The following analysis is based on a survey that I did for body lotion. The survey was sent to over 250 people and 97 responses were received. Of those 97, 67 were used in this analysis.

We will be looking at the results of the survey to test and analyze three different body lotion brands. To determine respondents’ feelings towards each of the three test brands a brand index score was calculated for each brand by summing up the responses to 10 brand-related Likert items appearing on the survey. A score of 50 was the highest possible positive response indicating favorable feelings, and a score of 10 the least, indicating less favorable feelings towards the brand.

1. Paired T-test Comparing the Brand Index Score for All Combinations of Body Lotion Brands

The Brand Index Score Mean indicates which brand the respondents liked better. In table 1 we see that Aveeno had the highest Brand Index Score Mean, followed by Olay then Curel. This indicates that the majority of respondents favored the Aveeno brand more than Olay and Curel.

Total Respondents = 67 *p < 0.15

When looking at the t ratio in table 2 we see that each result is significantly different from the others. This means that in 85 or more samples, out of 100 samples drawn from the same population as this sample, it would be expected that the mean Brand Index Scores for each brand would be about what they are in this sample.

2. Independent Samples T-test for one Brand

As we see in table 3 the mean Brand Index and Ad Index scores for both up movers and down movers only vary slightly. The variances being 0.8 between the up and down movers in the Ad Index score and only ).4 for the Brand Index score. Thus, those respondents who either moved up or down after viewing the ads more often than not moved up or down for both Brand and Ad Index Scores.

When we look at the t-ratio we can see for sure that there was not a significant difference for either the Brand or Ad Index Score after viewing the ad. This means that we cannot expect that in 85 or more samples, out of 100 samples drawn from the same population as this sample of 67, that the mean Brand Index Scores would be about what they are in this sample for the up movers and down movers. Neither can we expect the same for the Ad Index Score.

3. Chi-Squared Significance test

Chi-Squared = 4.89*
Total respondents = 67
*p < 0.15

The respondents with a Brand Index Score above median who moved up in the Row percentage are 60.9%. This shows that there is a positive relation between the liking of the Brand and liking of the Ad. It is important to note the fact that 66.7% of the respondents with Brand Index Score below the median stayed the same and had no change (Row %). Thus indicating that the majority of those who had a low Brand Index Score where not persuaded into liking the brand more or less after seeing the ad.

The Chi-squared value is 4.89 and is significant. This means that in 85 or more samples, out of 100 samples drawn from the same population as this sample, it would be expected that the percentage distribution would be about the same as found in table 4.

4. Change Score for all brands (Frequency)

Total respondents = 67

The Change score is calculated by taking the post – pre allocation of “likeliness to buy” point. At least 42% of all respondents’ “likeliness to buy” numbers stayed the same on all brands. But two more people stayed the same after seeing the Aveeno ad indicating that the ad had less of an effect on attitude than the other two brands.
Curel had 40% of respondents move up on the “likeliness to buy” scale. Indicating that the ad positively affected attitude of almost half of the respondents. Olay and Aveeno, both had more respondents move down than Curel.

5. Number of respondents scoring Curel > Olay on the Brand Index Scale

Number of respondents with higher Brand Index Score for Curel than Olay = 20
 
Total respondents = 67

The number of respondents with a Brand Index Score for Curel that was higher than the Brand Index Score for Olay was 20 out of 67 respondents. This means that those respondents scored higher, on the summed Likert responses, for Curel than for Olay. This result indicates a more favorable attitude towards Curel lotion after viewing the ad than for Olay.

6. Correlation between Curel and Olay Brand Index Scores

Curel and Olay Pearson Correlation = 0.1*
*p < 0.15

The correlation between Curel and Olay Brand Index Score is 0.1 for all 67 respondents. It is a positive correlation meaning that if a respondent likes Curel they are also probably going to like Olay. While this is true, .1 is a low correlation indicating that it is not highly likely that a respondent who likes Curel will also like Olay.

Although the correlation is week, it is significant. This means we have reason to expect that in 85 or more samples, out of 100 samples drawn from the same population as this sample, the mean Brand Index Scores for Curel and Olay would be about what they are in this sample.

7. Change Score for each brand from a group of respondents that use lotion frequently.

Total Respondents = 47

In table 6 we are taking into consideration only respondents that use lotion frequently. For Curel, just like in table 5, more respondents moved up in their “likeliness to buy” than any other brand. This shows that even among the respondents that buy lotion often, the ad for Curel affected their attitude positively toward purchase intent. Also, as we see in table 5, at least 40% of all respondents who buy lotion frequently did not change their answers for “likeliness to buy” after seeing the ads.

For each of the three test brands, a multiple linear regression analysis was conducted where the dependent variable is its change score and the ten Likert items are the independent variables. The purpose of the analysis is to uncover the connection, that the sample respondents made between the advertisements and how they rated the brands.

