1. What is the Chi-Squared Test?

The Chi-Squared (χ²) test is a statistical method used to determine if there is a significant difference between observed and expected frequencies in one or more categories. It's commonly used in hypothesis testing to assess goodness of fit or independence.

2. How Does the Calculator Work?

The calculator uses the Chi-Squared formula:

Where:

• \( O_i \) — Observed frequency for category i
• \( E_i \) — Expected frequency for category i
• \( \sum \) — Summation over 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-Squared Test

Details: The Chi-Squared test is widely used in research to test hypotheses about categorical data, including survey analysis, genetics, and quality control. It helps determine if observed deviations from expected results are statistically significant.

4. Using the Calculator

Tips: Enter observed and expected frequencies as comma-separated values. Both lists must have the same number of values. Expected frequencies cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a good chi-squared value?
A: There's no "good" or "bad" value - the significance depends on the degrees of freedom and the chosen significance level (typically 0.05).

Q2: When should I use a chi-squared test?
A: Use it when you have categorical data and want to test if observed frequencies differ significantly from expected frequencies.

Q3: What are the assumptions of the chi-squared test?
A: The test assumes independence of observations, adequate sample size, and expected frequencies of at least 5 in each category.

Q4: How do I interpret the p-value?
A: A p-value less than 0.05 typically indicates that the difference between observed and expected frequencies is statistically significant.

Q5: Can I use chi-squared for small sample sizes?
A: For small samples (expected frequencies < 5), consider using Fisher's exact test instead.