Part 1: Correlated t-Test

A brand index score was calculated for each of the three brands of body lotion, Johnson's, Aveeno, and Vaseline, in order to determine overall sample consumer preference. The lowest possible score is 10 and with the highest possible score being 50. In the sample of 61 respondents, a slight preference for Johnson's and Aveeno can be observed.

Each brand index score was then correlated with another to determine if results could be projected onto the population from which the original sample was taken.

In the first correlated t-test, Johnson's and Aveeno, the results were not statistically significant. The second correlated t-test was performed between Aveeno and Vaseline. With a t-ratio of 1.92, results were found to be significant with a preference for Aveeno. The final t-test was performed on Johnson's and Vaseline. With a t-ratio of 1.60, results were found to be significant with a preference for Johnson's. From this we can conclude that out of a sample of 100 from the original sample population, 85 of those samples will prefer Aveeno and Johnson's to Vaseline when presented with those three options.

Overall, Vaseline was the brand that was preferred the least. This sample also displayed equal preference for Johnson's and Aveeno.

Part 2: Between Groups t-Test

Using a sample of 61 respondents 2 between groups t-tests were conducted to determine the whether or not pre- and post-test scores had any significance. What was learned is that in 85 or more samples of every 100 samples chosen from the same population as this sample, we would expect up-movers (people who have a more favorable perception of the brand Vaseline after seeing the Vaseline advertisement than before) to have a more favorable perception of the Vaseline advertisement.

Part 3: Chi-Squared Significance Test

To determine if there is a significant relationship between those whose perceptions of the brand Aveeno went up, down or stayed the same after exposure to the advertisements for Aveeno, Johnson's, and Vaseline body lotion, a chi-squared test was conducted. Respondents were divided based on the median score (30) for the Aveeno's brand index score and on whether or not their opinions of Aveeno improved after exposure to the ad.

More respondents with above-median brand perceptions (57.1%) had improved brand perceptions after ad exposure than respondents with below-median brand perceptions (42.9%). Also notable is the finding that the majority of down-movers (71.4%) had above-median brand perceptions.

In 85 or more out of every 100 samples drawn from the same population as this sample, we would expect to find a cross tabulation distribution with the same proportions as this sample.

Part 4: Frequency Test for Changed Scores

A frequency test was conducted for all three brands of body lotion to analyze pre-to-post exposure changes in respondent's attitudes for each advertisement.

The most favorable pre-to-post scores are for Johnson's body lotion. 39.3% of respondents felt more favorably towards Johnson's body lotion after viewing the advertisements. Another notable change is the number of respondents (24) that felt more negatively towards Aveeno body lotion after viewing the advertisements.

Part 5: Frequencey Test for Brand Preference

In order to establish respondent preference for Aveeno or Johnson's body lotion, a frequency test was run on the difference between brand index scores for each brand. The results found that of the 61 respondents, 33 people preferred Aveeno to Johnson's.

Part 6: Simple Correlation Coefficient

A simple correlation coefficient test was conducted between the brand index scores for Johnson's and Aveeno body lotion to determine if a relationship between preferences for the two products exists. It was found that a very week positive correlation exists for the brands. It is also important to note that this correlation was found to be significant. As a result, if this study was conducted again on the same population from which this sample was taken, we would expect to see the same results.

Part 7: Subset Correlation Coefficient (females)

A simple correlation coefficient test was conducted between the brand index scores for Johnson's and Aveeno body lotion to determine if a relationship between preferences for the two products exists. It was found that a very weak positive correlation exists for the brands. What's interesting about this sample, is that once the males were eliminated from the sample, the correlation decreased and is also no longer significant.

This is a regression analysis for 3 brands of body lotion: Johnson’s, Vaseline, and Aveeno. It will show the contribution of 10 likert items in determining the pre-to-post change score. Data comes from 61 respondents of an online questionnaire and have been analyzed with the help of SPSS.

