1. What Is Expected Frequency In Chi Squared?

Expected frequency is a fundamental concept in chi-squared tests, representing the theoretical frequency that would be expected in each cell of a contingency table if the null hypothesis of independence between variables were true.

2. How Does The Calculator Work?

The calculator uses the expected frequency formula:

Where:

• \( Row\ Sum \) — Total count for the row
• \( Column\ Sum \) — Total count for the column
• \( N \) — Grand total of all observations

Explanation: This formula calculates the expected count for each cell in a contingency table under the assumption that the row and column variables are independent.

3. Importance Of Expected Frequency Calculation

Details: Calculating expected frequencies is essential for performing chi-squared tests of independence and goodness-of-fit tests. These tests help determine whether observed frequencies significantly differ from expected frequencies, indicating potential relationships between categorical variables.

4. Using The Calculator

Tips: Enter the row sum, column sum, and total count (N). All values must be positive numbers. The calculator will compute the expected frequency for the corresponding cell in the contingency table.

5. Frequently Asked Questions (FAQ)

Q1: When should I use expected frequency calculations?
A: Expected frequencies are used in chi-squared tests to analyze categorical data and test hypotheses about relationships between variables in contingency tables.

Q2: What if my expected frequency is less than 5?
A: Chi-squared tests generally require expected frequencies of at least 5 in each cell. If values are lower, consider using Fisher's exact test or combining categories.

Q3: Can expected frequencies be decimal values?
A: Yes, expected frequencies are theoretical values and can be decimals, though observed frequencies are always whole numbers.

Q4: How does this relate to the chi-squared statistic?
A: The chi-squared statistic is calculated by summing (observed-expected)²/expected for all cells in the contingency table.

Q5: What are common applications of expected frequency calculations?
A: These calculations are widely used in market research, medical studies, social sciences, and any field analyzing categorical data relationships.