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

Definition: The χ² goodness-of-fit test determines whether observed frequencies differ significantly from expected frequencies.

Purpose: Used in statistics to test hypotheses about distributions and to check if observed data matches theoretical expectations.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \chi^2 \) — Chi-square test statistic (dimensionless)
• \( O_i \) — Observed frequency (dimensionless)
• \( E_i \) — Expected frequency (dimensionless)

Explanation: For each category, the difference between observed and expected values is squared, divided by the expected value, and summed across all categories.

3. Importance of Chi-square Test

Details: This test helps determine whether deviations between observed and expected values are due to chance or represent statistically significant differences.

4. Using the Calculator

Tips: Enter comma-separated lists of observed and expected frequencies. Both lists must have the same number of values. Expected values cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What does the degrees of freedom represent?
A: Degrees of freedom (df) equals the number of categories minus 1. It's used when interpreting the χ² value against critical values.

Q2: What's considered a "significant" χ² value?
A: Compare your χ² value to critical values from a χ² distribution table at your desired significance level (typically 0.05).

Q3: When should I use this test?
A: Use when you have categorical data and want to test if observed counts match expected counts based on a theoretical distribution.

Q4: What are the assumptions of this test?
A: 1) Random sampling, 2) Independent observations, 3) Expected frequency ≥5 for each category.

Q5: How do I interpret the results?
A: If χ² > critical value, reject the null hypothesis (significant difference). If χ² ≤ critical value, fail to reject (no significant difference).