Analysis
Cluster Analysis
The purpose of K-means cluster analysis is to group respondents by their similar answers of brand attributes, also known as Likert items, for the snack bar Nature Valley into clusters. The cluster is a group that both minimizes variation within clusters and maximizes variation between clusters. For this analysis, 2 clusters and 3 clusters were conducted to evaluate the means between clusters and within clusters and to evaluate data for the purpose of classification. Results used in this analysis were from a total sample of 63 who participated in this on-line survey
Table 1: Descriptive Statistics and F-ratio for Two-Cluster Group (n=63)
|
Cluster 1 |
Cluster 2 |
F-ratio |
Brand Attributes |
n=31 |
n=32 |
Mean |
Standard Deviation |
Mean |
Standard Deviation |
Good brand |
3.5 |
.6 |
4.2 |
.4 |
35.74* |
Energy |
3.1 |
.6 |
3.8 |
.5 |
21.56* |
Healthy |
2.8 |
.5 |
3.7 |
.7 |
27.42* |
Substitute |
2.7 |
.9 |
3.6 |
.8 |
19.63* |
Expensive |
3.0 |
.4 |
3.2 |
.8 |
1.35 |
Appetite |
2.8 |
.7 |
3.7 |
.7 |
26.93* |
Good Taste |
3.2 |
.6 |
3.1 |
1.1 |
.10 |
Purchase |
3.0 |
.6 |
4.0 |
.5 |
46.97* |
Recommendation |
3.1 |
.7 |
3.5 |
.9 |
3.94* |
Attractive |
2.8 |
.8 |
3.9 |
.6 |
33.27* |
*p ≤ .15
Table 1 shows the results of dividing respondents into two clusters based on their brand attitude score from the 10 Likert items. There is a noticeable difference in the mean score of those in cluster 1 and 2. Cluster 2 respondents have a significantly higher mean score on every Likert item with the exception of the Likert item “Nature Valley has good taste.” The F-ratios show that every Likert item was found to be significant except “Nature Valley has good taste” and “Nature Valley is expansive.” These results indicate that in 85 or more samples out of every 100 drawn from the same population as this sample of 63, we would expect the means to be what they are here.
Table 2. Crosstab for Two Cluster Group (n=63)
|
Gender |
Chi-Squared |
Male |
Female |
Cluster 1 |
Count |
12 |
19 |
.81 |
Row % |
38.7% |
61.3% |
Column% |
42.9% |
54.3% |
Total % |
19.0% |
30.2% |
Cluster 2 |
Count |
16 |
16 |
Row % |
50.0% |
50.0% |
Column% |
57.1% |
45.7% |
Total % |
25.4% |
25.4% |
*p ≤ .15
A Chi-squared significance test was conducted to determine the relationship between cluster membership and gender for the Nature Valley brand. Table 2 shows the number of males and females in each cluster with Cluster 1 being slightly female-oriented and Cluster 2 is the same between male and female. However, because these results are not statistically significant, they cannot be used to describe a larger population. In 85 (or more) of 100 samples drawn from the same population as this sample, we would not expect to find the same results.
Table 3: Descriptive Statistics and F-ratio for Three-Cluster Group (n=63)
|
Cluster 1 |
Cluster 2 |
Cluster 3 |
F-ratio |
Brand Attributes |
n=21 |
n=18 |
n=24 |
Mean |
Standard Deviation |
Mean |
Standard Deviation |
Mean |
Standard Deviation |
Good brand |
4.2 |
.5 |
4.1 |
.3 |
3.3 |
.5 |
27.82* |
Energy |
3.9 |
.4 |
3.7 |
.6 |
3.0 |
.5 |
24.90* |
Healthy |
3.3 |
.9 |
3.7 |
.7 |
2.9 |
.4 |
7.30* |
Substitute |
3.0 |
.9 |
3.9 |
.6 |
2.6 |
.9 |
12.89* |
Expensive |
3.3 |
.6 |
3.0 |
.8 |
2.9 |
.3 |
3.16* |
Appetite |
3.5 |
.8 |
3.7 |
.6 |
2.7 |
.6 |
15.75* |
Good Taste |
4.1 |
.4 |
2.3 |
.6 |
3.0 |
.5 |
64.29* |
Purchase |
3.9 |
.5 |
3.9 |
.5 |
2.8 |
.5 |
28.74* |
Recommendation |
3.8 |
.8 |
3.2 |
.9 |
2.9 |
.6 |
7.93* |
Attractive |
3.2 |
.9 |
4.0 |
.5 |
3.0 |
.8 |
9.78* |
*p ≤ .15
Table 3 shows the results of dividing respondents into three clusters based on their brand attitude score from the 10 Likert items. The respondents in cluster 1 have the highest mean scores, followed by cluster 2 then cluster 3. The F-ratios were found to be significant for every Likert item. These results indicate that in 85 or more samples out of every 100 drawn from the same population as this sample of 63, we would expect the means to be what they are here.
Table 4. Crosstab for Three Cluster Group (n=63)
|
Gender |
Chi-Squared |
Male |
Female |
Cluster 1 |
Count |
10 |
11 |
.16 |
Row % |
47.6% |
52.4% |
Column% |
35.7% |
31.4% |
Total % |
15.9% |
17.5% |
Cluster 2 |
Count |
8 |
10 |
Row % |
44.4% |
55.6% |
Column% |
28.6% |
28.6% |
Total % |
12.7% |
15.9% |
Cluster 3 |
Count |
10 |
14 |
Row % |
41.7% |
58.3% |
Column% |
35.7% |
40.0% |
Total % |
15.9% |
22.2% |
*p ≤ .15
A Chi-squared significance test was conducted to determine the relationship between cluster membership and gender for the Nature Valley brand. Table 4 shows the number of males and females in Cluster 1 and Cluster 2 are almost same, while cluster 3 is slightly female oriented. However, because these results are not statistically significant, they cannot be used to describe a larger population. In 85 (or more) of 100 samples drawn from the same population as this sample, we would not expect to find the same results.