Factor Analysis
A factor analysis was conducted for each of the three brands of flavored water (Dasani, Tropicana, and Kellogg's) by placing related brand attributes (Likert items) into independent groups called factors to calculate brand attitude scores. The brand attitude scores were used to demonstrate which brand the respondents of the survey liked the most. Since there are no inferential statistics in factor analyses, the results can be used to explain the sample only, and cannot be projected to a larger population. Finally, the means of the new attitude scores were compared using a t-test to test for statistical significance.
Dasani Factor Analysis
Table 1A: Dasani Total Variance Explained
Factor |
Eigenvalue |
% of Variance |
Cumulative % |
I |
4.6 |
46.5% |
46.5% |
II |
1.4 |
13.9% |
60.4% |
III |
0.9 |
|
|
IV |
0.8 |
|
|
V |
0.6 |
|
|
VI |
0.5 |
|
|
VII |
0.4 |
|
|
VIII |
0.3 |
|
|
IX |
0.3 |
|
|
X |
0.2 |
|
|
Factors with Eigenvalues ≥ 1 will be retained. Two of the ten factors have Eigenvalues greater than or equal to one and are therefore important in this analysis because they explain the variance of at least one Likert item. Table 1A shows that together, these two factors account for 60.4% of the variance, leaving 39.6% unexplained, which is not that great of a percentage.
Table 1B: Communalities and Factor Loadings
Brand Attribute (Likert Item) |
Communalities |
Factor Matrix |
Varimax |
||
|
|
I |
II |
I |
II |
…good brand … |
0.7 |
0.8 |
0.0 |
0.8 |
0.1 |
…makes me feel healthy. |
0.6 |
0.7 |
-0.2 |
0.7 |
-0.2 |
…tastes great. |
0.5 |
0.7 |
0.2 |
0.7 |
0.3 |
…brand I trust. |
0.6 |
0.8 |
-0.2 |
0.8 |
-0.2 |
…fits my lifestyle. |
0.7 |
0.8 |
0.1 |
0.8 |
0.1 |
…is too expensive. |
0.7 |
-0.0 |
0.8 |
-0.0 |
0.8 |
…is just like any other… |
0.5 |
-0.1 |
-0.7 |
-0.0 |
-0.7 |
…would recommend to my friends. |
0.7 |
0.8 |
0.1 |
0.8 |
0.1 |
…prefer over regular water. |
0.5 |
0.7 |
0.1 |
0.7 |
0.1 |
…doesn't taste artificial. |
0.5 |
-0.7 |
0.2 |
-0.7 |
0.1 |
Bold values indicate which factor Likert items load onto (either I or II). According to the Factor Matrix in Table 1B, eight of the ten attributes loaded on Factor I. This indicates that these attributes are related to each other in some way independent from the other variables. The results of the factor matrix were clear and not ambiguous.
Tropicana Factor Analysis
Table 2A: Tropicana Total Variance Explained
Factor |
Eigenvalue |
% of Variance |
Cumulative % |
I |
3.3 |
32.5% |
32.5% |
II |
1.5 |
15.4% |
47.9% |
III |
1.2 |
11.6% |
59.5% |
IV |
0.9 |
|
|
V |
0.7 |
|
|
VI |
0.7 |
|
|
VII |
0.5 |
|
|
VIII |
0.4 |
|
|
IX |
0.4 |
|
|
X |
0.3 |
|
|
As seen in Table 2A, three of the ten Tropicana factors have Eigenvalues greater than or equal to one and are therefore important in this analysis because they explain the variance of at least one Likert item. These three factors account for 59.5% of the variance, leaving 40.5% unexplained.
Table 2B: Communalities and Factor Loadings
Brand Attribute (Likert Item) |
Communalities |
Factor Matrix |
Varimax |
||||
|
|
I |
II |
III |
I |
II |
III |
…good brand |
0.6 |
0.7 |
0.3 |
-0.1 |
0.8 |
-0.1 |
-0.0 |
…makes me feel healthy. |
0.6 |
0.8 |
0.1 |
-0.0 |
0.7 |
-0.2 |
0.2 |
…tastes great. |
0.6 |
0.7 |
-0.3 |
0.0 |
0.5 |
-0.4 |
0.4 |
…brand I trust. |
0.7 |
0.6 |
0.5 |
-0.3 |
0.8 |
0.0 |
-0.3 |
…fits my lifestyle. |
0.6 |
0.7 |
0.2 |
0.2 |
0.7 |
0.0 |
0.3 |
…is too expensive. |
0.6 |
0.1 |
-0.8 |
-0.0 |
-0.3 |
-0.6 |
0.4 |
…is just like any other… |
0.7 |
-0.3 |
0.4 |
0.7 |
-0.1 |
0.8 |
0.2 |
…would recommend to my friends. |
0.4 |
0.6 |
-0.0 |
0.1 |
0.5 |
-0.1 |
0.3 |
…prefer over regular water. |
0.8 |
0.4 |
-0.4 |
0.7 |
0.2 |
0.0 |
0.9 |
…doesn't taste artificial. |
0.5 |
-0.4 |
0.4 |
0.3 |
-0.2 |
0.6 |
-0.1 |
According to the Factor Matrix in Table 2B, six of the ten attributes loaded on Factor I. This indicates that these attributes are related to each other in a way that is independent from the attributes that loaded on other factors. Two attributes loaded on Factor II ("Tropicana is a brand I trust." and "Tropicana flavored water is too expensive.") and two other attributes loaded on Factor III (“Tropicana flavored water is just like any other flavored water.” and “I prefer Tropicana flavored water over regular water.”). Two attributes (“Tropicana is a brand I trust.” and “Tropicana flavored water doesn't taste artificial.”) proved to be ambiguous, meaning these rows had more (or none) than one factor greater than or equal to the absolute value of +/-0.5. A Varimax Rotation was used to elicit better results, and the rotated results turned out to be less ambiguous than the unrotated ones.
