Analysis
Discriminant Analysis
In order to know if the ten Likert items can effectively predict the respondents’ attitude toward the advertisement with a better accuracy, discriminant analysis for Nature Cereal Bar was conducted. This discriminant analysis was executed to test whether people like the advertisement based on the ten Likert items of the brand with two groups, ‘up-movers’, those who liked the advertisement for Nature and ‘down-movers’, those who did not like the advertisement for it. The independent variables in this analysis are the brand attributes as indicated by ten Likert items and the categorical dependent variable is group membership (up’s and down’s).
Table 1. Group Mean Scores and Standard Deviation
Likert Items |
Up-Movers (n=12) |
Down-Movers (n=36) |
Mean |
Standard Deviation |
Mean |
Standard Deviation |
Good brand |
3.9 |
.5 |
3.8 |
.6 |
Energy |
3.6 |
.7 |
3.3 |
.6 |
Healthy |
3.6 |
1.0 |
3.1 |
.6 |
Substitute |
3.3 |
.9 |
3.1 |
1.0 |
Expensive |
3.0 |
.7 |
3.0 |
.6 |
Appetite |
3.2 |
.8 |
3.1 |
.8 |
Good Taste |
3.0 |
1.0 |
3.1 |
.8 |
Purchase |
3.8 |
.5 |
3.3 |
.8 |
Recommendation |
3.6 |
.7 |
3.3 |
.8 |
Attractive |
4.1 |
.7 |
3.0 |
.9 |
(n=48)
When it comes to mean scores of each brand attribute, there are small differences between two groups in general. The most marked appeared in the attributes “Healthy,” “Purchase,” and “Attractive.”
Table 2. Standardized and Unstandardized Discriminant Function Coefficients
Likert Items |
Standardized Discriminant Function Coefficients |
Unstandardized Discriminant Function Coefficients |
Good brand |
-.2 |
-.3 |
Energy |
.5 |
.8 |
Healthy |
.5 |
.8 |
Substitute |
.1 |
.1 |
Expensive |
-.1 |
-.1 |
Appetite |
-.8 |
-1.0 |
Good Taste |
-.1 |
-.1 |
Purchase |
-.2 |
-.3 |
Recommendation |
.3 |
.4 |
Attractive |
1.0 |
1.2 |
Important standardized coefficients (i.e., at least half of the highest score) are highlighted
The attribute “Attractive” has the biggest absolute value of standardized discriminant function coefficients, 1.0. We assume that the items which have the equal or larger absolute value of the standard discriminant function coefficients than 0.5 (=1.0/2) are important independent variables in explaining differences in pre-to-post ad exposure change scores between up-movers and down-movers. The important variables in discriminating between up-movers and down-movers are brand attributes described as “Energy,” “Healthy”, “Appetite”, and “Attractive.”
The more respondents think Nature makes them feel energized, the more they like the ad;
-
The more respondents think Nature is a healthy cereal bar, the more they like the ad;
-
The more respondents think Nature takes care of their appetite, the less they like the ad;
-
The more respondents think Nature’s packaging is attractive, the more they like the ad.
Table 3. Group Centroids and Statistical Significance
Group Centroids |
Wilks’ Lambda |
Degrees of Freedom |
Chi-squared |
Up-Movers |
Down-Movers |
1.4 |
-.5 |
.60 |
10 |
20.77* |
*p ≤ .15 (n=48)
The group centroids, which are the average discriminant z scores of 1.4 for up-movers and of -0.5 for down-movers, are significant, due to the statistical significance found for Wilks’ Lambda at .60 and chi-squared at 20.77. Therefore, in 85 or more samples out of every 100 samples drawn from the same population as this sample, it is expected that the group centroids would be about what it is in this sample. Therefore, we can project the results of the survey to the population.
Table 4. Classification Matrix
Classification Matrix |
Predicted Group |
Actual Group |
|
Up-Movers |
Down-Movers |
Up-Movers |
8 |
4 |
Down-Movers |
3 |
33 |
85.4% of cases correctly classified
Observed t-ratio = .854 - .5 / square root [.854*(1-.854)/48 + .5(.5)/48] = 3.98*
(*p ≤ .15)
The classification matrix shows that 85.4% of the actual groups are predicted correctly. Out of 12 actual up-movers, 8 are correctly predicted to move up, and out of 36 actual down-movers, 33 are correctly predicted to move down.
If t0 > tc, then the result is significant. Since our observed t-ratio equals 3.98 and is more extreme than the critical t-ratio of 1.04, t-ratio to test classification accuracy is significant. Therefore, in 85 or more samples out of every 100 samples drawn from the same population as this sample, it is expected that the percentage of classification accuracy would be about what it is in this sample. Therefore, the results of the survey can be projected to the population.
This is a quite successful discriminant analysis because Wilks’ Lambda result shows that group centroids are statistically significant as indicated by chi-squared value of 20.77 and 85.4% of the original grouped cases were correctly classified as either an up-movers group or a down-movers group. Moreover, t-ratio to test this classification accuracy is significant.