*p < 0.15
Total Respondents = 67

*p < 0.15
Total Respondents = 67

Curel:
The coefficient of multiple determinations is 27.8% out of a 100%. This means that 27.8% of how much the respondents liked the Curel advertisement is explained by how much they liked the Curel brand. The coefficient of multiple correlations is significant, this means that in 85 or more samples, out of 100 samples drawn from the population, as this sample, it would be expected that the correlation would be about the same. The coefficient of multiple correlations is 0.5 and therefore the data has a low positive correlation.

In Table 2 we see that the Likert scale items “Constant”, “Good”, “Prefer”, “Greasy”, “Best” and “Feel Good” are all positively correlated with the Change Score, meaning as these items’ values increase so does the Change Score. On the other hand “Consider”, “Moisturize”, “Smooth”, “Only Buy” and “Smart” are all negatively correlated, meaning that as these items’ values increase the Change Score decreases.

Table 2 also shows that the Likert items that are important variables in explaining variance include the “Constant”, “Consider”, “Prefer” and  “Good”. The independent variables that are significant are the “Constant”, “Good”, “Prefer”, “Consider”, “Smooth” and “Smart.”  This means that their slopes can be projected by the sample of 85 or more samples of 100 samples drawn from the same population, as this sample.

Olay:
The coefficient of multiple determinations is 15.8% out of a 100%. This means that 15.8% of how much the respondents liked the Olay advertisement is explained by how much they liked the Olay brand. The coefficient of multiple correlations is not significant, this means that in 85 or more samples, out of 100 samples drawn from the population, as this sample, we could not expected that the correlation would be about the same. The coefficient of multiple correlations is 0.4 and therefore the data has a low positive correlation.

In Table 2 we see that one Likert scale item, “Feel Good”, and the “Constant” are positively correlated with the Change Score, meaning as these items’ values increase so does the Change Score. On the other hand the Likert items “Good”, “Prefer”, “Consider”, “Moisturize”, “Smooth”, “Greasy”, “Only Buy”, “Smart” and “Best” are all negatively correlated, meaning that as these items’ values increase the Change Score decreases.

Table 2 also shows that the Likert items that are important variables in explaining variance include “Good” and “Greasy”. The independent variables that are significant are the “Constant” and “Greasy”.  This means that their slope can be projected by the sample of 85 or more samples of 100 samples drawn from the same population, as this sample.

Aveeno:
The coefficient of multiple determinations is 8.9% out of a 100%. This means that 8.9% of how much the respondents liked the Olay advertisement is explained by how much they liked the Olay brand. The coefficient of multiple correlations is not significant, this means that in 85 or more samples, out of 100 samples drawn from the population, as this sample, we could not expected that the correlation would be about the same. The coefficient of multiple correlations is 0.3 and therefore the data has a low positive correlation.

In Table 2 we see that the Likert scale items that are positively correlated with the Change Score are the “Constant”, “Prefer”, “Consider”, “Moisturize”, “Smooth”, “Greasy”, “Only Buy” and “Feel Good”, meaning as these items’ values increase so does the Change Score. On the other hand the Likert items “Good”, “Smart” and “Best” are all negatively correlated, meaning that as these items’ values increase the Change Score decreases.

Table 2 also shows that the Likert items that are important variables in explaining variance include “Smooth” and “Best”. The independent variable that is significant is “Best”.  This means that its slope can be projected by the sample of 85 or more samples of 100 samples drawn from the same population, as this sample.

Multiple Regression Equation for Curel:
Change Score for Curel = Constant + Good + Prefer + Consider + Moisturize + Smooth + Greasy + Only Buy + Smart + Best  + Feel Good
1.8 = 2.0 + 0.3 +0.3 + (-0.4) + (-0.2) + (-0.3) +0.1 + (-0.1) + (-0.2) +0.2 +0.1

The purpose of the Multiple Discriminant Analysis is to examine how well independent variables, in this case the 10 Likert items, classify sample members, up and down movers, into different groups. This analysis demonstrates the connection between how respondents rated the body lotion brand Aveeno, by the 10 Likert items, and their pre to post exposure or change scores.

Total respondents = 36
These mean scores represent the averages for all 10 Likert items for the up and down mover categories. These values are used in further analysis to determine discriminant function coefficients.

From Table 2 we can see that the important variables in discriminating between the up and down movers are “Good”, “Consider”, “Smooth” and “Best” out of the 10 Likert items.

*p < 0.15
The Wilks’s Lambda test, when converted to Chi-squared, is not statistically significant. Therefore, in 85 out of every 100 samples drawn from the same sample population as this sample, we could not expect similar results. This means that the centriod function values can’t be projected to the general population.

The group centroid function for the up movers is 0.6 and for the down movers is -0.5. These are moderately (0.9) different scores. The Likert items therefore have a moderate discriminant function between up and down movers.

75% of the original grouped cases have been correctly classified.

to =  (0.75 – 0.50)  /  [ √ {  (0.75)(0.25) / (36)  +  (0.5)(0.5) / (36)  } ] = 2.27*
*p < 0.15 level

75% is noticeably above the random probability of 50%, and the percentage of original grouped cases correctly classified is statistically significant.  In 85 samples out of 100 samples drawn from the same population as this sample, it would be expected that the percentage of cases correctly classified would be about what it is here.

