How to find out expected value in chi square test?

How to Find Out Expected Value in Chi Square Test?

In statistical analysis, the chi square test is a method used to determine whether there is a significant association between two categorical variables. One key aspect of the chi square test is finding the expected value for each cell in the contingency table.

To find out the expected value in a chi square test, you need to calculate the following formula for each cell:
[E = frac{(row total times column total)}{grand total}]

This formula gives you the expected value for each cell in the contingency table, which is then used to calculate the chi square statistic and determine if there is a significant association between the variables.

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

1. **Calculate the row totals and column totals:** Add up the values in each row and column of the contingency table.

2. **Calculate the grand total:** The grand total is the sum of all the values in the contingency table.

3. **Apply the formula:** Use the formula mentioned above to find the expected value for each cell in the table.

4. **Repeat for each cell:** Calculate the expected value for each cell in the contingency table.

5. **Compare to observed values:** Once you have found the expected values for each cell, compare them to the observed values to determine the chi square statistic.

Finding the expected value is a crucial step in conducting a chi square test as it helps determine if the observed frequencies in the contingency table are significantly different from what would be expected by chance.

FAQs on Expected Value in Chi Square Test

1. What is the purpose of finding the expected value in a chi square test?

The expected value helps determine whether the observed frequencies in the contingency table are significantly different from what would be expected by chance.

2. How is the expected value calculated in a chi square test?

The expected value is calculated using the formula: (E = frac{(row total times column total)}{grand total}).

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

Finding the expected value helps in determining the chi square statistic, which in turn indicates whether there is a significant association between the variables being studied.

4. Can the expected value be less than 1 in a chi square test?

Yes, the expected value can be less than 1 in a chi square test, especially when dealing with small sample sizes.

5. How does the expected value differ from the observed value in a chi square test?

The expected value is the value that would be expected in each cell of the contingency table if there is no association between the variables, while the observed value is the actual count in each cell.

6. What does it mean if the observed value is greater than the expected value in a chi square test?

If the observed value is greater than the expected value, it suggests that there may be a significant association between the variables being studied.

7. What happens if the expected value is zero in a chi square test?

If the expected value is zero, it can cause issues with calculating the chi square statistic and may require special adjustments in the analysis.

8. Can the expected value be negative in a chi square test?

No, the expected value cannot be negative in a chi square test as it represents the expected frequency in each cell, which cannot be negative.

9. How many expected values are calculated in a chi square test?

An expected value is calculated for each cell in the contingency table, so the number of expected values depends on the size of the table.

10. What is the significance of the chi square statistic in relation to the expected value?

The chi square statistic compares the observed frequencies to the expected frequencies, helping to determine if there is a significant association between the variables.

11. How can the expected value be used to interpret the results of a chi square test?

By comparing the expected values to the observed values, researchers can determine if there is a significant association between the variables or if any differences are due to chance.

12. Are there any assumptions to consider when calculating expected values in a chi square test?

One assumption is that the expected values should be greater than 5 for the chi square test to be valid. If any expected value is less than 5, adjustments may need to be made in the analysis.

Dive into the world of luxury with this video!