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

The Chi-Squared Goodness of Fit test determines whether observed categorical data matches an expected distribution. It compares observed counts to expected counts under a null hypothesis.

2. How Does the Calculator Work?

The calculator uses the Chi-Squared formula:

Where:

• \( O \) — Observed counts
• \( E \) — Expected counts under null hypothesis
• \( df \) — Degrees of freedom (number of categories - 1)
• \( \chi^2 \) — Chi-squared test statistic
• \( P\text{-value} \) — Probability under chi-squared distribution

Explanation: The test measures how much the observed data deviates from expected. A high chi-squared value (and low p-value) suggests significant deviation.

3. Interpreting Results

Details:

• P-value < 0.05 typically indicates significant deviation from expected
• Higher chi-squared values indicate greater deviation
• Degrees of freedom affect the critical chi-squared value

4. Using the Calculator

Tips:

• Enter observed and expected counts as comma-separated values
• Both lists must have same number of values
• Expected counts should be ≥5 for each category
• At least 2 categories required

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between goodness of fit and test of independence?
A: Goodness of fit compares to a theoretical distribution, while test of independence examines relationship between two variables.

Q2: When is chi-squared test not appropriate?
A: When expected counts are <5 (use Fisher's exact test) or with continuous/non-categorical data.

Q3: How are degrees of freedom determined?
A: For goodness of fit, df = number of categories - 1.

Q4: What does a p-value of 0.05 mean?
A: There's a 5% probability of seeing this much deviation if the null hypothesis were true.

Q5: Can I use this for small sample sizes?
A: Not recommended if any expected count is <5. Consider exact tests for small samples.