Discriminant Analysis

In performing this multiple linear discriminant analysis, only two groups were included in the analysis. Subjects were originally divided into three groups based on their pre to post ad exposure change scores for the Big Red brand. The three groups consisted of those who had positive change scores, those who had negative change scores on the constant-sum scale, and those who indicated no change in their pre to post ad exposure change scores. The last group (the respondents who revealed no change in their change scores) was not used in this analysis. The categorical dependent variable in the analysis is the group membership, while the independent variables are the ten brand characteristics (or the Likert items). This analysis was conducted in order to show if we can accurately predict the up-movers (had a positive change score) from the down-movers (those with a negative change score) according to their Likert responses. Although a total of 83 participants completed the survey, only 35 will be used in this analysis.

Big Red Brand Characteristics
Brand Characteristic	Moved Up n = 16		Moved Down n = 19
	Mean	Standard Deviation	Mean	Standard Deviation
1. Is a flavorful gum.	4.3	0.5	4.2	0.6
2. Is an excellent brand of gum.	3.6	1.1	3.8	0.9
3. Has a long lasting flavor.	2.9	1.0	3.1	1.2
4. Is too overwhelming.	3.1	1.2	3.5	1.0
5. Keeps your breath fresh.	2.6	1.2	3.2	1.2
6. Has an odd texture.	3.4	0.9	3.6	0.8
7. Packaging is appealing.	3.3	0.8	3.5	0.8
8. Is too sugary.	3.1	0.8	3.7	0.6
9. Gets hard after chewing.	2.1	0.7	3.1	1.1
10. Prefer over other gums.	2.5	0.8	3.1	1.1

By comparing the mean scores of the up-movers and the down-movers we find that there is not much variation between the two groups, but there are several group means that do have notable discrepancies. The largest differences between mean scores are on item 8 (“Is too sugary”), with a magnitude of change of -.08, and item 9 (“Gets hard after chewing”), with a magnitude of change equal to -1.0. These differences explain that the down-movers believed that Big Red was slightly more sugary, and that the brand also became harder after extensive chewing, as compared to the up-movers. Overall, the mean scores between the two groups proved that there were very little dissimilarities between the two groups perceptions of Big Red based on the ten Likert items. Therefore, the ten Likert items do not show a great difference between the up-movers and the down-movers.

Big Red Discriminant Coefficients
Brand Characteristic	Standardized Discriminant Coefficient	Unstandardized Discriminant Coefficient
1. Is a flavorful gum.	-0.2	-0.3
2. Is an excellent brand of gum.	-0.6	-0.6
3. Has a long lasting flavor.	-0.3	-0.3
4. Is too overwhelming.	-0.2	-0.2
5. Keeps your breath fresh.	0.1	0.1
6. Has an odd texture.	0.4	0.5
7. Packaging is appealing.	0.2	0.2
8. Is too sugary.	0.4	0.6
9. Gets hard after chewing.	0.8	0.8
10. Prefer over other gums.	0.6	0.6

There are only three brand characteristics considered to be important, implying that these three attributes best explain the variance in the pre to post ad exposure change scores between the up-movers and the down-movers. Those attributes being that: Big Red is an excellent brand of chewing gum (#2), that the gum becomes hard after chewing (#9 and the most important in accounting for the variation), and finally, preferring Big Red over other gums (#10). The Unstandardized Discriminant Coefficients suggest the relationship between each brand characteristic and how the different respondents liked the Big Red print ad. The data output can be interpreted as:

• The more respondents thought that Big Red was a flavorful chewing gum, the less they liked the ad.

• The more individuals thought that Big Red was an excellent brand of chewing gum, the less they liked the ad.

• The more individuals thought that Big Red had a long lasting flavor, the less they liked the advertisement.

• The more people thought that Big Red was overwhelming, the less they liked the print ad.

• The more respondents thought that Big Red kept their breath fresh, the more they liked the ad.

• The more people thought that Big Red had an odd texture, the more they liked the ad.

• The more individuals thought that Big Red had appealing packaging, the more they liked the ad.

• The more individuals thought that Big Red was too sugary, the more they liked the advertisement.

• The more respondents thought that Big Red became hard after extensive chewing, the more they liked the print ad.

• The more respondents believed that they preferred Big Red over other brands, the more they liked the ad.

Wilks' Lambda
Wilks’ Lambda(Λ)	Chi – Squared (χ²)
0.63	12.80

 

Functions at Group Centroids
Change on Constant-Sum Scale	Average z Scores
Up-Movers	-0.8
Down-Movers	.07

 

 

 

 

The group centroids, -0.8 and .07, are not significant at their current levels due to the Wilks’ Lambda value of 0.63 not being statistically significant. The group centroids, which are the means of the discriminant function scores, for the up-movers and the down-movers are not distinguishable from each other. The Chi-Squared value of 12.80 yields results that are not statistically significant, signifying that a relationship does not exist between the up and down-movers and the ten brand characteristics. Both the Wilks’ Lambda and Chi-Squared values are not significant at the .15 level, meaning that in 85 or more out of 100 samples drawn from the same population as this sample, we could not expect to observe group centroid values of the same magnitude, or obtain a similar Chi-Squared score, or find a similar relationship between movement on the constant sum-scale and the brand characteristics. As a result, we would not be able to project the group centroid values and the Chi-Squared value onto the population as a whole, and are not clear of what the two group centroids would be.

Big Red Confusion Matrix		Predicted Group		Total
		Up-Movers	Down-Movers
Actual Group	Up-Movers	12	4	16
	Down-Movers	5	14	19

74.3% of cases correctly classified

 

t 0 = (0.743 - .5) = 2.17*

√[(0.743 x .257)/35] + [(.5 x .5)/35]

* indicates t 0 <= 1.04 p < = 0.15

The discriminant function predicts the classification for up-movers and down-movers with 74.3% accuracy. This is a moderately high accuracy when compared to the random probability of 50%. Based on the observed t-ratio compared to the critical t-value of 1.04 at an alpha level of 0.15, this accuracy result can be projected to the entire population. Hence, in 85 or more samples out of every 100 drawn from the same population as this one, we would expect to find equally accurate classification of up and down-movers on the constant-sum scale.

Advertising Implication

The discriminant analysis output was not helpful in illustrating the psychographic differences between the up-movers and the down-movers and their certain perception of the advertised brand. It appears that the ten Likert items do not discriminant between the up and down-movers at a high level. Knowing respondents’ attitudes towards Big Red, we are not able to project if they actually liked the ad. It can not be predicted that favorable opinions toward the Big Red brand would translate into favorable feelings toward the brand’s print ad.