Chi Square Test Calculator 3x2

Chi Square Formula:

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

Chi Square Value (χ²):

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1. What is Chi Square Test for 3x2 Table?

The Chi Square test for a 3x2 table is a statistical test used to determine if there is a significant association between two categorical variables with 3 and 2 categories respectively. It compares observed frequencies with expected frequencies under the null hypothesis of independence.

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 (unitless)
\( E \) — Expected frequency (unitless)
\( \chi^2 \) — Chi square value (unitless)

Explanation: The test calculates expected frequencies based on the assumption of independence, then compares them with observed frequencies to determine if there's a statistically significant relationship.

3. Importance of Chi Square Test

Details: The Chi Square test is crucial for analyzing categorical data in various fields including medicine, social sciences, and market research to determine if variables are independent or associated.

4. Using the Calculator

Tips: Enter observed frequencies in the 3x2 table. All values must be non-negative numbers. The calculator will compute expected frequencies and the chi square statistic.

5. Frequently Asked Questions (FAQ)

Q1: What degrees of freedom for a 3x2 table?
A: For a 3x2 table, degrees of freedom = (rows-1) × (columns-1) = 2 × 1 = 2

Q2: When is Chi Square test appropriate?
A: When you have categorical data, expected frequencies are ≥5 in most cells, and observations are independent.

Q3: What does a significant chi square value mean?
A: A significant result suggests that the variables are not independent and there is an association between them.

Q4: What are the limitations of Chi Square test?
A: Not reliable with small expected frequencies (<5), only detects association not causation, and doesn't indicate strength or direction of relationship.

Q5: How to interpret the chi square value?
A: Compare the calculated chi square value with critical values from chi square distribution table with appropriate degrees of freedom at your chosen significance level.