Find Expected Frequency Calculator

Expected Frequency Formula:

\[ \text{Expected Frequency} = \frac{(\text{Row Total} \times \text{Column Total})}{\text{Grand Total}} \]

Expected Frequency:

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1. What Is Expected Frequency?

Expected frequency is a statistical measure used in contingency tables to determine the expected count for each cell under the assumption of independence between variables. It helps in comparing observed frequencies with expected values in chi-square tests.

2. How Does The Calculator Work?

The calculator uses the expected frequency formula:

\[ \text{Expected Frequency} = \frac{(\text{Row Total} \times \text{Column Total})}{\text{Grand Total}} \]

Where:

Row Total — Sum of all counts in a specific row
Column Total — Sum of all counts in a specific column
Grand Total — Sum of all counts in the entire table

Explanation: This formula calculates what the frequency would be if there was no association between the row and column variables (i.e., if they were independent).

3. Importance Of Expected Frequency

Details: Expected frequency is crucial for statistical tests like chi-square tests of independence, helping researchers determine whether observed distributions differ significantly from expected distributions.

4. Using The Calculator

Tips: Enter the row total, column total, and grand total as positive numbers. All values must be valid (greater than 0) for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: When is expected frequency used?
A: Expected frequency is primarily used in chi-square tests to compare observed and expected counts in contingency tables.

Q2: What if expected frequency is less than 5?
A: In chi-square tests, expected frequencies below 5 may require alternative statistical methods like Fisher's exact test for accurate results.

Q3: Can expected frequency be a decimal?
A: Yes, expected frequency can be a decimal value as it represents a theoretical count rather than an actual observed count.

Q4: How does expected frequency relate to probability?
A: Expected frequency represents the count we would expect to see if the probability of an event was distributed according to the marginal totals.

Q5: What are the limitations of expected frequency?
A: The calculation assumes independence between variables and may not be valid for small sample sizes or when expected counts are too low.