Factor Analysis

A factor analysis was conducted for each of the three print advertisements for brands of chewing gums in order to place related brand attributes variables into independent, yet correlated groups. This analysis allowed us to build an attitude scale, in order to observe respondents individual opinions towards each individual brand.

Total Variance Explained: Winterfresh
Component	Item Value Total	% of Variance	Cumulative % of Variance
1	3.1	31.4	31.4
2	1.5	14.7	46.1
3	1.1	11.2	57.3
4	0.9	9.4	66.7
5	0.8	8.1	74.8
6	0.7	7.1	81.9
7	0.7	6.6	88.4
8	0.5	5.3	93.7
9	0.3	3.2	96.9
10	0.3	3.1	100.0

For the Winterfresh brand, 57.3% of the variance can be explained by the first three factors. These three Eigenvalues factors retained were greater than one, an important quality to consider because we do not want to retain components that explains less variance than that which was in one of the variables. The first factor (or component) accounts for 31.4% of the variance, while the second and third retaining factors together 25.9% of the variance in the original variables. Though these three factors collectively explain a little more than half of the variance, there is still a great number of variance left unexplained, making this an inadequate factor analysis.

Factor and Varimax Rotated Matrices: Winterfresh
Brand Characteristic	Factor Loading Matrix			Varimax Rotated Matrix			Communalities
	1	2	3	1	2	3
1. Is a flavorful gum.	0.8	0.01	0.2	0.6	0.5	0.1	0.6
2. Is an excellent brand of gum.	0.8	0.1	0.2	0.7	0.4	0.1	0.7
3. Has a long lasting flavor.	0.5	0.6	0.1	0.8	0.1	0.3	0.7
4. Is too overwhelming.	0.6	0.6	0.1	0.01	0.9	0.1	0.8
5. Keeps your breath fresh.	0.5	0.5	0.1	0.7	0.1	0.1	0.6
6. Has an odd texture.	0.6	0.2	0.3	0.3	0.5	0.3	0.4
7. Packaging is appealing.	0.3	0.5	0.1	0.1	0.5	0.2	0.3
8. Is too sugary.	0.6	0.3	0.1	0.3	0.6	0.1	0.5
9. Gets hard after chewing.	0.2	0.2	0.8	0.1	0.1	0.9	0.8
10. Prefer over other gums.	0.5	0.1	0.5	0.5	0.3	0.4	0.5

The Varimax Matrix was used in this analysis because it had the least amount of problems when compared to the Factor Matrix. The Likert item “Is a flavorful gum” loaded on Factor 1. The brand characteristics #2, #3, #5, and #10 all loaded onto Factor 1. These 5 brand attribute items are somehow related to each other independent of the other factors.

Total Variance Explained: Big Red
Component	Item Value Total	% of Variance	Cumulative % of Variance
1	3.4	34.0	34.0
2	1.4	14.1	48.1
3	1.1	11.0	58.7
4	0.9	9.2	67.9
5	0.8	7.7	75.6
6	0.8	7.5	83.1
7	0.7	6.5	89.5
8	0.4	4.2	93.7
9	0.3	3.2	96.9
10	0.3	3.1	100.0

 

Factor and Varimax Rotated Matrices: Big Red
Brand Characteristic	Factor Loading Matrix			Varimax Rotated Matrix			Communalities
	1	2	3	1	2	3
1. Is a flavorful gum.	0.6	0.1	0.1	0.5	0.4	0.2	0.4
2. Is an excellent brand of gum.	0.8	0.03	0.04	0.6	0.6	0.3	0.7
3. Has a long lasting flavor.	0.5	0.7	0.1	0.1	0.5	0.7	0.7
4. Is too overwhelming.	0.5	0.6	0.4	0.9	0.1	0.02	0.7
5. Keeps your breath fresh.	0.6	0.2	0.2	0.2	0.6	0.2	0.4
6. Has an odd texture.	0.6	0.3	0.3	0.7	0.2	0.2	0.6
7. Packaging is appealing.	0.5	0.1	0.7	0.004	0.8	0.2	0.7
8. Is too sugary.	0.4	0.5	0.1	0.5	0.2	0.3	0.4
9. Gets hard after chewing.	0.4	0.5	0.6	0.1	0.04	0.8	0.7
10. Prefer over other gums.	0.8	0.1	0.1	0.4	0.6	0.3	0.6

Three of the ten factors created for Big Red have Eigenvalues greater than one, indicating that they explain the variance of at least one of the Likert items. These three factors collectively explain 58.7% of the variance, which is slightly better than the Winterfresh brand but indicates that there is still 41.3% of the variance left unexplained.

