X 2 Test Statistic Calculator

Chi-Square Formula:

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

Chi-Square Test Statistic (χ²):

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1. What Is The Chi-Square Test Statistic?

The chi-square test statistic (χ²) measures how observed categorical data compare to expected values under a specific hypothesis. It's widely used in statistics to test for independence, goodness of fit, and homogeneity in contingency tables.

2. How Does The Calculator Work?

The calculator uses the chi-square formula:

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

Where:

\( O \) — Observed frequency values
\( E \) — Expected frequency values
\( \sum \) — Summation across all categories

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

3. Importance Of Chi-Square Calculation

Details: The chi-square test statistic is essential for determining whether there's a significant difference between observed and expected frequencies, helping researchers validate hypotheses in various fields including medicine, social sciences, and biology.

4. Using The Calculator

Tips: Enter observed and expected values as comma-separated lists. Both lists must have the same number of values. Ensure expected values are greater than zero for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What does a high chi-square value indicate?
A: A high chi-square value suggests a significant difference between observed and expected frequencies, potentially leading to rejection of the null hypothesis.

Q2: When should I use the 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 the chi-square test?
A: The test assumes independence of observations, adequate sample size, and expected frequencies of at least 5 in each category.

Q4: Can chi-square be used with small sample sizes?
A: For small sample sizes or when expected frequencies are low, Fisher's exact test may be more appropriate than chi-square.

Q5: How do I interpret the p-value from a chi-square test?
A: A p-value less than your significance level (typically 0.05) indicates that the observed differences are statistically significant.