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

The Chi-Square Goodness-of-Fit test determines whether observed categorical data follow an expected distribution. It compares observed counts to expected counts to assess how likely the observed 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 how much the observed counts deviate from the expected counts. A large chi-square value indicates the observed data likely doesn't follow the expected distribution.

3. Interpretation of Results

Details: Compare the calculated chi-square statistic to critical values from the chi-square distribution table with appropriate degrees of freedom (df = number of categories - 1). A p-value < 0.05 typically indicates statistical significance.

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 want to test if categorical data matches an expected distribution (e.g., genetic ratios, survey responses, dice rolls).

Q2: What are the assumptions?
A: 1) Independent observations, 2) All expected counts ≥5, 3) Categorical (not continuous) data.

Q3: What if my expected counts are less than 5?
A: Combine categories or use exact tests like Fisher's exact test for small samples.

Q4: How do I find the p-value?
A: Use the chi-square statistic and degrees of freedom with a chi-square distribution table or online calculator.

Q5: What does degrees of freedom mean?
A: It's the number of categories minus one minus the number of estimated parameters (for simple GOF test, df = categories - 1).