1. What is Expected Frequency?

Expected frequency is a statistical term used in chi-square tests that represents the theoretical frequency that would be expected in a cell of a contingency table if the null hypothesis of independence were true.

2. How Does the Calculator Work?

The calculator uses the expected frequency formula:

Where:

• \( Row\ Total \) — Sum of all values in the row
• \( Column\ Total \) — Sum of all values in the column
• \( Grand\ Total \) — Sum of all values in the table

Explanation: This formula calculates what the frequency would be if the two variables were independent of each other.

3. Importance of Expected Frequency

Details: Expected frequencies are crucial for conducting chi-square tests of independence, which determine whether there's a significant association between two categorical variables.

4. Using the Calculator

Tips: Enter the row total, column total, and grand total values. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the purpose of calculating expected frequency?
A: Expected frequency is used in chi-square tests to compare against observed frequencies and determine if there's a statistically significant relationship between variables.

Q2: When should I use this calculation?
A: Use this when conducting chi-square tests of independence for categorical data arranged in contingency tables.

Q3: What if my expected frequency is less than 5?
A: Chi-square tests require expected frequencies of at least 5 in each cell. For values less than 5, consider using Fisher's exact test instead.

Q4: Can expected frequency be a decimal?
A: Yes, expected frequencies are often decimal values as they represent theoretical averages.

Q5: How does expected frequency relate to the chi-square statistic?
A: The chi-square statistic is calculated by summing the squared differences between observed and expected frequencies, divided by the expected frequencies.