ANALYSIS
This section explains how the initial data was gathered from the sample group.
| Basic Statistics Report | Regression Analysis | Discriminant Analysis |
| ANOVA / MANOVA | Factor Analysis | Cluster Analysis |
Basic Statistics Report
Below are some basic statistical methods performed on the survey data. This initial report identifies many concepts and relationships (such as Brand Index Scores, frequency counts, t-tests, and crosstabs) that will be used throughout the duration of this project.
1. Correlated (paired) t-tests comparing the Brand Index Scores (a sum of the 10 Likert question responses) for each of the three brands:
Based on the Brand Index Scores in Table 1.1, consumers rated Gillette the highest out of the three, but only by a very small margin. The paired t-tests (Table 1.2) are not significant, however, meaning that the above results may not be the same in 85 out of 100 samples from the same population.
2. For the brand Gillette, a between-groups t-test comparing the Brand Index Scores and Ad Index Scores (number of ‘favorable’ survey responses answered for the ad) of (1) the respondents whose constant-sum scale moved up pre-to-post exposure, and (2) those whose scale moved down:
Those in the “move up” group gave a higher Brand Index Score for the Gillette brand and they also liked the Gillette ad better than those in the “move down” group. The Ad Index Score of both groups is significant, so the means will be the same in 85 out of every 100 samples drawn from the same population. This significance will not necessarily be true for the Brand Index Score, however.
3. For the Sure brand, a crosstab table of a Chi-square significance test that will show if there is a relationship between up, same, and down pre-to-post movers and being above or below the median Brand Index Score:
According to Table 3.1, the relationship appears to be a negative or opposite one — a larger number of those whose pre-to-post score moved up or stayed the same had Brand Index Scores that were below the median (8 above/9 below for up-movers, 12 below/7 above for stayed-samers). And a larger number who moved down after seeing the ad still had Brand Index Scores above the median (11 above, 9 below for down-movers). This may suggest that the Sure ad is not effective enough; in other words, it cannot bring up the brand perception enough to get people over the median score. This Chi-squared test is not significant, so it is uncertain if these same results will occur in 85 out of every 100 samples from the same population.
4. Frequency chart showing how many respondents’ constant-sum scores moved up, stayed the same, or moved down after being exposed to the ads for all three brands:
Table 4.1 shows that the Adidas ad was the most effective one in the study, bringing up the change score of 28 respondents after exposure. Conversely, the Sure ad was the least effective, only increasing the change score of 18 respondents. The Sure ad also caused the most scores to move down (23). Advertisers at Adidas might see these results and give themselves a pat on the back, while marketers at Sure might want to kick themselves and try to create a better ad next time.
5. Comparison of Brand Index Scores for Gillette versus Brand Index Scores for Adidas to see which brand the respondents have ranked higher:
Table 5.1 shows us that 35 respondents had a higher Brand Index Score for Gillette, meaning that a majority (56.5%) of those who took the survey favored the Gillette brand over the Adidas brand. Referring back to Table 1.1 will confirm this result, as the Gillette brand had the highest overall mean Brand Index score.
6. Simple correlation coefficient between Gillette Brand Index Scores and Adidas Brand Index Scores:
A correlation coefficient of .43 suggests that the relationship between the two Brand Index Scores is only a moderate positive one. This result is significant, meaning that the same correlation coefficient can be expected in 85 out of 100 samples drawn from the same population.
7. Brand Index Score comparison (Gillette vs. Adidas, from problem #5 above) repeated, but with only a select number of cases included. All respondents of age 35 and older are not considered in this chart:
Remaining consistent with the results from the initial comparison shown in Table 5.1, the younger respondents (under age 35) in the survey have also given Gillette a higher Brand Index Score than Adidas, as seen in Table 7.1 above. Advertisers at Gillette may see such results and be glad that their brand has a favorable perception among young people.
