Chi Square Proportion Test Calculator

Chi-square Formula for Proportions:

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

Chi-square Statistic (χ²):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Chi-square Proportion Test?

The Chi-square proportion test is a statistical method to determine if observed counts differ significantly from expected counts. It's commonly used to test goodness of fit or test for independence in categorical data.

2. How Does the Calculator Work?

The calculator uses the Chi-square formula:

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

Where:

\( O \) — Observed counts
\( E \) — Expected counts
\( \sum \) — Sum over all categories

Explanation: The test compares observed frequencies with expected frequencies under the null hypothesis.

3. Importance of Chi-square Test

Details: The Chi-square test is widely used in research to test hypotheses about distributions and associations in categorical data.

4. Using the Calculator

Tips: Enter observed and expected counts as comma-separated values. Both lists must have the same number of values.

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions of the Chi-square test?
A: The test assumes random sampling, independence of observations, and expected counts ≥5 in each category.

Q2: How do I interpret the Chi-square statistic?
A: Compare the calculated χ² value to a critical value from the Chi-square distribution table based on your degrees of freedom and significance level.

Q3: What are degrees of freedom in Chi-square test?
A: For goodness-of-fit, df = number of categories - 1. For contingency tables, df = (rows-1)*(columns-1).

Q4: When should I use Fisher's exact test instead?
A: When expected counts are <5 or with small sample sizes, Fisher's exact test is more appropriate.

Q5: Can Chi-square test prove causation?
A: No, it only tests for association between categorical variables, not causation.