Chi Square Test Statistic Calculator

Chi-square Formula:

\[ \chi^2 = \sum \frac{(O - E)^2}{E} \]

Chi-square Statistic (χ²):

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1. What is the Chi-square Test Statistic?

The chi-square (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-square formula:

\[ \chi^2 = \sum \frac{(O - E)^2}{E} \]

Where:

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

Explanation: For each category, we calculate the squared difference between observed and expected counts, divided by the expected count. These values are summed across all categories to get the chi-square statistic.

3. Importance of Chi-square Test

Details: The chi-square test is fundamental for analyzing categorical data in fields like biology, social sciences, and market research. It helps determine if observed distributions differ significantly from expected distributions.

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 cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What does a significant chi-square result mean?
A: A significant result suggests the observed data are unlikely under the null hypothesis, indicating a statistically significant difference.

Q2: What are the assumptions of the chi-square test?
A: The test assumes random sampling, independence of observations, and that expected counts are ≥5 in most cells.

Q3: How do I interpret the chi-square value?
A: Compare your calculated χ² to critical values from the chi-square distribution table based on your degrees of freedom and significance level.

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

Q5: When should I use Yates' correction?
A: For 2×2 tables with small sample sizes (expected counts <5), consider using Yates' continuity correction.