1. What Is The Expected Frequency Formula?

The expected frequency formula calculates the theoretical frequency for a cell in a contingency table under the assumption of independence between variables. It's used in statistical tests like chi-square to compare observed and expected frequencies.

2. How Does The Calculator Work?

The calculator uses the expected frequency formula:

Where:

• \( E_{ij} \) — Expected frequency for cell in row i, column j
• \( Row_i Total \) — Total count for row i
• \( Column_j Total \) — Total count for column j
• \( N \) — Grand total of all observations

Explanation: This formula calculates what the frequency would be if there was no association between the row and column variables.

3. Importance Of Expected Frequency Calculation

Details: Expected frequencies are essential for statistical tests of independence, particularly the chi-square test. They provide a baseline to compare against observed frequencies to determine if variables are related.

4. Using The Calculator

Tips: Enter the row total, column total, and grand total (N). All values must be positive numbers. The calculator will compute the expected frequency for that specific cell.

5. Frequently Asked Questions (FAQ)

Q1: When should I use the expected frequency formula?
A: Use it when performing chi-square tests of independence to compare categorical variables in contingency tables.

Q2: What if my expected frequency is less than 5?
A: For chi-square tests, it's generally recommended that expected frequencies should be at least 5. If they're lower, you might need to use Fisher's exact test instead.

Q3: Can I use this for multiple cells in a table?
A: Yes, you would calculate expected frequencies for each cell in your contingency table using the same formula with the appropriate row and column totals.

Q4: What does it mean if observed and expected frequencies differ greatly?
A: Large differences suggest that the variables may not be independent and there might be a relationship between them.

Q5: Are there limitations to this calculation?
A: The formula assumes that observations are independent and that the sample is representative of the population. It works best with large sample sizes.