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Expected Value Formula:
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The expected value (EV) in a chi-square test is 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 calculated based on the marginal totals of the table.
The calculator uses the expected value formula:
Where:
Explanation: The formula calculates what the count would be in each cell if the row and column variables were independent (no association).
Details: Expected values are crucial for chi-square tests as they provide the benchmark against which observed values are compared. The chi-square statistic is calculated by summing the squared differences between observed and expected values, divided by the expected values.
Tips: Enter the row total, column total, and grand total from your contingency table. All values must be positive numbers, and grand total must be greater than zero.
Q1: Why do we need expected values in chi-square tests?
A: Expected values represent what we would observe if the null hypothesis were true. Comparing observed and expected values helps determine if there's a statistically significant association between variables.
Q2: What if my expected value is less than 5?
A: Chi-square tests become unreliable when expected values are less than 5. In such cases, consider using Fisher's exact test or combining categories.
Q3: Can expected values be non-integers?
A: Yes, expected values are often decimals since they're calculated from proportions, unlike observed counts which are whole numbers.
Q4: How do I get row and column totals?
A: Row total is the sum across a row in your contingency table. Column total is the sum down a column. Grand total is the sum of all cells.
Q5: What's the relationship between EV and degrees of freedom?
A: Degrees of freedom in chi-square tests depend on table dimensions (rows-1 × columns-1), while EV calculations use the marginal totals.