Part 1: Regression Analysis

Part 2: Johnson's Body Lotion

A regression analysis was done to determine the relationship between how respondents rated Johnson’s brand attributes and the change in scores pre-post ad exposure. R-squared is the percent of variance in the dependent variable explained by the independent variables. In this case, R-squared is 12.5% which indicates an extremely low explained variance. It also indicates that there is a very minimal relationship between how respondents rated Johnson’s brand attributes and the scores pre-post ad exposure. Furthermore, we can conclude that as a result of a low explained variance, the standard error of the estimate will be high. The F-ratio is 0.71 and was not found to be significant. As a result, in 85 or more samples of every 100 samples drawn from the same population as this sample, we would not expect to find the same results.

One brand attribute (prefer this brand to other brands) was found to be significant when looking at the t-ratio, which means that it is important in explaining the variance in pre-post ad exposure change scores. In 85 or more of the samples drawn from the same population as this sample, we would expect to find the same result for the “prefer this brand to other brands” brand attribute.

The following brand attributes are considered to be the most important variables in explaining the ad exposure change scores relative to other brand attributes: “Prefer this brand to other brands”, “will keep skin moisturized”, “People who use this brand are smart”, “Best brand of those listed”, and “Makes me feel good”.

Part 3: Vaseline Body Lotion

A regression analysis was done to determine the relationship between how respondents rated Vaseline brand attributes and the change in scores pre-post ad exposure. R-squared is the percent of variance in the dependent variable explained by the independent variables. In this case, R-squared is 16.4% which indicates an extremely low explained variance. It also indicates that there is a very minimal relationship between how respondents rated Vaseline brand attributes and the scores pre-post ad exposure. Furthermore, we can conclude that as a result of a low explained variance, the standard error of the estimate will be high. The F-ratio is 0.98 and was not found to be significant. As a result, in 85 or more samples of every 100 samples drawn from the same population as this sample, we would not expect to find the same results.

Two brand attributes (“prefer this brand to other brands” and “is the only brand I would buy”) were found to be significant when looking at the t-ratio, which means that they are important in explaining the variance in pre-post ad exposure change scores. In 85 or more of the samples drawn from the same population as this sample, we would expect to find the same results for the “prefer this brand to other brands” and “is the only brand I would buy” brand attributes.

The following brand attributes are considered to be the most important variables in explaining the ad exposure change scores relative to other brand attributes: “Good brand of body lotion”, “prefer this brand to other brands”, “will make skin feel smooth”, “is the only brand I would buy”, and “best brand of those listed”.

Part 4: Aveeno Body Lotion

A regression analysis was done to determine the relationship between how respondents rated Aveeno brand attributes and the change in scores pre-post ad exposure. R-squared is the percent of variance in the dependent variable explained by the independent variables. In this case, R-squared is 14.6% which indicates an extremely low explained variance. It also indicates that there is a very minimal relationship between how respondents rated Aveeno brand attributes and the scores pre-post ad exposure. Furthermore, we can conclude that as a result of a low explained variance, the standard error of the estimate will be high. The F-ratio is 0.58 and was not found to be significant. As a result, in 85 or more samples of every 100 samples drawn from the same population as this sample, we would not expect to find the same results.

One brand attributes (“is the only brand I would buy”) was found to be significant when looking at the t-ratio, which means that it is important in explaining the variance in pre-post ad exposure change scores. In 85 or more of the samples drawn from the same population as this sample, we would expect to find the same results for the “is the only brand I would buy” brand attribute.

The following brand attributes are considered to be the most important variables in explaining the ad exposure change scores relative to other brand attributes: “Would consider buying this brand” and “is the only brand I would buy”.

A discriminant analysis was conducted for one brand of body lotion, Vaseline, to determine if a relationship exists between how respondents rated ten brand attributes and their change in preference for the brand post after advertisement exposure. The respondents were split into three groups: up-movers if their perception of the brand improved after exposure to the advertisement, non-movers if their opinion of the brand stayed the same after exposure to the ad, and down-movers if their perception of the brand decreased after exposure to the ad. For the purposes of this analysis, only up-movers and down-movers were analyzed. This move score was used as the dependent variable and 10 different brand attributes (ten likert items) were used as independent variables.

