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

The Chi-square goodness of fit test is a statistical hypothesis test used to determine whether a categorical variable follows a hypothesized distribution. It compares observed frequencies with expected frequencies under the null hypothesis.

2. How Does the Calculator Work?

The calculator uses the Chi-square formula:

Where:

• \( O \) — Observed count
• \( E \) — Expected count under null hypothesis
• \( \sum \) — Sum over all categories

Explanation: The test statistic measures how much the observed counts deviate from the expected counts. A large value suggests the observed data doesn't fit the expected distribution.

3. Importance of Chi-square Test

Details: This test is widely used in research to examine whether sample data matches a population distribution, test genetic crosses, or verify survey results against expected patterns.

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 this test?
A: The test assumes random sampling, independence of observations, and that expected counts are at least 5 for each category.

Q2: How do I interpret the chi-square value?
A: Compare the calculated χ² to a critical value from chi-square distribution tables with (k-1) degrees of freedom (where k is number of categories).

Q3: What's the difference between goodness of fit and test of independence?
A: Goodness of fit compares observed to expected counts in one variable, while test of independence examines relationship between two categorical variables.

Q4: When should I use Fisher's exact test instead?
A: When sample size is small (expected counts < 5), Fisher's exact test is more appropriate.

Q5: Can I use this for continuous data?
A: No, the test is for categorical data. Continuous data must be binned into categories first.