In this Multiple Discriminant Analysis the Wilks’ Lambda is not significant, thus the group centroid values are not significant. Though, it should be noted that the t-ratio is significant, and the classification accuracy is relatively high.

The ANOVA analysis is conducted in order to uncover the relationship between the gender of the respondents and their change scores for the variable “I prefer Olay to other body lotions” for Olay body lotion. The dependent variable is the Likert Item: “I prefer Olay to other body lotions” and the two Independent variables are the change score and the gender of the respondents. The MANOVA analysis is the same; the only difference is that the dependent variable is all 10 Likert Items for the Olay brand. The data set came from 67 respondents, 18 men and 49 women.

ANOVA

Number of respondents = 67

*p < 0.15
Number of respondents = 67

Of the two main effects and the interaction, none were significant (*p < 0.15).  This means that in 85 or more samples drawn from the same population as this sample, the expected mean scores on this Likert item, “I prefer Olay to other body lotions,” would not be the same as those reported here.  The results of this sample cannot be projected to the general population for this test.”

MANOVA

*p < 0.15

The main effect for gender was found significant (*p < 0.15).  This means that in 85 or more samples drawn from the same population as this sample, the expected mean scores on the gender of the respondents would be the same as those reported here.  The other main effect for attitude change and the interaction of attitude change and gender were not significant.  This means that these specific mean scores apply only to this sample and do not project to the general population.

To find out which of the three body lotion brands the respondents liked the best, a factor analysis was conducted. The goal was to find their respective brand attitude scores.
T-tests were then carried out to determine the statistical significance for the differences of means between brand attitude scores.

When a Likert item “loads” it needs to have a number ³ 0.5. In Table 1 we can see that the majority of the factors load under Factor 1 for Aveeno except for “Smart.” The “Only Buy” Likert item is ambiguous whether is loads under Factor 1 or 2. This means we should look at the Varimatrix Rotated Matrix where we can see that it’s much more clear that “Only Buy” loads under Factor 2. For Aveeno it is recommended to use the Varimatrix Rotated Matrix.
In Table 2 two factors had Eigenvalues > 1.0 (red, bolded numbers) and were extracted from the 10 Likert items. Both factors combined explained 62.7% of the variance in the original 10 Likert items.

In the Table 4 we can see that the majority of the factors load under Factor 1 for Olay except for “Smart.” There are no ambiguous numbers. For Olay we don’t have to look at the Varimatrix Rotated table because the Factor Matrix clearly shows under which factor each Likert item loads.
In Table 5 two factors had Eigenvalues > 1.0 (red, bolded numbers) and were extracted from the 10 Likert items. Both factors combined explained 58.9% of the variance in the original 10 Likert items.

In the Table 6 we can see that, once again, the majority of the factors load under Factor 1 except for “Greasy,” “Only Buy” and “Smart.” It is unclear which factor “Smart” loads under. When looking at the Varimatrix table it is clear that “Smart” loads under Factor 3, but “Consider” and “Best” are ambiguous. The Factor Matrix is not perfect, but it is better than the Varimatrix Rotated Matrix.
In Table 7 three factors had Eigenvalues > 1.0 (red, bolded numbers) and were extracted from the 10 Likert items. All three factors combined explain 67.5% of the variance in the original 10 Likert items.

# of Respondents = 67                                                                                             *p < 0.15

Olay had the highest Attitude Score, showing that the respondents had a more favorable attitude towards that brand. Although most of the respondents liked Olay, the difference between those who liked Aveeno and Olay was very small. Most respondents didn’t like Curel. Curel and Aveeno were the only two brands that were significantly different from each other, which means that in 85 or more samples drawn from the same population as this sample, only the Curel mean score would be about the same as reported here.

The data set from the 67 respondents were subjected to a K-Means Cluster analysis to determine if  the respondents could be grouped into clusters based on their responses to the ten brand attitude Likert items for Aveeno.  The clusters were then analyzed to determine if the clusters were differentiated on the basis of sex.

Total # of Respondents = 67                                                                                   *p < 0.15
SD = standard deviation

In the Two-Means Cluster group, the mean Likert score is higher in cluster 1 than cluster 2 for all attributes except for “Greasy.”  The pattern for the Three-Means Cluster is that the mean Likert score is higher for Cluster 2 except for “Greasy” again. The respondents are also distributed more evenly in the Two-Means Cluster than the Three-Means Cluster group.

The F ratios for the Two-Means Cluster indicate that all but “Smart” mean scores are significant meaning that in 85 or more samples out of every 100 samples drawn from the same population as this sample, it would be expected that the mean scores would be the same magnitude as in this sample expect for the “Smart” Likert Item.

The F ratios for the Three-Means Cluster indicate that all mean scores are significant meaning that in 85 or more samples out of every 100 samples drawn from the same population as this sample, it would be expected that the mean scores would be the same magnitude as in this sample.

*p < 0.15

The significance of Chi-Squared indicates that in 85 samples out of 100 samples drawn from the same population as this sample, the cross-tabulation displayed in Table 2 above would be about what it is here.  The results of this test can be projected to the population.