1. What is the Chi-Squared Test Statistic?

The chi-squared (χ²) test statistic measures how observed counts differ from expected counts under a null hypothesis. It's widely used in tests of independence and goodness-of-fit in categorical data analysis.

2. How Does the Calculator Work?

The calculator uses the chi-squared formula:

Where:

• \( O \) — Observed count
• \( E \) — Expected count under null hypothesis
• \( \sum \) — Sum over all categories

Explanation: The formula sums the squared differences between observed and expected counts, divided by the expected counts for each category.

3. Importance of Chi-Squared Test

Details: The chi-squared test is fundamental for analyzing categorical data, testing hypotheses about distributions, and examining relationships between categorical variables.

4. Using the Calculator

Tips: Enter matching sets of observed and expected counts. Values must be positive numbers. The number of observed and expected values must be equal.

5. Frequently Asked Questions (FAQ)

Q1: What's a good chi-squared value?
A: There's no "good" value - it depends on degrees of freedom and significance level. Compare to critical values from chi-squared distribution tables.

Q2: When is chi-squared test appropriate?
A: For categorical data with expected counts ≥5 in most cells (some allow ≥1 if few cells have <5).

Q3: What does a high chi-squared value mean?
A: Higher values indicate greater divergence between observed and expected counts, suggesting rejection of the null hypothesis.

Q4: What are degrees of freedom?
A: For a contingency table, df = (rows-1)*(columns-1). For goodness-of-fit, df = categories-1-parameters estimated.

Q5: Can chi-squared test show causation?
A: No, it only shows association between categorical variables, not causation.