Basic Statistics
Multiple Regression Analysis
Discriminant Analysis
ANOVA/MANOVA
Factor Analysis
Cluster Analysis

Basic Statistics

Question 1. Paired t-Test
The paired t-test utilizes Brand Index Scores for each brand examined and aims to determine if the differences in the means between each brand and each other brand are statistically significant.

Table 1. Brand Index Score Statistics

Sample Size=70

The perception of Dove is higher than for Suave, which is in turn higher than Sunsilk, as indicated by the Brand Index Scores which are a compilation of ten judgments by the respondents. This is the case for both the sample respondents and the target audience members.

Table 2. Paired t Test of Mean Brand Index Scores

*p ≤ .15

In 85 or more samples out of every 100 samples drawn from the same populations as this sample, the mean scores for Sunsilk & Dove, Sunsilk & Suave, and Dove & Suave would be about what they are in this sample. The results of this sample can be projected to the population for these tests.

Question 2. Independent t-Test
Respondents were asked to rate their likelihood of purchasing each of the three brands on a constant-sum scale both before and after viewing the advertisement for each brand. Two groups are formed based on whether they are more likely to purchase post ad (Move Up) or less likely to purchase (Move Down). The independent t-test analysis is used in conjunction with the Ad Index Score and Brand Index Score Variables.

Table 3. Suave Statistics for Purchase Intention after viewing ad

Sample Size Intention Move Up = 10, Sample Size Intention Move Down = 38

The constant-sum scale shows that for Suave, 10 respondents had increased intentions of purchasing while 38 had decreased intentions. For respondents whose Suave scores increased after exposure (“Move Up”), mean Brand Index Scores were lower and mean Ad Index scores were higher than respondents whose Suave scores decreased after exposure (“Move Down”).

Table 4. Suave Independent Samples t Test Comparing “Up” & “Down” Movers

*p ≤ .15

In 85 or more samples out of every 100 samples drawn from the same populations as this sample, the mean Brand Index Scores between “Up” and “Down” movers for Suave was not found to be significant, and therefore cannot be projected to the population for this test. However, in 85 or more samples out of every 100 samples drawn from the same populations as this sample, the mean Ad Index Scores for Suave would be about what they are in this sample. The results of this sample can be projected to the population for this test.

Question 3. Chi-Square
A chi-square significance test is used to determine if there is a significant relationship between Suave up, same, and down pre/post movers and being above or below the median Suave Brand Index Score.

Table 5. Relationship between Suave Purchase Intent and Brand Index Score

Table 6. Suave Chi-Square

*p ≤ .15

A chi-square test determined that there is a statistically significant relationship between a respondent’s intention to purchase Suave (moving up, moving down, or staying the same) and whether the respondents brand index score for Suave was above or below the median Suave brand index score of 32. In 85 samples of out 100 samples taken from the same population as this sample, it would be expected that the results would be about what it is here. The results of this sample can be projected on the population.

Question 4. Frequency Count
A frequency count will determine how many respondents’ purchase intentions went up, stayed the same, or went down pre-to-post ad exposure based on the constant-sum scale for the brands Sunsilk, Suave, and Dove.

Table 6. Post Ad Exposure Purchase Intent Change

Question 5. Brand Preference Comparison
The total number of respondent Brand Index Scores for Dove and Sunsilk are compared to determine which brand is preferred more often among the respondents.

Table 7. Brand Index Score Comparison: Dove versus Sunsilk

In a sample size of 70 people, there were 39 people who preferred Dove shampoo to Sunsilk shampoo.

Question 6. Correlation
The Pearson correlation coefficient is used to determine if the Suave and Dove Brand Index Scores are significant.

Table 8. Correlation Coefficient

*p ≤ .15

The correlation coefficient between the Suave and Dove Brand Index Scores did not prove significant.

Question 7. Female Respondent Correlation
The Pearson correlation coefficient is used again to determine if the Suave and Dove Brand Index Scores are significant among only female survey respondents.

Table 9. Female Respondent Correlation Coefficient

*p ≤ .15

The correlation coefficient for only Female respondents between Suave and Dove Brand Index Scores did not prove significant.

