Expected Frequency Calculator

Expected Frequency Formulas:

For independence test: \[ E = \frac{\text{(row total)} \times \text{(column total)}}{\text{grand total}} \]

For goodness of fit: \[ E = n \times p \]

Calculation Type:

Row Total:

Column Total:

Grand Total:

Expected Frequency (E):

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1. What is Expected Frequency?

Expected frequency (E) is the theoretical frequency that would be expected in a cell of a contingency table if the null hypothesis were true. It's used in chi-square tests to compare with observed frequencies.

2. How Does the Calculator Work?

The calculator provides two formulas for different statistical tests:

For test of independence: \[ E = \frac{\text{(row total)} \times \text{(column total)}}{\text{grand total}} \]

For goodness of fit test: \[ E = n \times p \]

Where:

\( E \) — Expected frequency count
row total — Sum of counts in the row
column total — Sum of counts in the column
grand total — Total sample size
\( n \) — Sample size
\( p \) — Theoretical probability

3. Importance of Expected Frequency

Details: Expected frequencies are crucial for chi-square tests, which assess whether observed frequencies differ significantly from expected frequencies under the null hypothesis.

4. Using the Calculator

Tips: Select the appropriate test type (independence or goodness of fit) and enter the required values. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: When should I use each formula?
A: Use the independence formula for contingency tables (chi-square test of independence). Use the goodness of fit formula when testing if sample data matches a theoretical distribution.

Q2: What if my expected frequency is less than 5?
A: For chi-square tests, expected frequencies should generally be ≥5. For smaller values, consider Fisher's exact test or combine categories.

Q3: Can expected frequency be a decimal?
A: Yes, expected frequencies are often decimal values, though observed counts must be whole numbers.

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

Q5: What's the difference between expected and observed frequency?
A: Observed is what you actually measured, expected is what you would get if the null hypothesis were true.