1. What is Chi-Square Expected Value?

The expected value (E) in a chi-square test represents the count we would expect to see in a cell of a contingency table if the null hypothesis of independence were true. It's calculated based on the row and column totals.

2. How Does the Calculator Work?

The calculator uses the chi-square expected value formula:

Where:

• \( row\ total \) — Sum of all values in the row
• \( column\ total \) — Sum of all values in the column
• \( grand\ total \) — Sum of all values in the table

Explanation: The formula assumes independence between row and column variables, distributing counts proportionally based on marginal totals.

3. Importance of Expected Value

Details: Expected values are crucial for calculating the chi-square statistic, which measures how much observed counts deviate from expected counts 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.

5. Frequently Asked Questions (FAQ)

Q1: When should I use this calculation?
A: Use it when performing chi-square tests of independence or goodness-of-fit tests for categorical data.

Q2: What if my expected value is less than 5?
A: Chi-square tests may not be valid when expected counts are <5. Consider Fisher's exact test or combine categories.

Q3: Can expected values be decimals?
A: Yes, expected values often have decimal places even when observed counts are whole numbers.

Q4: How does this relate to the chi-square statistic?
A: The chi-square statistic sums (observed-expected)²/expected across all cells in the table.

Q5: What's the difference between expected and observed values?
A: Observed values are actual data counts, while expected values are theoretical counts assuming no association.