1. What is Goodness of Fit Chi-Square?

The chi-square goodness of fit test is a statistical hypothesis test used to determine whether sample data match a population with a specific distribution. It assesses how well observed data fit expected data based on a theoretical distribution.

2. How Does the Calculator Work?

The calculator uses the chi-square formula:

Where:

• \( O \) — Observed frequency
• \( E \) — Expected frequency
• \( \sum \) — Summation across all categories

Explanation: The test compares observed frequencies with expected frequencies under the null hypothesis. A large chi-square value indicates a poor fit between observed and expected data.

3. Importance of Chi-Square Test

Details: The goodness of fit test is crucial for determining whether sample data come from a population with a specific distribution, validating statistical models, and testing theoretical assumptions in research.

4. Using the Calculator

Tips: Enter observed and expected values as comma-separated lists. Both lists must have the same number of values. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a good chi-square value?
A: A smaller chi-square value indicates a better fit. The significance depends on degrees of freedom and the chosen alpha level (typically 0.05).

Q2: What are the assumptions of the chi-square test?
A: The test assumes independence of observations, adequate sample size (expected frequency ≥5 in each category), and categorical data.

Q3: When should I use this test?
A: Use it when you want to test whether your data follow a specific distribution, such as testing if a die is fair or if survey responses match expected proportions.

Q4: How do I interpret the p-value?
A: A p-value less than your significance level (usually 0.05) suggests that observed data significantly differ from expected data, leading to rejection of the null hypothesis.

Q5: What are the limitations of this test?
A: The test requires sufficiently large expected frequencies and may not be reliable with small sample sizes or many categories with low expected counts.