SOCIOL 350 University of Massachusetts Amherst Analysis of Variance Questions

I’m working on a statistics question and need an explanation to help me study.

1.Use the following sample of 32 GSS cases to analyze the relationship between social class and health assessment. Health is measured according to a four-point scale: 1 = excellent, 2 = good, 3 = fair, and 4 = poor. Four social classes are reported here: lower, working, middle, and upper.

Lower Class	Working Class	Middle Class	Upper Class
3	2	2	2
2	1	3	1
2	3	1	1
2	2	1	2
3	2	2	1
3	2	3	1
4	3	3	1
4	3	1	2

a. Using this data, fill in the following table:

Lower Class	Working Class		Middle Class	Upper Class
n1 =	n2 =		n3 =	n4 =
Sample mean (Y1) =	Sample mean (Y2) =		Sample mean (Y3) =	Sample mean (Y4) =
Sample variance (S1) =	Sample variance (S2) =		Sample variance (S3) =	Sample variance (S4) =
Sample SD (S21) =	Sample SD (S22) =		Sample SD (S23) =	Sample SD (S24) =
Sum of scores (EY1) =	Sum of scores (EY2) =		Sum of scores (EY3) =	Sum of scores (EY4) =
Sum of scores2 (EY21)=	Sum of scores2 (EY22)=		Sum of scores2 (EY23)=	Sum of scores2 (EY24)=
	Mean of all respondents (Y) =
		N =

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b. Calculate the between-group sum of squares (SSB). SSB = ___________________________________________

• Calculate degrees of freedom (df_b). df_b = ________________________________________________________
• Calculate the mean square between (MSB). MSB = ________________________________________________

• Calculate the within-group sum of squares (SSW). SSW = ___________________________________________
• Calculate degrees of freedom (df_w). df_w = ________________________________________________________
• Calculate the mean square within (MSW). MSW = ________________________________________________
• Calculate the F statistic. F = _________________________________________________________________
• Will we reject or fail to reject the null hypothesis using an alpha = .05? __________________________________

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QUESTION 2

1. A researcher is interested in whether there is a significant difference between the mean age of marriage across three racial groups . Based on the data below, calculate the between group sum of squares (SSB).

Race	N	Mean
Black	113	25.39
White	904	22.99
Other	144	23.87
All Groups	1,161	23.33

QUESTION 3

Using the data from Question #2, calculate the degrees of freedom between (df_b).

QUESTION 4

Using the data from Question #2, calculate the mean square between (MSB).

QUESTION 5

If the mean square within calculated for this data is 36.87, what is the value of the F statistic?

QUESTION 6

If alpha is .05 and df_w is 1,158, will you reject or fail to reject the null hypothesis?

QUESTION 6

The 2006 General Social Survey contains information on the number of years of education that respondents have completed. The data are presented below.

	White	Black	Other	Total Sample
Mean	13.66	12.87	11.69	13.29
Standard deviation	2.93	2.95	4.36	3.23
N	3,277	630	592	4,499

1.Specify the assumptions required in order to employ ANOVA procedures and conduct an F-test and state the null and research hypotheses.

2.Calculate the between group sum of squares.

3.Next, we need to calculate the sum of squares within. However, as you probably noticed, this would be quite a cumbersome task considering the number of observations in the data set. Instead, let’s work backwards to arrive this quantity. Begin by calculating the degrees of freedom for the sum of squares between and the sum of squares within.

4.Suppose that the value of the F-statistic is 104.65. Using this information and your answers from Questions #4-5, calculate the value of the sum of squares within.

5.Although you calculated these values indirectly in arriving at your answer to Question #6, what are the values of the mean square between and the mean square within?

6.Given your work thus far, what is the critical value for an F-statistic of 104.65 with the associated degrees of freedom you calculated in Question #5, assuming an alpha level of .05? On the basis of your work thus far, can we reject the null hypothesis?