Chi Square Formula Calculator

Chi-Square Formula:

\[ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \]

Chi-Square Test Statistic (χ²):

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1. What is the Chi-Square Test Statistic?

The Chi-Square test statistic measures how observed frequencies differ from expected frequencies under a specific hypothesis. It is widely used in statistics for hypothesis testing, particularly for categorical data analysis.

2. How Does the Calculator Work?

The calculator uses the Chi-Square formula:

\[ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \]

Where:

\( O_i \) — Observed frequency (count)
\( E_i \) — Expected frequency (count)
\( \sum \) — Summation over all categories

Explanation: The formula calculates the sum of squared differences between observed and expected values, normalized by the expected values.

3. Importance of Chi-Square Calculation

Details: The Chi-Square test is essential for determining whether there is a significant association between categorical variables, testing goodness of fit, and checking independence in contingency tables.

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 should not be zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the Chi-Square test used for?
A: It's used to test hypotheses about categorical data, including goodness of fit tests and tests of independence in contingency tables.

Q2: What are the assumptions of the Chi-Square test?
A: The test assumes that data are frequency counts, observations are independent, and expected frequencies are sufficiently large (typically ≥5).

Q3: How do I interpret the Chi-Square value?
A: Larger Chi-Square values indicate greater discrepancy between observed and expected frequencies. The value is compared to critical values from the Chi-Square distribution based on degrees of freedom.

Q4: What are degrees of freedom in Chi-Square tests?
A: For goodness of fit: (number of categories - 1). For contingency tables: (rows - 1) × (columns - 1).

Q5: When should I not use the Chi-Square test?
A: When expected frequencies are too small, when data are not frequency counts, or when observations are not independent.