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

The Chi-Square Goodness of Fit Test determines whether observed sample data matches an expected theoretical 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 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 distributional assumptions, checking model fits, and analyzing categorical data in fields like biology, marketing, and social sciences.

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 ≥5 for validity.

5. Frequently Asked Questions (FAQ)

Q1: How do I perform this test on a TI-83 Plus?
A: Enter observed in L1, expected in L2. In L3, enter formula (L1-L2)²/L2. Sum L3 to get χ². Use χ²cdf for p-value.

Q2: What are degrees of freedom in this test?
A: For goodness of fit, df = number of categories - 1 - number of estimated parameters.

Q3: When is this test not appropriate?
A: When expected counts are too small (typically <5) or when data are not independent.

Q4: How to interpret the chi-square value?
A: Compare to critical value from chi-square distribution table with appropriate df. Higher values indicate greater discrepancy.

Q5: What's the difference between goodness of fit and test of independence?
A: Goodness of fit compares to a theoretical distribution, while test of independence examines relationship between two variables.