1. What is Chi-Squared Test?

The chi-squared (χ²) test is a statistical hypothesis test that measures the discrepancy between observed and expected frequencies in categorical data. It's commonly used for goodness-of-fit tests and tests of 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 test compares observed counts with expected counts under the null hypothesis, with larger discrepancies producing larger chi-squared values.

3. Interpretation of Results

Details: The calculated χ² value is compared against a critical value from the chi-squared distribution table based on degrees of freedom (number of categories minus 1) and significance level (typically 0.05).

4. Using the Calculator

Tips: Enter observed and expected frequencies as comma-separated values. Both lists must have the same number of values, and expected frequencies must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: When should I use a chi-squared test?
A: Use it when you have categorical data and want to test whether observed frequencies differ significantly from expected frequencies.

Q2: What are the assumptions of the chi-squared test?
A: The test assumes random sampling, independence of observations, and that expected frequencies are at least 5 in each category.

Q3: How do I determine degrees of freedom?
A: For goodness-of-fit, df = number of categories - 1. For contingency tables, df = (rows - 1) × (columns - 1).

Q4: What if my expected frequencies are too small?
A: For small expected frequencies, consider Fisher's exact test or combine categories to increase expected counts.

Q5: Can I use this for continuous data?
A: No, the chi-squared test is for categorical data. For continuous data, consider Kolmogorov-Smirnov or Anderson-Darling tests.