1. What is a Chi-square Test Statistic?

Definition: The chi-square (χ²) statistic measures how observed counts compare to expected counts under a null hypothesis.

Purpose: Used in hypothesis testing to determine if there's a significant difference between expected and observed data.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \chi² \) — Chi-square test statistic (dimensionless)
• \( O_i \) — Observed frequency for category i
• \( E_i \) — Expected frequency for category i

Explanation: For each category, we calculate the squared difference between observed and expected counts, divided by the expected count, then sum all these values.

3. Importance of Chi-square Test

Details: The chi-square test is widely used in:

• Goodness-of-fit tests
• Tests of independence in contingency tables
• Homogeneity tests

4. Using the Calculator

Tips:

• Enter observed and expected values as comma-separated lists
• Both lists must have the same number of values
• All expected values must be greater than 0

5. Frequently Asked Questions (FAQ)

Q1: What does a high chi-square value mean?
A: A higher χ² value indicates greater discrepancy between observed and expected values, suggesting the null hypothesis may be rejected.

Q2: What's considered a "significant" chi-square value?
A: Significance depends on degrees of freedom and chosen significance level (typically 0.05). Compare to critical values from chi-square tables.

Q3: Can I use this for 2x2 contingency tables?
A: Yes, but for 2x2 tables with small expected counts, consider Yates' correction or Fisher's exact test.

Q4: Why can't expected values be zero?
A: Division by zero is undefined. Categories with expected counts of 0 should be combined or omitted.

Q5: How many decimal places should I use?
A: Typically 2-4 decimal places are sufficient for most applications.