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

The Chi-Squared Goodness of Fit Test is a statistical hypothesis test used to determine whether observed categorical data matches an expected distribution. It compares observed frequencies with expected frequencies to assess how well a theoretical distribution fits the empirical data.

2. How Does the Calculator Work?

The calculator uses the Chi-Squared formula:

Where:

• \( O \) — Observed count
• \( E \) — Expected count
• \( \sum \) — Sum over all categories

Explanation: For each category, the difference between observed and expected counts is squared, divided by the expected count, and summed across all categories.

3. Importance of the Test

Details: This test is widely used in research to verify hypotheses about distributions, such as testing genetic ratios, survey response distributions, or quality control in manufacturing.

4. Using the Calculator

Tips: Enter observed and expected counts as numbers separated by spaces or commas. Both lists must be the same length. All expected counts should be > 0.

5. Frequently Asked Questions (FAQ)

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

Q2: How do I interpret the χ² value?
A: Higher values indicate greater discrepancy between observed and expected. Compare to critical values from χ² distribution tables.

Q3: What's the degrees of freedom for this test?
A: For goodness of fit, df = number of categories - 1 - number of estimated parameters.

Q4: When should I use this test?
A: When you want to test if your data follows a specific distribution (e.g., uniform, normal, or other theoretical distribution).

Q5: What are alternatives if expected counts are too small?
A: Consider combining categories or using exact tests like Fisher's exact test.