In: Statistics and Probability
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 |
6 | 8 | 6 |
5 | 8 | 7 |
4 | 7 | 6 |
5 | 7 | 5 |
6 | 8 | 6 |
4 | 7 | 6 |
Sum of Squares, Treatment | |
Sum of Squares, Error | |
Mean Squares, Treatment | |
Mean Squares, Error |
Difference | Absolute Value | Conclusion |
x 1 - x2 | Select Significant difference No significant differenceItem 10 | |
x1 - x3 | Select Significant difference No significant differenceItem 12 | |
x 2 - x3 |
using minitab>stat>ANOVA
we have
One-way ANOVA: Marketing Managers, Marketing Research, Advertising
Method
Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level α = 0.05
Equal variances were assumed for the analysis.
Factor Information
Factor Levels Values
Factor 3 Marketing Managers, Marketing Research, Advertising
Analysis of Variance
Source DF Seq SS Contribution Adj SS Adj MS F-Value
P-Value
Factor 2 19.000 71.70% 19.000 9.5000 19.00 0.000
Error 15 7.500 28.30% 7.500 0.5000
Total 17 26.500 100.00%
Model Summary
S R-sq R-sq(adj) PRESS R-sq(pred)
0.707107 71.70% 67.92% 10.8 59.25%
Means
Factor N Mean StDev 95% CI
Marketing Managers 6 5.000 0.894 (4.385, 5.615)
Marketing Research 6 7.500 0.548 (6.885, 8.115)
Advertising 6 6.000 0.632 (5.385, 6.615)
Pooled StDev = 0.707107
Fisher Pairwise Comparisons
Grouping Information Using the Fisher LSD Method and 95% Confidence
Factor N Mean Grouping
Marketing Research 6 7.500 A
Advertising 6 6.000 B
Marketing Managers 6 5.000 C
Means that do not share a letter are significantly different.
Fisher Individual Tests for Differences of Means
Difference SE of Adjusted
Difference of Levels of Means Difference 95% CI T-Value
P-Value
Marketing Re - Marketing Ma 2.500 0.408 ( 1.630, 3.370) 6.12
0.000
Advertising - Marketing Ma 1.000 0.408 ( 0.130, 1.870) 2.45
0.027
Advertising - Marketing Re -1.500 0.408 (-2.370, -0.630) -3.67
0.002
Simultaneous confidence level = 88.31%
Sum of Squares, Treatment | 19 |
Sum of Squares, Error | 7.5 |
Mean Squares, Treatment | 9.5 |
Mean Squares, Error | 0.5 |
Difference | Absolute Value | Conclusion |
x 1 - x2 | 6.12 | significant difference |
x1 - x3 | 2.44 | significant difference |
x 2 - x3 | 3.67 | significant difference |