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 8 5 6 7 5 7 6 4 6 7 4 5 8 5 6 6 4 6 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 Use .05 to test for a significant difference in perception among the three groups. Calculate the value of the test statistic (to 2 decimals). Using .05 , determine where differences between the mean perception scores occur. Calculate Fisher's LSD value (to 2 decimals). Difference Absolute Value Conclusion x1-x2 - Select your answer -No significant differenceSignificant differenceItem 10 x1-x3 - Select your answer -No significant differenceSignificant differenceItem 12 x2-x3 - Select your answer -No significant differenceSignificant differenceItem 14

Answer 1

	Marketing Managers	Marketing Research	Advertising
	8	5	6
	7	5	7
	6	4	6
	7	4	5
	8	5	6
	6	4	6
Total(yi)	42	27	36
Averages y̅i	7	4.5	6
Treatment Effect	7 - 5.833 = 1.167	4.5 - 5.833 = -1.333	6 - 5.833 = 0.167

	Sum of Squares	Degree of freedom	Mean Square	F0 = MST / MSE	P value
Treatment	18.999	2	9.5	19	< 0.01
Error	7.5	15	0.5
Total	26.499	17

Overall total = 105
Overall mean Y̅.. = 105 / 18 = 5.833

Y̅ .. is overall mean
y̅i . is treatment mean
SS total = ΣΣ(Yij - & Y̅..)² = 26.499
SS treatment = ΣΣ(Yij - & y̅i.)² = 18.999
SS error = Σ(y̅i. - & Y̅..)² = 7.5

MS treatment = ΣΣ(Yij - & y̅i.)² / a - 1 = 9.5
MS error = Σ(y̅i. - & Y̅..)² / N - a = 0.5

Part a)

SST = 19.00

SSE = 7.50

MST = 9.50

MSE = 0.50

To Test :-
H0 :- µ1 = µ2 = µ3 = 0  
H0 :- µ1 = µ2 = µ3 ≠ 0  

Test Statistic :-
f = MS treatment / MS error = 19.00

Test Criteria :-
Reject null hypothesis if f > f(α , a-1 , N-a )
Critical value f(0.05, 2 , 15 ) = 3.682 (From F table)
Since 19 > 3.682, we reject H0
conclusion = Treatment means differs  

Decision based on P value
Reject null hypothesis if P value < α = 0.05
Since P value = 0 < 0.05, hence we reject the null hypothesis
Conclusion :- Treatment means differs  

Fisher's Least significant Difference ( LSD Method )
The pair of means µi. and µj. would be declared significantly different if > LSD
t(α/2 , N-a ) = 2.131 ( Critical value from t table )

LSD = = 0.87 Since the design is balanced n1 = n1 = n3 = n

= | 7 - 4.5 | = 2.5
= | 7 - 6 | = 1
= | 4.5 - 6 | = 1.5

Since | 7 - 4.5 | > 0.87, we conclude that the population means µ1. and µ2. differ.
Since | 7 - 6 | > 0.87, we conclude that the population means µ1. and µ3. differ.
Since | 4.5 - 6 | > 0.87, we conclude that the population means µ2. and µ3. differ.