1. What is Chi-square Goodness of Fit?

The Chi-square goodness of fit test determines whether sample data matches a population distribution. It compares observed counts (O) with expected counts (E) to assess how likely any 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 measures how much the observed counts deviate from the expected counts. Larger χ² values indicate greater deviation from the expected distribution.

3. Interpreting Results

Details: Compare the calculated χ² value to critical values from the Chi-square distribution table based on degrees of freedom (df = number of categories - 1). Significant results suggest the observed distribution differs from the expected.

4. Using the Calculator

Tips: Enter matching numbers of observed and expected values. All expected values must be > 0. Values can be separated by commas or new lines.

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions of this test?
A: The test assumes: 1) Random sampling, 2) Adequate sample size (all expected counts ≥5), and 3) Independent observations.

Q2: When should I use this test?
A: Use for categorical data to test if observed frequencies match expected frequencies (e.g., genetic ratios, survey results).

Q3: What if my expected counts are too small?
A: For small expected counts, consider Fisher's exact test or combine categories.

Q4: How is degrees of freedom determined?
A: df = number of categories - 1 - number of estimated parameters.

Q5: What does a significant result mean?
A: It suggests the observed distribution is unlikely to match the expected distribution (reject null hypothesis at chosen significance level).