Question

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, answer these questions.

Race	N	Mean
Black	118	21.57
White	882	24.59
Other	120	28.39
All Groups	1,120	24.68

1. Calculate the value of the between group sum of squares (SSB, 20 pts).

Race	Y bar for each group	Total mean	Group mean – Total mean	Square of the difference	The number of cases	Nk*Square of the difference
Black	21.57	24.68
White	24.59	24.68
Other	28.39	24.68
						Sum up=

2. Calculate the degrees of freedom for the between group sum of squares. Then, use this quantity to calculate the mean square between (6 pts).

3. If the F statistic calculated for these data is 15.29, what is the value of the mean square within (4 pts)?

4. Following answer of #3, calculate the within group sum of squares and the number of degrees of freedom for the within group sum of squares (6 pts).

5. Imagine you are interested in whether there is a significant difference between the mean age of marriage across educational groups. If the critical value for an F statistic of 15.29 is 2.99, are these results statistically significant or not (4 pts)?

Answer 1

1.

Race	Y bar for each group	Total mean	Group mean – Total mean	Square of the difference	The number of cases	Nk*Square of the difference
Black	21.57	24.68	-3.11	9.6721	118	1141.3078
White	24.59	24.68	-0.09	0.0081	882	7.1442
Other	28.39	24.68	3.71	13.7641	120	1651.692
						Sum up=2800.144

2. Degrees of freedom for the between group sum of squares=3-1=2

Sum of square between=SSB=2800.144

Mean square between=MSB=SSB/2= 2800.144/2=1400.072

3. F=MSB/MSW= 15.29, or, MSW=1400.072/15.29=91.5678

where MSW=mean square within=91.5678

4. The number of degrees of freedom for the within group sum of squares=1120-3= 1117

SSW=sum of square within=1117*91.5678=102281.2.

5. Yes, this is statistically significant F statistic= 15.29 >2.99.