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Multiple Regression Analysis

This report analysis derives from an online survey distributed online to test three print advertisements for shampoo brands. Seventy usable respondent data was collected.  Each brand results of this survey are subjected to multiple linear regression analyses.  The independent variables consist of ten Likert questions regarding specific attributes of the three shampoo brands. The dependent variable is the change in the respondent’s intention to purchase the brand after exposure of the three advertisements on a constant-sum scale.

Table 1. Multiple Linear Regression Analysis of Shampoo Brands

Table 2: Sunsilk Brand Attributes

In this sample, the brand attributes for Sunsilk accounted for a small portion (14.0%) of the variance in pre/post change scores. This means that only 14.0% of how much respondents liked the ad is explained by how much they like the brand. Neither the F-ratio of .96, nor the un-standardized regression coefficient constant of -1.0 were found to be statistically significant; therefore the results of these sample cannot be projected to the population. Only one of the brand attributes – I would recommend Sunsilk to a friend – had a statistically significant impact; in 85 out of 100 samples drawn from the same population as this sample, it would be expected that this coefficient would be about what they are here. The brand attributes that are important independent variables in explaining variance include: good shampoo, prefer over other brands, good smell, and recommend.

Table 3: Dove Brand Attributes

In this sample, the brand attributes for Dove accounted for a small portion (13.2%) of the variance in pre/post change scores. This means that only 13.2% of how much respondents liked the ad is explained by how much they like the brand. The F-ratio of .90 was not found to be statistically significant; therefore the results of this sample cannot be projected to the population. The un-standardized coefficient constant value of 3.9 was found to be statistically significant which means in 85 or more samples out of every 100 drawn from the same population as this sample, we would expect the un-standardized regression coefficient to be about what they are in this sample. Only one of the brand attributes – I think Dove is a good smelling shampoo – had a statistically significant impact; in 85 out of 100 samples drawn from the same population as this sample, it would be expected that these two coefficients would be about what they are here. The brand attributes that are important independent variables in explaining variance include: good shampoo, like how the shampoo makes their hair feel, improves hair quality, and has a good smell.

Table 4: Suave Brand Attributes

In this sample, the brand attributes for Suave accounted for a small portion (16.3%) of the variance in pre/post change scores. This means that only 16.3% of how much respondents liked the ad is explained by how much they like the brand. Neither the F-ratio of 1.15, nor the un-standardized regression coefficient constant of -.9 were found to be statistically significant; therefore the results of these sample cannot be projected to the population.  None of the brand attributes for Suave were found to be significant and therefore cannot be projected to the population. The brand attributes that are important independent variables in explaining variance include: prefer brand to others, the brand is expensive, improves hair quality, makes user feel confident, and do not use brand.

Multiple Regression Equation for Suave:
Change Score Suave= -.9 -.2(good) -.4(prefer) +.5(expensive) -.1(likehair) +.3(improves) +0(same) -.4(confident) +.3(notuse) -.2(goodsmell) -.2(recommend)

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Discriminant Analysis

In a sample of 70 respondents, a multiple discriminant analysis is conducted in order to determine if respondents’ attitudes towards the Dove brand affected whether the respondents were “up-movers” or “down-movers.”  “Up-movers” are those respondents who had a positive change score for Dove on the constant sum scale after viewing the advertisements, while “down-movers” had a negative score.  The dependent variable in this analysis is group membership (up and down movers), while the independent variables are the scores on the ten brand attitude Likert items.

Note: None of the brands under consideration provided an ideal, balanced distribution of up- and down- movers for discriminant analysis. Dove was selected as the brand with the smallest difference between up-movers and down-movers.

Table 1: Dove Brand Attributes

In the table above, the majority of the mean ten Likert attributes do not vary much from up movers to down movers. Eight differ only .2 point or less, while two (I prefer Dove and Dove has a good smell) differ by .5 points. Because of the relatively close means between up movers and down movers, it can be concluded that there are few if any differences between the two groups’ perceptions of Dove as a brand. The attributes that appear to be the most important brand in determining whether respondents were up movers or down movers are “I prefer Dove,” “Dove improves my hair quality,” “Dove has a good smell,” and “I would recommend Dove to my friends.”

Table 2: Group Centroids

The difference between the average discriminant scores of up movers (-0.4) and down movers (0.6) is 1.  This difference is neither great nor statistically significant.

