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Expected Frequency Formula:
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Expected frequency is a statistical measure used in contingency tables to calculate the theoretical frequency that would be expected in each cell if there were no association between the variables. It is fundamental to chi-square tests and other statistical analyses.
The calculator uses the expected frequency formula:
Where:
Explanation: This formula calculates what the frequency would be if the row and column variables were independent of each other.
Details: Expected frequencies are crucial for conducting chi-square tests of independence, which determine whether there is a significant association between categorical variables in a contingency table.
Tips: Enter the row total, column total, and grand total as positive numbers. All values must be greater than zero and the grand total must be equal to or greater than both row and column totals.
Q1: When is expected frequency used?
A: Expected frequency is primarily used in chi-square tests to compare observed frequencies with expected frequencies under the null hypothesis of independence.
Q2: What if expected frequency is less than 5?
A: When expected frequencies are less than 5, the chi-square test may not be valid. In such cases, Fisher's exact test is often recommended as an alternative.
Q3: Can expected frequency be a decimal?
A: Yes, expected frequencies are often decimal values as they represent theoretical averages rather than actual counts.
Q4: How does expected frequency relate to probability?
A: Expected frequency represents the probability of an event occurring multiplied by the total number of trials or observations.
Q5: What's the difference between observed and expected frequency?
A: Observed frequency is the actual count from collected data, while expected frequency is the theoretical count calculated under the assumption of no association between variables.