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Expected Count Formula:
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Expected counts are the theoretical frequencies that would be expected in each cell of a contingency table if the null hypothesis of independence were true. They form the basis for comparison with observed counts in chi-square tests.
The calculator uses the expected count formula:
Where:
Explanation: The formula calculates what count would be expected in each cell if the row and column variables were independent (no association).
Details: Expected counts are crucial for chi-square tests as they provide the benchmark against which observed counts are compared. The chi-square statistic measures how much the observed counts deviate from these expected counts.
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 count for the cell at the intersection of that row and column.
Q1: What if my expected counts are very small?
A: Chi-square tests become unreliable when expected counts are below 5. Consider Fisher's exact test or combine categories.
Q2: Can expected counts be non-integers?
A: Yes, expected counts are often decimals since they represent theoretical averages.
Q3: How many expected counts do I need for a chi-square test?
A: You need to calculate expected counts for every cell in your contingency table.
Q4: What does it mean if observed and expected counts are very different?
A: Large differences suggest an association between the variables (reject the null hypothesis of independence).
Q5: Can I use this for goodness-of-fit tests?
A: For goodness-of-fit, expected counts are typically based on theoretical distributions rather than row/column totals.