Question

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 5 9 11 4 9 12 3 8 11 4 8 10 5 9 11 3 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 to test for a significant difference in perception among the three groups. Calculate the value of the test statistic (to 2 decimals). The -value is What is your conclusion?

c. Using , 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). Difference Absolute Value Conclusion

Answer 1

Given data is,

Marketing Managers Marketing Research Advertising

5 9 11

4 9 12

3 8 11

4 8 10

5 9 11

3 8 11

a

Let Ti be the total score for group i, ni be number of observations of group i.

Let G be the total scores of all observations and N be total number of observations.

ΣX^2 is sum of squares of all observations.

T1 = 24, T2 = 51 , T3 = 66

G = 24 + 51 + 66 = 141

ΣX^2 = 100 + 435 + 728 = 1263

SST = ΣX^2 - G^2/N = 1263 - 141^2/18 = 158.5

Treatment Sum of Squares SSTR = ΣT^2/n - G^2/N = (24^2 /6 + 51^2 /6 + 66^2 /6 ) - 141^2/18 = 151

Error Mean Squares, SSE = 158.5 - 151 = 7.5

DF Treatment = Number of groups - 1 = 3 - 1 = 2

DF Error = Number of observations - Number of groups = 18 - 3 = 15

Treatment Mean Squares, MSTR = SSTR / DF Treatments = 151 / 2 = 75.5

Error Mean Squares, MSE = SSE / DF Error = 7.5 / 15 = 0.5

b.

Test statistic, F = MSTR / MSE = 75.5 / 0.5 = 151

Critical value of F at 0.05 significance level and df = 2, 15 is 3.68

Since  the observed F (3.51) is greater than the critical value, we fail to reject the null hypothesis H0 and conclude that there is significant evidence of difference in perception among the three groups.

c.

Critical value of t at 0.05 significance level and df = 15 is  2.13

Fisher's LSD value = t

= 2.13

= 0.87

If the differences between the mean perception scores is greater than 0.87, there will be significant difference between the means.

Mean Score for Marketing Managers = 24/6 = 4

Mean Score for Marketing Research = 51/6 = 8.5

Mean Score for Advertising = 66/6 = 11

Mean difference between marketing research specialists and marketing managers = 8.5 - 4 = 4.5

Mean difference between marketing managers and advertising specialists = 11.5 - 4 = 7.5

Mean difference between marketing research specialists and advertising specialists = 11 - 8.5 = 2.5

Since all differences are greater than 0.87, all groups have significant differences between the mean perception scores .