Question: Analyzing with ANOVA
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):
What are the independent variables and their levels? What is the dependent variable?
State all null hypotheses associated with independent variables and their interaction? Also suggest alternate hypotheses?
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?
Calculate the mean square for 1) gender, 2) marital status, 3) interaction between gender and marital status, and 4) error or within variance.
Calculate the F ratio for 1) gender, 2) marital status, and 3) interaction between gender and marital status.
Identify the critical Fs at alpha = .05 for 1) gender, 2) marital status, and 3) interaction between gender and marital status.
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) |
41.9 |
? |
? |
? |
? |
| 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.
Correctly identified the independent and dependent variables.
Provided appropriate null and alternative hypotheses.
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.
Correctly calculated the mean square for 1) gender, 2) marital status, 3) interaction between gender and marital status, and 4) error or within variance.
Correctly calculated the F ratio for 1) gender, 2) marital status, and 3) interaction between gender and marital status.
Correctly identified the critical Fs at alpha = .05 for 1) gender, 2) marital status, and 3) interaction between gender and marital status.
Provided the correct conclusion based on alpha = .05.
Wrote in a clear, concise, and organized manner; demonstrated ethical scholarship in accurate representation and attribution of sources; displayed accurate spelling, grammar, and punctuation.