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

The Chi-Square Goodness of Fit Test is a statistical hypothesis test used to determine whether observed categorical data matches an expected distribution. It compares observed counts with expected counts to assess how likely any differences are due to chance.

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 calculates a chi-square statistic that measures how much the observed counts deviate from the expected counts.

3. Importance of Chi-Square Test

Details: This test is widely used in research to determine if sample data matches a population distribution, test fairness of categorical variables, and validate assumptions about data distributions.

4. Using the Calculator

Tips: Enter observed and expected counts as comma-separated values. Both lists must have the same number of values and all expected counts should be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: When should I use a Chi-Square Goodness of Fit Test?
A: Use it when you have categorical data and want to test how well it fits an expected distribution.

Q2: 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.

Q3: How do I interpret the chi-square statistic?
A: Higher values indicate greater deviation from the expected distribution. Compare to critical values from chi-square distribution tables.

Q4: 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.

Q5: Can I use this with small sample sizes?
A: For small samples (expected counts < 5), consider Fisher's exact test or combine categories.