A two-way ANOVA has two independent variables and in this assignment the two variables are gender and marital status. The levels for these independent variables are 2 x 3; gender has two levels which are male and female and marital status has three single, married and divorced; the dependent variables are the all the scores of happiness. The null hypothesizes are: there is no difference between male and female happiness. There is no difference in the happiness of a person based on marital status, and finally there is no interaction between gender and marital status when it comes to happiness. The alternative hypotheses would be: there is a difference between male and female happiness. There is a difference in the happiness of a person based on marital status; and there is a difference between gender and marital status when it comes to happiness.
The degrees of freedom for gender are as follows: gender has two levels 2 - 1 = 1, 1 is the degree of freedom for gender. Marital status (3 levels): 3 – 1 = 2, 2 is the degree of freedom for marital status. Gender * Marital Status: 1 * 2 = 2, we take the degrees of freedom from gender and marital status and multiple them to get the degrees of freedom for gender * marital status. Errors: (100 – 1) – 2 * 3 = 93, we take the mean or in other words the number of observations and take away 1 then we get the levels of both independent variables and the degrees of freedom is given.
To obtain the mean square we simply take the sum of squares and divide that by the degrees of freedom. Gender: 68.15/1 = 68.15, Marital Status: 127.37/2=63.685, Gender and Marital Status: 41.90/2=20.95, and Errors: 864.82/93=9.299. To find the F ratio you take the mean of square from gender, marital status and gender * marital status and divide it by the mean square of errors. Gender: 68.15/9.299=7.33, Marital Status: 63.685/9.299=6.85, Gender and Marital Status: 20.95/9.299=2.25.
The critical F for gender is 3.94, we take the degrees of...