Part 1: Brand Attributes

The analysis shows that the mean scores for up-movers and down-movers are similar to each other.  This means that there is not a significant connection between perceptions of the brand and how much they liked the advertisement.  The standardized discriminant coefficients showed that 3 attributes were found to be important: Vaseline won’t make skin feel greasy, people who use Vaseline are smart, and Vaseline is the best brand of body lotion. This means that these 3 likert items best account for the differences in pre-post exposure change scores between the two groups.
     
The unstandardized discriminant coefficients illustrate the relationship between each brand attribute and how much the respondents liked the ad:

1. The more respondents think Vaseline is a good brand, the less they liked the ad.             
2. The more respondents prefer Vaseline, the less they liked the ad.                                          
3. The more respondents would consider buying Vaseline, the more they liked the ad.
4. The more respondents think Vaseline will keep skin moisturized, the more they liked the ad.
5. The more respondents think Vaseline will make skin smooth, the less they liked the ad.
6. The more respondents think Vaseline won’t make skin feel greasy, the more they liked the ad.
7. The more respondents think Vaseline is the only brand of body lotion they would buy, the more they liked the ad.
8. The more respondents think Vaseline-users are smart, the less they liked the ad.                                                             
9. The more respondents think Vaseline is the best brand, the more they liked the ad.           
10. Whether or not respondents felt Vaseline would make them feel good had no effect on how much they liked the ad.

Part 2: Inferential Statistics

Neither the Wilks’ Lambda nor Chi-Squared were found to be significant in this analysis. This indicates that there is little relationship between how respondents perceived the brand and whether or not they liked the ad or not.  Therefore, the results indicate that in 85 or more samples out of every 100 samples drawn from the same population as this sample, we would not expect to find the same results.  Because Wilks’ Lambda is not significant we can also conclude that the Group Centroids, or the mean of the discriminant function scores, are also not significant and cannot be projected to the population.

Part 3: Classification

The classification matrix shows that 82.1% of the actual group cases were predicted correctly. This indicates a moderate to high accuracy rate when compared with the random probability of 50%. Of the 18 up-movers, 16 were grouped correctly into the predicted up-movers group and 2 were not grouped correctly. Of the 13 down-movers, 6 were grouped correctly into the predicted down-movers group and 7 were placed incorrectly.

The observed t-ratio of 2.70 is statistically significant when compared with critical t value of 1.04. Since the t-ratio is significant, in 85 or more samples out of 100 drawn from the same population as this sample, we would expect to find an accuracy rate of the same magnitude.

Part 1: Total Variance Explained

Two of 10 factors created for Johnson’s, Vaseline, and Aveeno body lotions have Eigenvalues greater than 1, indicating that they explain the variance of at least one likert item. For Johnson’s body lotion, 64.6% of the variance in ten likert item scores can be explained with these two factors (35.4% is unexplained variance). For Vaseline body lotion, 67.1% of the variance in ten likert item scores can be explained with these two factors (32.9% is unexplained variance). For Aveeno body lotion, 62.5% of the variance in ten likert item scores can be explained with these two factors (37.5% is unexplained variance).

Part 2a: Communalities - Johnson's

The Varimax Rotated Matrix was used in this analysis as it had the least amount of ambiguous rows (rows that had more than one factor greater than or equal to the absolute value of 0.5). For the brand, Johnson’s, all the items except for “would not make my skin feel greasy,” “I would only buy this brand,” and “people who use this brand are smarter than those who don’t,” loaded on factor 1. Thus, the factors that loaded in factor 1 are somehow related to one another and independent of other factors.

Part 2b: Communalities - Vaseline

The Factor Matrix was used in this analysis as it had the least amount of ambiguous rows (rows that had more than one factor greater than or equal to the absolute value of 0.5). For the brand, Vaseline, all the items except for “people who use this brand are smarter than those who don’t,” loaded on factor 1. Thus, the factors that loaded in factor 1 are somehow related to one another and independent of other factors.

Part 2c: Communalities - Aveeno

The Factor Matrix was used in this analysis as it had the least amount of ambiguous rows (rows that had more than one factor greater than or equal to the absolute value of 0.5). For the brand, Aveeno, all the items except for “people who use this brand are smarter than those who don’t,” loaded on factor 1. Thus, the factors that loaded in factor 1 are somehow related to one another and independent of other factors.

Part 3: Attitudes and Paired t-Tests