1. What is Chi-Square?

The chi-square (χ²) statistic is a measure used in statistical analysis to assess how observed data compare to expected data under a specific hypothesis. It's commonly used in tests of independence and goodness-of-fit tests.

2. How Does the Calculator Work?

The calculator uses the chi-square formula:

Where:

• \( O \) — Observed values (unitless)
• \( E \) — Expected values (unitless)
• \( \chi^2 \) — Chi-square value (unitless)

Explanation: The formula calculates the sum of squared differences between observed and expected values, divided by the expected values.

3. Importance of Chi-Square Calculation

Details: Chi-square tests are crucial for determining whether there's a significant association between categorical variables or whether observed data fit an expected distribution.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a good chi-square value?
A: There's no "good" or "bad" value - significance depends on degrees of freedom and the chosen significance level (typically p < 0.05).

Q2: When should I use a chi-square test?
A: Use it when you have categorical data and want to test for independence between variables or goodness-of-fit to a distribution.

Q3: What are the assumptions of chi-square tests?
A: Observations should be independent, expected frequencies should be ≥5, and data should be in frequency/count form.

Q4: Can chi-square be negative?
A: No, chi-square values are always positive or zero because they're sums of squared quantities.

Q5: How do I interpret the p-value?
A: A small p-value (typically < 0.05) suggests that the observed data significantly differ from the expected values under the null hypothesis.