Calculate Expected Value In Chi Square Test

Expected Value Formula:

\[ E = \frac{(\text{row total} \times \text{column total})}{\text{grand total}} \]

Expected Value (E):

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1. What is Expected Value in Chi-Square Test?

The expected value in a chi-square test represents the theoretical frequency that would be expected in each cell of a contingency table if the null hypothesis of independence between the variables were true. It's a crucial component in calculating the chi-square statistic.

2. How Does the Calculator Work?

The calculator uses the expected value formula:

\[ E = \frac{(\text{row total} \times \text{column total})}{\text{grand total}} \]

Where:

\( E \) — Expected value (unitless)
\( \text{row total} \) — Sum of all values in the row (unitless)
\( \text{column total} \) — Sum of all values in the column (unitless)
\( \text{grand total} \) — Sum of all values in the table (unitless)

Explanation: The formula calculates what the count would be in each cell if the row and column variables were independent of each other.

3. Importance of Expected Value Calculation

Details: Comparing observed values with expected values helps determine whether there's a statistically significant association between categorical variables. The chi-square test quantifies how much the observed data deviate from what would be expected under the null hypothesis.

4. Using the Calculator

Tips: Enter the row total, column total, and grand total from your contingency table. All values must be positive numbers. The calculator will compute the expected frequency for that cell.

5. Frequently Asked Questions (FAQ)

Q1: When should I use this calculation?
A: Use it when performing a chi-square test of independence on categorical data arranged in a contingency table.

Q2: What if my expected value is less than 5?
A: When expected values are below 5, the chi-square approximation may not be valid. Consider using Fisher's exact test instead.

Q3: Can I use this for 2x2 tables?
A: Yes, this formula works for any size contingency table, including 2x2 tables.

Q4: How does this relate to the chi-square statistic?
A: The chi-square statistic is calculated by summing (observed-expected)²/expected for all cells in the table.

Q5: Why is the expected value unitless?
A: Since all inputs are counts (unitless), the output is also unitless. It represents an expected count, not a measurement with units.