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

The Chi-Square (χ²) Goodness of Fit test determines whether sample data matches a population with a specific distribution. It compares observed counts with expected counts to assess how well a theoretical distribution fits observed data.

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 statistic measures how much the observed counts deviate from the expected counts. Larger values indicate greater discrepancy.

3. Importance of the Test

Details: This test is widely used in statistics to check if categorical data follows an expected distribution, such as testing genetic ratios, survey results, or quality control.

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: What are the assumptions of this test?
A: The test assumes: 1) Random sampling, 2) Large enough sample size (all expected counts ≥5), and 3) Independent observations.

Q2: How to interpret the χ² value?
A: Compare your χ² value to a critical value from the chi-square distribution table 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: When should I use Fisher's exact test instead?
A: Use Fisher's exact test when sample sizes are small (expected counts <5) or when dealing with 2x2 contingency tables.

Q5: How is this calculated in R?
A: In R, use chisq.test(observed, p = expected/sum(expected)) or chisq.test(matrix(c(observed, expected), ncol=2)).