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# ANOVA statistics (Term Paper Sample)

Instructions:

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)?
b.What would be an appropriate null hypothesis? Alternate hypothesis?
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?
d.Calculate the mean square for 1) gender, 2) marital status, 3) interaction between gender and marital status, and 4) error or within variance.
e.Calculate the F ratio for 1) gender, 2) marital status, and 3) interaction between gender and marital status.
f.Identify the critical Fs at alpha = .05 for 1) gender, 2) marital status, and 3) interaction between gender and marital status.
g.If alpha is set at .05, what conclusions can you make? source..

Content:

ANOVA
Name
Institution
Analyzing with ANOVA
The source of questions for the assignment is the ANOVA source table. The contents of the table comprise a two â€“way ANOVA where gender is grouped into two classes (female and male), marital status is grouped into three classes (divorced, married, single never married), and happiness scores (n=100). From the provided data, both dependent and independent variables can be identified. Both the null and alternate hypotheses will be formulated from the research question. The necessary calculations from the data include the degrees of freedom for gender, marital status, the interaction between marital status and gender, and the error. Other calculations are the F ratios and the critical Fs for the named variables. Conclusively, there is need to explain how the situation will be if alpha is set at 0.05.
ANOVA table
The sum of squares is the total sum of the squares of each and every raw data.
The degree of freedom is N-1 (100-1).
The mean square is the sum of squares divided by degrees of freedom.
Source
Sum of Squares
(degrees of freedom [df])
Mean Square
Fobt.
Fcrit.
Gender
68.15
99
0.688
1.392
1.392
Marital Status
127.37
99
1.287
1.392
1.392
Gender * Marital Status (A x B)
41.90
99
0.423
1.392
1.392
Error (Within)
864.82
99
8.736
NA
NA
Total
1102.24
99
NA
NA
NA
From the table, two classes of variables are determinable.
Independent variables include:
* Gender (male and female)
The independent variables are the input variables of the study or the variables that can be controlled to determine the authenticity of the hypothesis.
Independent variable (s)
* Marital status (married, single never married, and divorced).
* Happiness index
Gender is the independent variable because it is the determinant of the marital status of an individual (dependent variable). It therefore determines the rate of getting married and the happiness index that accompanies it. The dependent variables form the output of the test. They cannot be controlled and but can be observed.
Null hypothesis: Gender and marital status of an individual are not related. The hypothesis is the opposite of the expectations of the study. The calculations will form a platform where the null hypothesis will either be rejected or accept...

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