# ANOVA questions

1. If F(4,48) = 2.51, is it significant at the .05 level? .01 level? What is the total sample size?

Note that F(4, 48) refers to the two different degrees of freedom for this F test.

1. 2. Study the ANOVA summary table below and provide the missing information for the cells designated a-e.

2.

Source Sum of Squares df Mean Square F *Level of Significance

Between groups 1104 a b 3.00

Within groups c d 184

Total 4416 e

3. In the table above, use the F distribution table in your book to determine p. Is it significant at the .05 level? The .01 level? How many groups are there? What is the total sample size?

4. Suppose we studied the relationship between social support and stress. We categorized our subjects as either having NO support, ONE support person, BETWEEN 2 and 5 support people and OVER 5 support people. We have 20 subjects in each group. We then look at their stress ratings. You are given the following data:

Sum of squares within = 2350

Sum of squares between = 291

a. How many independent variables do we have and what type of ANOVA design is this? Calculate the F ratio

b. Identify the criterion F at alpha = .05

c. What are your conclusions?

5. For each of the following, identify the statistical test that would be used to test the hypothesis. Be specific (e.g., one-way ANOVA, 2 x 3 ANOVA, t-test for independent groups, t-test for dependent groups).

a. You want to test three temperatures and four combinations of ingredients to see if they all result in the same maximum height of a cake. _____________________

b. You want to know if people in four regions of the country spend the same amount of money on fast food. _____________________

c. You want to know if workers on an assembly line are more productive when they are offered an incentive. You measure the productivity of the same workers before and after the incentive program. _______________________

d. You want to compare whether the average waiting time in the checkout lane is the same for two chains of stores. __________________________

e. You want to know if scores on a mechanics test differ by gender and three different levels of income. ________________________

6. What is the null hypothesis of a one-way ANOVA? What is the alternate hypothesis?

7. An experimenter is looking at the effects of four different climates on happiness. He collects data on 10 subjects within each climate group. What are the dfbetween? dfwithin?

8. Using the example in #9 and the F distribution table in your book, what F score would you need to exceed in order to find significance at the .05 level?

#### Solution Preview

1. If F(4,48) = 2.51, is it significant at the .05 level? .01 level? What is the total sample size?

Note that F(4, 48) refers to the two different degrees of freedom for this F test.

Using the F-distribution table at http://www.itl.nist.gov/div898/handbook/eda/section3/eda3673.htm

Critical F(4, 48, 0.05) = 2.565

Critical F(4, 48, 0.01) = 3.737

Since 2.51 < 2.565 < 3.737, therefore it is not significant at any of the 0.05 or 0.01 level.

dfbetween = k-1

=> k - 1 = 4

=> k = 5

dfwithin = N-k

N - k = 48

N - 5 = 48

N = 53

Total sample size = 53

2. Study the ANOVA summary table below and provide the missing information for the cells designated a-e.

Source Sum of Squares df Mean Square F *Level of Significance

Between groups 1104 a b 3.00

Within groups c d 184

Total 4416 e

Answer:

Source Sum of Squares df Mean Square F *Level of Significance

Between groups 1104 2 552 3.00 0.0751

Within groups 3312 18 184

Total 4416 20

3. In the table above, use the F distribution table in your book to ...

#### Solution Summary

Step by step solutions to all the problems is provided.