# Analyzing with a Two-Way Anova

Topics: Analysis of variance, Null hypothesis, Degrees of freedom Pages: 3 (790 words) Published: February 18, 2013
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Analyzing with ANOVA|
Two-Way|
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1/23/2013|

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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): a. What is/are the independent variable(s)? What is/are the dependent variable(s)? The independent variables are gender and marital status. The dependent variable is the happiness. b. What would be an appropriate null hypothesis? Alternate hypothesis? Alternate hypothesis about gender can be that females will have greater happiness mean score than males. There is also an alternative hypothesis in marital status that females who are married would have lower happiness mean scores than males that are married. The Null hypothesis in both situations would be that differences would not exist. c. 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? 1. A-1=There are 2 groups of gender; male and female, so it would be 2-1=1 as the degree of freedom. 2. B-1=There are 3 groups for marital status; married, single, and divorced, so it would be 3-1=2 as the degree of freedom. 3. (A-1)*(B-1) =That would be the answer from gender (1)* The answer from marital status (2) which would be 1*2=2 for the degree of freedom. 4. N-AB= That would be the total number of observations which is given as N=100 minus gender*marital status. This would be; 100-6=94 for the error. d. Calculate the mean square for 1) gender, 2) marital status, 3) interaction between gender and marital status, and 4) error or within variance. 5. Sum of squares due to effect A/degrees of freedom of effect A=____. This would be 68.15/1= 68.15 for the mean square. 6. Sum of squares due to effect...