Regression Analysis
In statistics, one method of studying the relationship between sets of variables is the regression model. Between only two variables, a simple regression line can be drawn. If there is one dependent variable but many independent variables, the multiple regression model must be employed. Using recent survey results, three multiple regression analyses were conducted, one for each test brand — Sure, Gillette, and Adidas. For each analysis, the dependent variable is the brand’s change score from pre-to-post advertisement exposure and the independent variables are its ten Likert items. Results are given below:
1. Sure: Based on the coefficient of multiple determination (R2), the relationship between the dependent and independent variables is not very strong at all. Table 8.1 shows that only 17.6 percent of the variance in Sure’s change score (dependent variable) is explained by its 10 Likert items (independent variables). This means that respondents’ perception of the Sure brand was not greatly affected by the Sure advertisement they were shown. The F-ratio is not significant so we are unable to project the results from Sure’s model onto the whole population.
2. Gillette: The coefficient of multiple determination indicates the relationship between Gillette’s variables is slightly stronger than the one in the first model (Sure), but it is still relatively weak overall. As seen in Table 8.1, 22.4 percent of the variance in Gillette’s change score is explained by its 10 Likert items. A small percentage for R2 shows that perception of the Gillette brand was not greatly affected by the Gillette ad seen in the survey. Since its F-ratio is not significant, these multiple regression statistics may not be similar in 85 out of 100 samples taken from this same population.
3. Adidas: The statistics for the Adidas multiple regression model are nearly identical to the figures in the row above it (Gillette). The relationship between the dependent and independent variables is not very strong, as seen in Table 8.1 which lists 22.3 percent of the variance in Adidas’s change score is explained by its 10 Likert items. This means that respondents’ perception of the Adidas brand did not greatly change due to the ad they were shown. The F-ratio is not significant so the above results may not be the same in 85 out of 100 samples from this same population.
All the numbers in the b column give the coefficients for the multiple regression equation. Using these figures, the regression model for the Sure brand can be written as follows:
Sure’s constant-sum score change = -5.8 – 1.0(good brand) – 0.2(prefer brand) –
1.3(consider buying) + 0.7(men only) + 0.1(fit lifestyle) + 0.9(best brand) + 1.2(trusted brand) – 0.2(only brand) + 0.2(not use) + 1.2(recommend)
The same format can be used to write the regression models for the other two brands, as well.
Important Beta (β) items (those highlighted in Table 9.1) are ones that have a noticeable effect on the variance of the dependent variable. Betas are important if they equal at least half of the largest Beta score. For Sure, “consider buying,” “best brand,” “trusted brand,” and “recommend” are the largest factors that account for the variance in the change score. The t-ratios indicate significance of the constant term (a) and/or the unstandardized regression coefficients (b), telling which of these statistics can be accurately projected to the whole population. In the Sure model, constant term, “consider buying,” “men only,” “best brand,” and “trusted brand” are the figures that should end up nearly the same in 85 out of 100 samples taken from this same population.
For Gillette, the important Beta items are “fit lifestyle,” “trusted brand,” “not use,” and “recommend.” These impact the variance in the change score the most. Significant items for Gillette are “fit lifestyle” and “trusted brand,” meaning the numbers from those two should come out very similar in 85 out of 100 samples taken from this population. All other Likert items are insignificant and may not generate the same results in further samples.
The important Beta items for Adidas are “good brand,” “prefer brand,” “consider buying,” “fit lifestyle,” “best brand,” and “not use.” These items affect the variance in the change score the most. For Adidas, constant term, “consider buying,” and “not use” are significant, so the results from those three would likely be almost the same in 85 out of 100 samples taken from the same population. The rest of the Likert items are not significant and cannot be accurately projected to the whole population.
