Question

he following data are from an experiment designed to investigate the perception of corporate ethical values among individuals who are in marketing. Three groups are considered: management, research and advertising (higher scores indicate higher ethical values). Marketing Managers Marketing Research Advertising 8 7 10 7 7 11 6 6 10 7 6 9 8 7 10 6 6 10 Compute the values identified below (to 1 decimal, if necessary). Sum of Squares, Treatment Sum of Squares, Error Mean Squares, Treatment Mean Squares, Error Use

Answer 1

Sum of Squares=50.5

Treatment Sum of Squares, 4.5

Error Mean Squares, 0.3

Treatment Mean Squares 0.9

Error Sum of Square = 3

Explanation:

Given data

Observation A B C

1 8 7 10

2 7 7 11

3 6 6 10

4 7 6 9

5 8 7 10

6 6 6 10

A B C Row total (xr)

1 8 7 10 25

2 7 7 11 25

3 6 6 10 22

4 7 6 9 22

5 8 7 10 25

6 6 6 10 22

Col total (xc) 42 39 60 141

Using calculator for summarizing data

∑x²=1155 ⇒(A)

∑x²c/r=16(42²+39²+60²)

=1/6(1764+1521+3600)

=1/6(6885)

=1147.5⇒(B)

∑x²r/c=13(25²+25²+22²+22²+25²+22²)

=1/3(625+625+484+484+625+484)

=1/3(3327)

=1109⇒(C)

(∑x)²/n=(141)²/18

=19881/18

=1104.5⇒(D)

Sum of squares total

SST=∑x²-(∑x)²/n=(A)-(D)

=1155-1104.5

=50.5

Sum of squares between rows

SSR=∑x²r/c-(∑x)²/n=(C)-(D)

=1109-1104.5

=4.5

Sum of squares between columns

SSC=∑x²c/r-(∑x)²n=(B)-(D)

=1147.5-1104.5

=43

Sum of squares Error (residual)

SSE=SST-SSR-SSC

=50.5-4.5-43

=3

ANOVA table

Source Sums Degrees of Mean Squares

of Variation of Squares freedom F- value

SS DF MS

Between Treatments SSR=4.5 r-1=5 MSR=0.9 3

Between Blocks SSC=43 c-1=2 MS =21.5 71.6667

Error (residual) SSE=3 (r-1)(c-1)=10 MSE=0.3

Total SST=50.5 rc-1=17