1. What is a Chi-Square Goodness of Fit Calculator?

Definition: This calculator computes the chi-square test statistic to determine how well observed data fit expected distribution.

Purpose: It helps researchers and statisticians test hypotheses about whether observed frequencies differ from expected frequencies.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

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

3. Importance of Chi-Square Test

Details: The goodness-of-fit test helps determine if sample data match a population with specific characteristics, useful in quality control, genetics, and social sciences.

4. Using the Calculator

Tips: Enter comma-separated observed and expected values. Both lists must have same length and expected values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What does the chi-square value mean?
A: Higher values indicate greater discrepancy between observed and expected values. Compare to critical values from chi-square distribution tables.

Q2: What are common applications?
A: Testing genetic ratios, survey response distributions, quality control, and any categorical data analysis.

Q3: What are the assumptions?
A: Independent observations, adequate sample size (all expected counts ≥5), and categorical data.

Q4: How many categories can I test?
A: This calculator handles any number of categories as long as observed and expected lists match.

Q5: What's next after calculating χ²?
A: Compare to critical value from chi-square distribution table using appropriate degrees of freedom (categories - 1).