Discriminant Analysis
In statistics, discriminant analysis is used to show differences between certain qualities or groups based on their independent variables. A discriminant function line drawn through a scatterplot of data can be thought of as an imaginary “fence” that separates similar points into groups. Using recent survey results, a discriminant function was conducted using the Sure brand of deodorant. For this analysis, the two groups selected are (1) respondents whose change score moved up on pre-to-post advertisement exposure and (2) respondents whose change score moved down. The independent variables tested are the ten Likert items from the Sure brand’s survey section. Results are given below:
In the survey results, the Sure brand contained the most even split of up- and down-movers with 18 and 23 respondents, respectively. Most of the mean scores for the 10 Likert items are very similar between these two groups. This suggests that the points are not very far apart on a scatterplot and therefore they will be sitting fairly close to the discriminant function line that separates the groups.
The group centroids indicate the mean function score of each group, or the average location of all the points. The distance between these two means is 1.2, which tells us that there is a moderate level of separation between the two groups. Wilks’ Lambda tests the significance of these group centroids using the Chi-squared distribution. Since Wilks’ Lambda is not significant in this case, we cannot be certain that the same values will be generated for the group centroids in 85 out of 100 samples from this population.
The above coefficients in Table 10.3 can be used to write the linear discriminant function (the actual line that separates the two groups). Important coefficients, those highlighted in the “Standard” column above, are ones that have the most noticeable effect on the variance of the dependent variable. Coefficients are considered important if they equal at least half of the largest value (i.e., 1.3 is the largest value; any coefficient greater than 0.65 is important). For Sure, “good brand,” “best brand,” and “only brand,” are the largest factors that account for the variance in respondents’ change scores.
Table 10.4 shows how accurate the discriminant function is in separating the two groups. For this particular analysis, 11 of the up-movers and 17 of the down-movers were correctly categorized, for an overall accuracy of 68.3 percent. To determine the significance of this accuracy, a t-ratio is calculated:
The critical value for t in a one-tailed test at p ≤ .15 is 1.04. Because t-observed (1.72) is greater than
t-critical (1.04), the classification accuracy in this analysis is significant, meaning that we can expect a very similar accuracy (68.3%) to occur in at least 85 out of 100 samples from this population.
ANOVA / MANOVA
In statistics, analysis of variance (ANOVA) is a model in which the overall variance of a certain group is broken down into smaller components to see how much each individual variable affects the overall group variation. For this particular report, a two-way factorial ANOVA is conducted on the Gillette brand of deodorant, where the two independent factors are (1) respondents’ change score from pre-to-post advertisement exposure and (2) whether or not respondents always buy the same brand of deodorant. The dependent variable is a Likert item from a survey that asked respondents to rank the statement, “Gillette is a good brand.”
Also conducted is a multiple analysis of variance (MANOVA) which utilizes all the same inputs as the ANOVA test, except it includes all 10 Likert items as dependent variables instead of just one.
Results are given below:
The groups of respondents who do not always buy the same brand of deodorant have a higher mean score for the “good brand” Likert item, meaning that those consumers who are not loyal to a particular brand feel slightly more favorable to the Gillette brand based on the advertisement they saw.
The F-ratios for both the “Change Score” and the “Change Score by Same Brand” analyses are significant. Since the F-ratio for the multiplied Interaction ANOVA (3rd row of numbers) is significant, we can apply this significance to all groups. Therefore, we can expect all the Group Means in Table 11.1 to be very similar in 85 out of 100 samples taken from this same population.
In the Gillette MANOVA, none of the F-ratios are significant at the 85 percent confidence level, so none of the Group Means in Table 12.1 can be accurately projected to the whole population. The statistics may vary if more samples are taken.
Factor Analysis
In statistics, factor analysis is a model in which many variables and data are summarized by being reduced into a fewer number of variables called factors. For this particular report, we are using factor analysis to conduct an “item analysis” which will then be used to create an attitude score. A total of three factor analyses will be performed, one for each brand of men’s deodorant: Sure, Gillette, and Adidas. The variables used in the analyses are the 10 Likert items for each brand.
When it is determined which factor the “good” Likert item loads in, all of the Likert items that load in the same “good” factor will be averaged to come up with an Attitude Score for each brand.
