sizes.

Q5: Can I use this for continuous data?
A: No, the test is for categorical data. For continuous data, consider Kolmogorov-Smirnov or Anderson-Darling tests.