A multiple discriminant analysis was conducted to determine if respondents’ attitudes to the Zest brand affected whether the respondents were “up-movers” or “down-movers.” “Up-movers” are those respondents who had a positive change score for Zest on the constant sum scale after viewing the advertisements, while “down-movers” had a negative score. The categorical dependent variable is group membership, while the independent variables are the scores on the ten brand attitude Likert items. The sample is drawn from 58 respondents.
Table 1: Zest brand attributes
Zest... |
Up-movers |
Down-movers |
Unstandardized discriminant function coefficient |
Standardized discriminant function coefficient |
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Mean |
Standard deviation |
Mean |
Standard deviation |
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... is a good brand of body wash. |
3.8 |
0.8 |
3.3 |
0.6 |
0.8 |
0.5 |
... is preferred over other body washes. |
3.3 |
0.9 |
2.9 |
0.9 |
0.6 |
0.5 |
... gets me cleaner than other body washes. |
3.0 |
1.1 |
3.2 |
0.9 |
-0.8 |
-0.8 |
... smells nicer than other body washes. |
3.2 |
1.1 |
3.1 |
0.5 |
0.0 |
0.0 |
...isn’t recommended |
3.5 |
0.8 |
3.1 |
0.6 |
0.2 |
0.1 |
... is a good value. |
3.7 |
0.9 |
3.3 |
0.6 |
0.2 |
0.1 |
...is healthy. |
3.4 |
0.8 |
3.2 |
0.6 |
0.2 |
0.1 |
... makes me feel good. |
3.4 |
1.1 |
3.3 |
0.5 |
-0.3 |
-0.2 |
...is bad for my skin. |
3.7 |
0.9 |
3.4 |
0.6 |
-0.1 |
-0.1 |
...is a brand I would purchase |
3.8 |
0.8 |
3.4 |
0.6 |
0.1 |
0.1 |
Down movers sample size: 18, Up movers sample size: 19 |
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In the above table, the mean Likert scores for each attribute varies no more than 0.5 points between up-movers and down-movers – thus there appear to be few if any great differences between the two groups’ perceptions of the Zest brand. “Zest is a good brand of body wash”, “I prefer Zest over other body washes,” “I would recommend Zest to other people,” “Zest is a good value” and “Zest is a brand I would purchase” appear to be the most important brand attributes in determining whether respondents were up movers or down movers.
Table 2: Group centroids and inferential statistics
Group |
Average discriminant score |
Up movers |
0.47 |
Down movers |
0.50 |
Wilks’s Lambda |
Chi-squared |
0.80 |
6.60 |
|
* p ≤ 0.15 |
The Wilks’s Lambda test, when converted to Chi-squared, is not statistically significant. Thus it would not necessarily be expected that in 85 samples out of 100 samples drawn from the same population as this sample, the difference between the up movers’ and down movers’ group centroids would be what it is here. The group centroids cannot be projected to the larger population.
At 0.03, the difference between the average discriminant scores of up movers (0.47) and down movers (0.50) is not great and not statistically significant.
Table 3: Classification matrix
Actual membership |
Predicted membership |
|
Up movers |
Down movers |
|
Up movers |
13 |
6 |
Down movers |
4 |
14 |
73.0% of original grouped cases correctly classified |
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According to the classification matrix, only 27 respondents out of 37 (73.0%) fall into their predicted groups.
t = .9407
(.73 - .5) / √ (.73)((1-.73)/37)) + (.5)(.5)/37
.23/ √ .0053 + .0068
.23/ .2445
.9407 = t
Although 73.0% is a moderately good percentage, the percentage of original grouped cases correctly d is not statistically significant. In 85 samples out of 100 samples drawn from the same population as this sample, it would not necessarily be expected that the percentage of cases correctly classified would be about what it is here.