Results are given below:
The Eigenvalue is the sum of squared factor loadings for each given factor. It indicates how much of the overall variance is accounted for in that one factor. An Eigenvalue less than 1.0 means that particular factor accounts for less than 10 percent of the variance in the initial variables (the ten Likert items) — any such factors therefore are not strong enough to be significant. For the Sure brand, 2 factors have Eigenvalues greater than 1.0. These 2 factors combine to explain 62.0% of the variance in the original ten Likert items (38.0% of the variance is unexplained). For Gillette, 3 strong factors account for 71.0% of the variance (29.0% is unexplained). The Adidas analysis also has 3 significant factors that explain 63.5% of the variance (36.5% is unexplained variance).
[ Communalitiy and Factor Loading ]
Squared factor loadings indicate the percentage of variance in the original variables explained by each factor. For example, in Table 14.1, 80 percent of the variance in the Sure brand’s original “Good” variable is explained by Factor I. Important factor loadings are any that have an absolute value of 0.5 or higher. When all the squared factor loadings are added together, the result is called a communality (h2). Communalities show how much of the original variable’s variance is explained by all factors together.
For the Sure brand, the original Factor Matrix columns can be used to generate the attitude score because there were not any ambiguous or problem rows. There is no need to use the Varimax Rotated Matrix columns because they do not improve the results.
For the Gillette brand, the original Factor Matrix columns will be used to generate the attitude score because there was a fewer number of ambiguous or problem rows (only 2). The Varimax Rotated Matrix columns do not improve the results; in fact, they give worse results (3 ambiguous rows).
For the Adidas brand, we will use the Varimax Rotated Matrix to generate the attitude score because it has a fewer number of ambiguous or problem rows (only 3) compared to the original Factor Matrix columns (6 problem rows). In this case, the Varimax Rotation does improve the results.
[ Attitude Scores ]
An attitude score was calculated for each brand by taking the average of all the Likert items that load on the same factor as the given brand’s “Good” item.
Paired t-tests are conducted between the three brands’ attitude scores to test their significance to the overall population.
The paired t-tests indicate that in 85 or more samples out of every 100 samples drawn from this same population, it is expected that the differences between brand attitude scores for Sure and Adidas and for Gillette and Adidas would be similar to what they are in this sample. The difference between brand attitude scores for Sure and Gillette is not significant and cannot be projected to the whole population.
Cluster Analysis
In statistics, cluster analysis is a classification model in which many variables and data are summarized by being reduced into a number of groups called clusters. Cluster analysis is often the first step in data mining, a process that involves searching through vast amounts of data to find certain information or relationships. For this report, the clusters are derived from survey responses to ten Likert item questions for the Gillette brand of men’s deodorant. After the clusters are determined they will be validated by comparing them to a demographic variable by use of a Chi-squared significance test and a crosstab table.
Results are given below:
Based on the mean scores between the two clusters, it appears that Cluster 1 had a more positive response to the Gillette brand while Cluster 2 had a more negative response to it. The mean response is higher in Cluster 1 for all but one row.
The two-cluster separation for Gillette had the closest group sizes among the three brands in both two- and three-cluster tests. Here is the breakdown of cluster group sizes:
Significance test:
For all ten Likert items, the F-ratios indicate that the cluster means and standard deviations from Table 16.1 are significant, telling us that all means and standard deviations from the Gillette two-means cluster analysis should be very similar in at least 85 out of 100 samples taken from this same population.
Clusters 1 and 2 from Table 16.1 are compared to a demographic variable that came from the same survey as the Likert items. The variable chosen is the set of responses to the question, “Do you always purchase the same brand of deodorant?” in which respondents could answer either Yes or No.
Since the Chi-squared value is significant, we can project the statistics from this crosstab table onto the whole population: In 85 out of 100 samples taken from the same population as this one, the cell counts and percentages would be about the same as they are in Table 16.4 above.
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