Chi-Square Goodness of Fit Test Calculator TI-83 Plus

Chi-Square Formula:

\[ \chi^2 = \sum \frac{(O - E)^2}{E} \]

Chi-Square Statistic (χ²):

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

The Chi-Square Goodness of Fit Test determines whether sample data matches a population distribution. It compares observed counts with expected counts to see if differences are statistically significant.

2. How Does the Calculator Work?

The calculator uses the Chi-Square formula:

\[ \chi^2 = \sum \frac{(O - E)^2}{E} \]

Where:

\( O \) — Observed counts
\( E \) — Expected counts
\( \sum \) — Sum over all categories

Explanation: The test measures how much the observed counts deviate from the expected counts under the null hypothesis.

3. Importance of Chi-Square Test

Details: This test is widely used in research to examine categorical data, test genetic ratios, check survey response distributions, and validate probability models.

4. Using the Calculator

Tips: Enter observed and expected counts as comma-separated values. Both lists must have the same number of values. Expected counts should not be zero.

5. Frequently Asked Questions (FAQ)

Q1: How do I perform this test on a TI-83 Plus?
A: Enter observed counts in L1, expected in L2. Compute (L1-L2)²/L2 in L3, then sum L3 to get χ².

Q2: What are the assumptions of this test?
A: Data should be categorical, observations independent, and expected counts ≥5 in each category.

Q3: How do I interpret the χ² value?
A: Compare to critical value from χ² distribution table with (k-1) degrees of freedom (k = number of categories).

Q4: What if my expected counts are less than 5?
A: Combine categories or use exact tests like Fisher's exact test for small expected counts.

Q5: Can I use this for continuous data?
A: No, you must first categorize continuous data into bins before applying this test.