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

The Chi-square goodness of fit test determines whether observed sample data matches an expected distribution. It's commonly used to test hypotheses about categorical data distributions.

2. How Does the Calculator Work?

The calculator uses the Chi-square formula:

Where:

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

Explanation: The test compares observed frequencies with expected frequencies, with larger discrepancies resulting in higher chi-square values.

3. Importance of Chi-square Test

Details: This test is fundamental in statistics for testing hypotheses about distributions, checking model fits, and analyzing categorical data in various fields.

4. Using the Calculator

Tips: Enter observed and expected counts as comma-separated values. Both lists must have the same number of values. All expected counts should be > 0.

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 frequencies are at least 5 for each category.

Q2: How do I interpret the chi-square value?
A: Compare your calculated χ² to a critical value from chi-square distribution tables with (k-1) degrees of freedom (k = 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: Can I use this with small sample sizes?
A: For small samples (expected counts < 5), consider Fisher's exact test or combine categories.

Q5: How is this performed on TI-83 Plus?
A: On TI-83 Plus, use STAT → TESTS → χ²GOF-Test (may require newer OS). Enter observed and expected lists, then calculate.