How do you find the expected value in chi-square 2×2?

In order to find the expected value in a chi-square 2×2 test, there are several steps that need to be followed. The chi-square test is used to determine if there is a significant association between two categorical variables. The expected value in a chi-square 2×2 test represents the number of observations that would be expected in each cell if there was no association between the variables.

Here is a step-by-step guide on how to find the expected value in a chi-square 2×2 test:

Step 1: Set up the observed values table

First, you need to set up a 2×2 contingency table with the observed frequencies for each cell. The table should have two rows and two columns, representing the two categorical variables being analyzed.

Step 2: Calculate the row totals

Next, calculate the sum for each row by adding up the observed frequencies in each row. These row totals will be used to determine the expected values.

Step 3: Calculate the column totals

Similarly, calculate the sum for each column by adding up the observed frequencies in each column. These column totals will also be used in the calculation of expected values.

Step 4: Calculate the grand total

Find the sum of all the observed frequencies in the table. This represents the overall total number of observations.

Step 5: Calculate the expected value for each cell

The expected value for each cell is calculated by multiplying the row total by the column total and then dividing it by the grand total. This can be represented by the formula: Expected Value (E) = (Row Total * Column Total) / Grand Total.

Step 6: Complete the expected values table

Using the expected value formula, calculate the expected value for each cell in the contingency table. Fill in the expected values in a new table.

Step 7: Perform the chi-square test

Once you have calculated the expected values, you can perform the chi-square test to determine if there is a significant association between the variables. This test compares the observed frequencies to the expected frequencies and calculates a chi-square statistic, which is then compared to the critical value.

FAQs:

1. What is a chi-square test?

A chi-square test is a statistical test used to determine if there is a significant relationship between categorical variables.

2. When is a chi-square 2×2 test used?

A chi-square 2×2 test is used when there are two categorical variables, each with two levels or categories.

3. Why is it important to find the expected value in a chi-square 2×2 test?

Finding the expected value helps us determine if there is an association between the variables based on what would be expected by chance alone.

4. What does the row total represent?

The row total represents the total number of observations in each row.

5. What does the column total represent?

The column total represents the total number of observations in each column.

6. What does the grand total represent?

The grand total represents the overall total number of observations.

7. How are the expected values calculated?

The expected values are calculated by multiplying the row total by the column total and then dividing it by the grand total.

8. What is the purpose of the chi-square test?

The purpose of the chi-square test is to determine if there is a significant association or relationship between two categorical variables.

9. How is the chi-square statistic calculated?

The chi-square statistic is calculated by comparing the observed frequencies to the expected frequencies and summing the squared differences.

10. What does the chi-square statistic indicate?

The chi-square statistic indicates the degree of association between the variables. A larger chi-square value suggests a stronger association.

11. What is the critical value in a chi-square test?

The critical value in a chi-square test is the value used to determine whether the observed association is statistically significant.

12. How do you interpret the results of a chi-square test?

The results of a chi-square test are interpreted by comparing the calculated chi-square statistic to the critical value. If the calculated chi-square value is greater than the critical value, it suggests a significant association between the variables.

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