1. What is Chi-Squared Goodness of Fit?

The Chi-Squared Goodness of Fit test determines whether observed sample data matches an expected theoretical distribution. It's commonly used in hypothesis testing to assess how well a theoretical distribution fits observed data.

2. How Does the Calculator Work?

The calculator uses the Chi-Squared formula:

Where:

• \( \chi^2 \) — Chi-squared statistic
• \( O \) — Observed value
• \( E \) — Expected value
• \( \sum \) — Summation over all categories

Explanation: For each category, we calculate the squared difference between observed and expected counts, divided by the expected count. These values are summed to produce the chi-squared statistic.

3. Interpreting the Results

Details: The chi-squared statistic is compared to a critical value from the chi-squared distribution table (based on degrees of freedom and significance level). A large chi-squared value suggests poor fit between observed and expected distributions.

4. Using the Calculator

Tips: Enter observed and expected values as comma-separated lists. Both lists must have the same number of values. Expected values should not be zero.

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions of the chi-squared test?
A: The test assumes random sampling, independent observations, and that expected frequencies are sufficiently large (typically ≥5).

Q2: How do I determine degrees of freedom?
A: For goodness of fit, df = number of categories - 1 - number of estimated parameters.

Q3: What is a good chi-squared value?
A: A "good" value depends on degrees of freedom and significance level. Lower values generally indicate better fit.

Q4: Can I use this for 2x2 contingency tables?
A: For 2x2 tables, use the chi-squared test of independence with Yates' correction for small sample sizes.

Q5: What alternatives exist for small expected counts?
A: Fisher's exact test is preferred when expected counts are small (<5).