Submit your answers to the following questions using the ANOVA source table below. The table depicts a two-way ANOVA in which gender has two groups (male and female), marital status has three groups (married, single never married, divorced), and the means refer to happiness scores (n = 100):

1. What is/are the independent variable(s)? What is/are the dependent variable(s)?
2. What would be an appropriate null hypothesis? Alternate hypothesis?
3. What are the degrees of freedom for 1) gender, 2) marital status, 3) interaction between gender and marital status, and 4) error or within variance?
4. Calculate the mean square for 1) gender, 2) marital status, 3) interaction between gender and marital status, and 4) error or within variance.
5. Calculate the F ratio for 1) gender, 2) marital status, and 3) interaction between gender and marital status.
6. Identify the criterion Fs at alpha = .05 for 1) gender, 2) marital status, and 3) interaction between gender and marital status.
7. If alpha is set at .05, what conclusions can you make?

Source Sum of Squares (degrees of freedom [df]) Mean Square Fobt. Fcrit.
Gender 68.15 ? ? ? ?
Marital Status 127.37 ? ? ? ?
Gender * Marital Status (A x B) 41.90 ? ? ? ?
Error (Within) 864.82 ? ? NA NA
Total 1102.24 99 NA NA NA

Please Note: The table that you see in the assignment has been slightly modified from the one presented in the module notes since it is beyond the scope of this unit to have students calculate p values. Instead you are asked to calculate the F value and compare it to the critical F value to determine whether the test is significant or not.

By Monday, February 27, 2012, deliver your assignment to the M4: Assignment 2 Dropbox.
Assignment 2 Grading Criteria
Maximum Points
Correctly identified the independent and dependent variables.
4
Provided appropriate null and alternative hypotheses.
8
Correctly identified the degrees of freedom for 1) gender, 2) marital status, 3) interaction between gender and marital status, and 4) error or within variance.
8
Correctly calculated the mean square for 1) gender, 2) marital status, 3) interaction between gender and marital status, and 4) error or within variance.
20
Correctly calculated the F ratio for 1) gender, 2) marital status, and 3) interaction between gender and marital status.
16
Correctly identified the criterion Fs at alpha = .05 for 1) gender, 2) marital status, and 3) interaction between gender and marital status.
16
Provided the correct conclusion based on alpha = .05.
8
Wrote in a clear, concise, and organized manner; demonstrated ethical scholarship in accurate representation and attribution of sources; displayed accurate spelling, grammar, and punctuation.
20
Total:
100

1. The independent variables in this ANOVA are gender and marital status. The dependent variable is happiness scores.

2. The appropriate null hypothesis would be that there is no significant difference in happiness scores based on gender or marital status. The alternative hypothesis would be that there is a significant difference in happiness scores based on gender or marital status.

3. The degrees of freedom for 1) gender would be 1 (since there are two groups, male and female), 2) marital status would be 2 (since there are three groups, married, single never married, and divorced), 3) the interaction between gender and marital status would be (1 * 2 = 2), and 4) the error or within variance would be (Number of observations - number of groups) = 100 - (2 * 3) = 94.

4. To calculate the mean square for each factor, divide the sum of squares for each factor by its respective degrees of freedom. For example, the mean square for gender would be 68.15 divided by the degrees of freedom for gender.

5. The F ratio is calculated by dividing the mean square for each factor by the mean square for error or within variance. For example, the F ratio for gender would be the mean square for gender divided by the mean square for error.

6. The criterion Fs at alpha = .05 can be found in a statistical table, such as the F-distribution table. Look for the critical F value at the appropriate degrees of freedom for each factor.

7. If alpha is set at .05, compare the calculated F ratio to the criterion F value. If the calculated F ratio is larger than the criterion F value, then the result is statistically significant and you can reject the null hypothesis. If the calculated F ratio is smaller than the criterion F value, then the result is not statistically significant and you fail to reject the null hypothesis.

1. The independent variables in this study are gender (with two groups: male and female) and marital status (with three groups: married, single never married, and divorced). The dependent variable is happiness scores.

2. Null hypothesis: There is no significant difference in happiness scores among different genders and marital statuses.
Alternate hypothesis: There is a significant difference in happiness scores among different genders and marital statuses.

3. Degrees of freedom:
- Gender: 1 (since there are two groups: male and female)
- Marital status: 2 (since there are three groups: married, single never married, and divorced)
- Interaction between gender and marital status: 2 (calculated as the product of the degrees of freedom for gender and marital status, which is 1 * 2 = 2)
- Error or within variance: 93 (calculated by subtracting the sum of the degrees of freedom for gender, marital status, and interaction from the total degrees of freedom, which is 99 - (1 + 2 + 2) = 93)

4. Mean square:
- Gender: 68.15 / 1 = 68.15
- Marital status: 127.37 / 2 = 63.69
- Interaction between gender and marital status: 41.90 / 2 = 20.95
- Error or within variance: 864.82 / 93 = 9.31

5. F ratio:
- Gender: 68.15 / 9.31 = 7.32
- Marital status: 63.69 / 9.31 = 6.84
- Interaction between gender and marital status: 20.95 / 9.31 = 2.25

6. Criterion Fs at alpha = .05:
- Gender: Fcrit = 3.95
- Marital status: Fcrit = 3.22
- Interaction between gender and marital status: Fcrit = 3.22 (same as for marital status)

7. Based on an alpha level of .05, the F ratio for gender (7.32) is greater than the criterion F (3.95), indicating a significant difference in happiness scores between males and females. The F ratio for marital status (6.84) is also greater than the criterion F (3.22), indicating a significant difference in happiness scores among different marital statuses. However, the F ratio for the interaction between gender and marital status (2.25) is less than the criterion F (3.22), indicating that the interaction is not statistically significant.