Analyzing with ANOVA
PSY/210
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 is/are the independent variable(s)? What is/are the dependent variable(s)?
Independent variable is gender and the dependent variable is marital status.
What would be an appropriate null hypothesis? Alternate hypothesis?
: There is no significant difference in happiness score based on gender and marital status.
: There is significance difference in happiness score based on gender and marital status.
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?
Done below
Calculate the mean square for 1) gender 2) marital status 3) interaction between gender and marital status and 4) error or within variance.
Done below
Calculate the F ratio for 1) gender, 2) marital status, and 3) interaction between gender and marital status.
Done below
Identify the critical Fs at alpha = .05 for 1) gender, 2) marital status, and 3) interaction between gender and marital status.
Done below
If alpha is set at .05, what conclusions can you make?
F-value is 2.277 and F-critical is 3.093266.Since F-value is less than F-critical, therefore null hypothesis is accepted and I conclude that the data provides sufficient evidence at 0.05 that there is no significant difference in happiness score based on gender and marital status.
| Source | Sum of Squares(SS) | (degrees of freedom [df]) | Mean SquareSS / df | Fobt. | Fcrit. |
|---|---|---|---|---|---|
| Gender | 68.15 | 2-1=1 | 68.15 | MS(G) / MS(W) =7.407 | 3.942303 |
| Marital Status | 127.37 | 3-1=2 | 63.685 | MS(Ms) / MS(W) =6.922 | 3.093266 |
| Gender * Marital Status (A x B) | 41.90 | 2×1=2 | 20.95 | MS(G*M) / MS(W) =2.277 | 3.093266 |
| Error (Within) | 864.82 | (N-ab)=94 | 9.2002 | NA | NA |
| Total | 1102.24 | 99 | NA | NA | NA |
References
Steinberg, W. J., & Price, M. Statistics alive! Los Angeles: Sage Publications.