Kellogg's Factor Analysis
Table 3A: Kellogg's Total Variance Explained
Factor |
Eigenvalue |
% of Variance |
Cumulative % |
I |
4.2 |
41.8% |
41.8% |
II |
1.5 |
15.2% |
56.9% |
III |
1.0 |
10.5% |
67.4% |
IV |
0.8 |
|
|
V |
0.6 |
|
|
VI |
0.6 |
|
|
VII |
0.4 |
|
|
VIII |
0.4 |
|
|
IX |
0.3 |
|
|
X |
0.2 |
|
|
Three of the ten factors for Kellogg's have Eigenvalues greater than or equal to one and are therefore important in this analysis. Table 3A shows that together, these three factors account for 67.4% of the variance, leaving 32.6% unexplained.
Table 3B: Communalities and Factor Loadings
Brand Attribute (Likert Item) |
Communalities |
Factor Matrix |
Varimax |
||||
|
|
I |
II |
III |
I |
II |
III |
…good brand |
0.7 |
0.8 |
0.1 |
0.2 |
0.7 |
0.0 |
0.4 |
…makes me feel healthy. |
0.6 |
0.8 |
0.1 |
0.1 |
0.7 |
0.0 |
0.4 |
…tastes great. |
0.6 |
0.7 |
0.2 |
-0.1 |
0.7 |
0.2 |
0.2 |
…brand I trust. |
0.7 |
0.4 |
0.3 |
0.7 |
0.1 |
0.1 |
0.8 |
…fits my lifestyle. |
0.7 |
0.8 |
-0.1 |
0.1 |
0.8 |
-0.1 |
0.2 |
…is too expensive. |
0.7 |
0.1 |
-0.8 |
-0.4 |
0.2 |
-0.8 |
-0.1 |
…is just like any other… |
0.8 |
0.2 |
0.8 |
0.2 |
0.2 |
0.9 |
-0.1 |
…would recommend to my friends. |
0.7 |
0.8 |
-0.1 |
-0.5 |
0.7 |
-0.2 |
0.4 |
…prefer over regular water. |
0.7 |
0.6 |
-0.2 |
0.3 |
0.8 |
-0.1 |
-0.3 |
…doesn't taste artificial. |
0.6 |
-0.7 |
0.1 |
0.1 |
-0.8 |
-0.0 |
0.0 |
According to the Factor Matrix in Table 3B, seven of the ten attributes loaded on Factor I. This indicates that these attributes are related to each other in a way that is independent from the attributes that loaded on other factors. Two attributes loaded on Factor II and two other attributes loaded on Factor III. However, one attribute (“I would recommend Kellogg's flavored water to my friends.”) proved to be ambiguous. Thus a Varimax Rotation was used to elicit better results, and the rotated results turned out to be less ambiguous than the unrotated ones and are consequently used in this analysis.
Table 4: Attitude Scale
Brand |
Mean |
Standard Deviation |
Dasani |
3.3 |
0.5 |
Tropicana |
3.2 |
0.4 |
Kellogg's |
2.9 |
0.4 |
Sample size: 82 respondents
The attitude scales developed in the previous three sections are used to compute a mean attitude score for each brand. After analyzing the responses derived from the data set of 82 people, Dasani has the highest attitude score of 3.3, followed by Tropicana with a score of 3.2 and finally Kellogg's with an attitude score of 2.9.
Table 5: Paired Sample t-tests
Brand Pair |
t-ratio |
Dasani - Tropicana |
0.35 |
Dasani – Kellogg's |
5.16* |
Tropicana – Kellogg's |
5.26* |
* p ≤ 0.15
Paired sample t-tests were conducted to determine the statistical significance of the differences in means between the brand attitude scores of the three brands. Based on the results, we can expect that in 85 (or more) samples of 100 samples drawn from the same population as this sample, the differences between the mean attitude scores for the pairs Dasani/Kellogg's and Tropicana/Kellogg's would be about the same as they are in this sample. However, the difference between mean attitude scores for Dasani/Tropicana is not significant and cannot be projected to a larger population.