1. What is Chi-Square Goodness Of Fit?

The Chi-square goodness of fit test is a statistical hypothesis test used to determine whether a set of observed frequencies differs from a set of expected frequencies. It's commonly used to test how well a sample matches a theoretical distribution.

2. How Does the Calculator Work?

The calculator uses the Chi-square formula:

Where:

• \( observed \) — Observed frequency values
• \( expected \) — Expected frequency values
• \( \chi^2 \) — Chi-square test statistic

Explanation: The test compares observed counts with expected counts under the null hypothesis. A large χ² value indicates a significant difference between observed and expected values.

3. Importance of Chi-Square Test

Details: The goodness-of-fit test is widely used in research to test distributions, validate models, and check assumptions about categorical data.

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 cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions of the Chi-square test?
A: The test assumes: 1) Random sampling, 2) Independent observations, 3) Adequate sample size (expected counts ≥5 for most cells).

Q2: How do I interpret the Chi-square value?
A: Compare your χ² value to a critical value from Chi-square distribution tables using appropriate degrees of freedom and significance level.

Q3: What are degrees of freedom in Chi-square test?
A: For goodness-of-fit, df = number of categories - 1 - number of estimated parameters.

Q4: When should I use Yates' correction?
A: For 2×2 contingency tables with small sample sizes, but not for goodness-of-fit tests.

Q5: What alternatives exist for small expected counts?
A: Fisher's exact test or combining categories may be appropriate when expected counts are too small.