Table 3: Inferential Statistics

The Wilks Lambda test, when converted to Chi-squared, is not statistically significant.  Thus it would not be expected that in 85 samples out of 100 samples drawn from the same population as this sample, the difference between the up movers’ and down movers’ group centroids would be what it is here.  The group centroids cannot be projected to the larger population.

Table 4: Classification Matrix

According to the classification matrix, 35 out of 48 respondents (72.9%) fall into their predicted groups.

Table 5: Significance of Classification Matrix

At 72.9%, 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 classification percentage of cases correctly classified would be about what it is here.

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ANOVA/MANOVA

The data was subjected to two analyses of variance – one univariate, one multivariate.  The independent categorical variables for these tests were mover group (up-, down- or non-) and gender. In the first test, the dependent variable is the respondent’s Likert score in response to the prompt “Suave has a good smell.”  In the second test, the dependent variables are the Likert scores for each of the brand attribute questions on the survey.

Table 1: Mean scores for different groups on "Suave has a good smell.”

Table 2: Tests of Between-Groups Effects

The F-Ratio is significant for all three effects. In 85 samples out of 100 samples drawn from the same population as this sample, it would be expected that the difference in the mean Likert scores on “Suave has a good smell” between males and females would be about what it is here. In 85 or more samples out of every 100 drawn from the same population as this sample, it would be expected that the results between “Suave has a good smell” and Up-,Non-, and Down-movers will be about what it is here. In 85 or more samples out of every 100 drawn from the same population as this sample, it would be expected that the results between “Suave has a good smell” by Up-,Non-, and Down-movers and gender will be about what it is here. The results of these three tests can be projected to the population.

Table 3: Multivariate Analysis of Variance for Suave

Table 4: Multivariate Tests

The F-Ratio is significant for all three effects. In 85 samples out of 100 samples drawn from the same population as this sample, it would be expected that the results between the dependent variables and gender would be about what it is here. In 85 or more samples out of every 100 drawn from the same population as this sample, it would be expected that the results between the dependent variables and Up-,Non-, and Down-movers will be about what it is here. In 85 or more samples out of every 100 drawn from the same population as this sample, it would be expected that the results between the dependent variables by Up-,Non-, and Down-movers and gender will be about what it is here. The results of these three tests can be projected to the population.

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Factor Analysis

The data was subjected to a factor analysis to conclude how the brand attitude Likert items for each brand are related to each other.  Variables that load on the same factor as “[Brand] is a good brand” were taken to be indications of how much a respondent liked a brand. These variables were then combined into new attitude scores for each brand.  The means of these new attitude scores were compared using a t-test to test for statistical significance.

Table 1: Brand Descriptive Statistics

For Sunsilk, there are three factors that can account for at least one Likert item, which together account for 64.9% of the variance.  For Dove, two factors can account for at least one Likert item and together they account for 62.8% of the variance.  For Suave, two factors can account for at least one Likert item and together they account for 70.7% of the variance.        

Table 2: Sunsilk Statistics

Table 3: Dove Statistics

Table 4: Suave Statistics

Table 5: Brand Means and Standard Deviations

The mean attitude scores show that overall, survey respondents prefer the shampoos in order of Dove (3.3), Suave (3.1), and Sunsilk (3.0).

Table 6: Paired t-Test

The results of these paired t-tests demonstrate that in 85 samples out of 100 samples drawn from the same population as this sample, the mean attitude scores for Sunsilk, Dove, and Suave would be about what they are here. The results of these tests can be projected to the population.

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Cluster Analysis

The data collected is subjected to a cluster analysis to determine if respondents can be grouped into clusters based on their responses to the ten brand attitude Likert items for Suave.  The clusters were then analyzed to determine if the clusters were differentiated on the basis of gender.

Table 1: Likert Means and Standard Deviations for Likerts per Cluster

In the this three-means cluster analysis, the mean Likert score is higher in cluster 3 than clusters 1 and 2 for all attributes except “Suave is the same as other brands,” and “Suave is expensive.”

Table 2: F-Ratios for Suave Likert Items, 3 Cluster Analysis

In 85 samples out of 100 samples drawn from the same population as this sample, the cross-tabulation displayed above would be about what it is here.  The results of this test can be projected to the