The 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 |
7 | 9 | 11 |
6 | 9 | 12 |
5 | 8 | 11 |
6 | 8 | 10 |
7 | 9 | 11 |
5 | 8 | 11 |
a. Compute the values identified below (to 2 decimal, if necessary).
Sum of Squares, Treatment:
Sum of Squares, Error:
Mean Squares, Treatment:
Mean Squares, Error:
b. Use a=.05 to test for a significant difference in perception among the three groups.
Calculate the value of the test statistic (to 2 decimals).
c. Using a=.05, determine where differences between the mean perception scores occur.
Calculate Fisher's LSD value (to 2 decimals).
Test whether there is a significant difference between the means for marketing managers (1), marketing research specialists (2), and advertising specialists (3).
(X= Xbar)
Difference | Absolute Value | Conclusion |
X1-X2 | Significant difference | |
X1-X3 | Significant difference | |
X2-X3 | Significant difference |
Applying one way ANOVA: (use excel: data: data analysis: one way ANOVA: select Array): |
Source | SS | df | MS | F | P value |
Between | 75.00 | 2 | 37.50 | 75.00 | 0.0000 |
Within | 7.50 | 15 | 0.50 | ||
Total | 82.50 | 17 |
a)
sum of sq;treatment= | 75.00 |
sum of sq; error= | 7.50 |
mean sq;treatment= | 37.50 |
mean square; error= | 0.50 |
c)
test statistic = | 75.00 |
p value is less than 0.01 | |
Conclude the treatment mean for the three groups are not all the same |
c)
critical value of t with 0.05 level and N-k=15 degree of freedom= | tN-k= | 2.131 | |||
Fisher's (LSD) for group i and j =(tN-k)*(sp*√(1/ni+1/nj) = | 0.87 |
Difference | Absolute Value | Conclusion |
x1-x2 | 2.50 | significant difference |
x3-x1 | 5.00 | significant difference |
x3-x2 | 2.50 | significant difference |
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