For the Big Red brand, the Factor Loading Matrix was used to create a component matrix for these factors. It is clear that the brand characteristic “Is a flavorful gum” loaded on Factor 1, as well as Likert items #2, #5, #6, and #10. The factors that loaded onto Factor 1 are somehow related to one another independent of other factors.

Total Variance Explained: Orbit
Component	Item Value Total	% of Variance	Cumulative % of Variance
1	4.4	44.0	44.0
2	1.6	15.6	59.6
3	0.9	8.7	68.3
4	0.7	7.1	75.4
5	0.6	5.7	81.1
6	0.5	5.1	86.2
7	0.5	4.5	90.7
8	0.5	4.3	95.0
9	0.3	2.8	97.8
10	0.2	2.2	100.0

Two of the ten components created for the Orbit brand have Item Values greater than one and together combine to explain 59.6% of the variance (40.4% is left unexplained). The first component explains 44.0% of the variance, expounding a large proportion (almost half) of the variation. Orbit’s two factors explain the most variance compared to the other two brands three factors, however, the proportion (59.6%) is still rather low and does not make for an explanatory factor analysis.

Factor and Varimax Rotated Matrices: Orbit
Brand Characteristic	Factor Loading Matrix		Varimax Rotated Matrix		Communalities
	1	2	1	2
1. Is a flavorful gum.	0.8	0.2	0.8	0.3	0.7
2. Is an excellent brand of gum.	0.7	0.01	0.6	0.4	0.5
3. Has a long lasting flavor.	0.8	0.4	0.9	0.1	0.8
4. Is too overwhelming.	0.6	0.6	0.1	0.8	0.7
5. Keeps your breath fresh.	0.7	0.3	0.8	0.03	0.6
6. Has an odd texture.	0.5	0.6	0.1	0.8	0.6
7. Packaging is appealing.	0.6	0.4	0.7	0.01	0.5
8. Is too sugary.	0.7	0.3	0.4	0.7	0.6
9. Gets hard after chewing.	0.4	0.5	0.1	0.6	0.4
10. Prefer over other gums.	0.8	0.1	0.8	0.3	0.7

The Varimax Matrix was used in this analysis because it had the least amount of obstructions when weighed against the Factor Loading Matrix. The Likert item “Is a flavorful gum” loaded onto Factor 1. The brand characteristics #2, #3, #5, #7, and #10 all loaded onto Factor 1. These 6 brand attribute items are somehow related to each other independent of the other factors.

Attitude Scale
Brand Name	Mean Attitude Score	Standard Deviation	Sample Size
Winterfresh	3.4	0.6	83
Big Red	3.3	0.7	83
Orbit	3.8	0.7	83

 

Paired t-Test for Attitude Scale Scores
Paired Brands	t-Ratios
Winterfresh – Big Red	1.90*
Big Red – Orbit	4.34*
Winterfresh -- Orbit	3.24*

According to the Attitude Scale, Orbit had a slightly higher mean attitude score compared to Winterfresh and Big Red. These results illustrate that respondents liked the Orbit brand best, but it is difficult to say if they really prefer one brand over the other. Based on the inferential statistics from this analysis, all three of the paired t-Tests are statistically significant at the alpha level of 0.15. When comparing all three of the paired brands, each are viewed about the same because all are statistically significant. Therefore, in 85 or more out of every 100 samples drawn from the same population as this sample of 83 respondents, we would expect to find the same magnitude of difference between the Winterfresh and Big Red mean attitude scores, among the Big Red and Orbit mean scores, and finally, between the Winterfresh and Orbit mean attitude scores. In other words, all three of the comparisons can be projected onto the population as a whole.