Question

A financial advisor studied the effects of women's and men's marital status on their sense of financial independence. On an independence measure, married women scored 3, 5, and 4; married men scored 4, 5, and 5. Divorced women scored 6, 8, and 7; Divorced men scored 6, 8, and 5. Women who had never been married scored 9, 8, and 8; men who had never been married scored 4, 5, and 3.

a) Analyze these data using the appropriate analysis. Set alpha at .05. Fill in the summary below.

Source	SS	df	Mean square	F
Row (gender)	Answer	Answer	Answer	Answer
Column (marital status)	Answer	Answer	Answer	Answer
Interaction	Answer	Answer	Answer	Answer
Within	Answer	Answer	Answer
Total	Answer	Answer

b. What are the critical values needed?

F needed for rows (gender) = Answer

F needed for column (marital status) = Answer

F needed for interaction = Answer

c. Summarize your results

Answer x Answer between-groups ANOVA that examined the effects of gender and marital status on sense of financial independence revealed a Answersignificantnon-significant main effects for gender,  F(Answer,Answer) =Answer, pAnswer<> .05, η² = Answer, a Answersignificantnon-significant main effect of marital status, F(Answer,Answer) =Answer, p Answer<> .05, η² = Answer, as well as a Answersignificantnon-significant gender by marital status interaction, F(Answer,Answer) =Answer, p Answer<> .05, η² = Answer.

Answer 1

The given data can be expressed in the form of a crosstab as:

We have to test whether Gender and Marital status has an effect on their sense of financial independence.

To test: H₀₁: Gender has no effect on sense of financial independence   H₀₂: Marital status has no effect on sense of financial independence H₀₃: There is no interaction effect between Gender and Marital status on sense of financial independence

Vs

H_a1:Gender has a significant effect on sense of financial independence H_a2: Marital status has a significant effect on sense of financial independence H_a3: There is a significant interaction effect between Gender and Marital status on sense of financial independence    

a. The appropriate test to test these hypotheses would be a two way ANOVA (with replication).

Using excel,

the two factors being 'Gender' and 'Marital Status'.

We get the output:

From the output obtained,

b. The critical values needed for:

F needed for rows (gender) = 4.747

F needed for column (marital status) = 3.885

F needed for interaction = 3.885

To find the eta square for gender:

η² = SS_Gender / SS_Total

= 9.389 / 59.611

= 0.158 = 15.8%

To find the eta square for marital status:

η² = SS_{Marital Status} / SS_Total

= 18.111 / 59.611

= 0.304 = 30.4%

To find the eta square for interaction:

η² = SS_Interaction / SS_Total

= 20.111 / 59.611

= 0.337 = 33.7%

c. Summarizing the results obtained:

Gender x Marital Status between-groups ANOVA that examined the effects of gender and marital status on sense of financial independence revealed a significant main effects for gender, F(1,12) =9.389, p = 0.010 < 0.05, η² = 15.8%, a significant main effect of marital status, F(2,12) =9.056, p = 0.004< 0.05, η² = 30.4%, as well as a significant gender by marital status interaction, F(2,12) =10.056, p =0.003<  0.05, η² = 3.37%.