basic analysis

regression analysis

discriminant analysis

anova/manova

factor analysis

basic

The three perfume ads featuring singers from three different genres of music brought varying results. In order to explain the findings several tests were conducted. They are as follows: paired t-test, between groups t-test, chi-squared significance test, frequency, and two simple correlation tests.

Problem One: Paired t-test Comparing Brand Index Scores

Table A: Brand Index Score

Sample Size = 60
*p ≤ .15
This table represents the Brand Index Scores for the three brands tested. It proves that Shania by Shania Twain has the highest mean for Brand Index Score at 30.2. Therefore it can be said that respondents prefer it to the other two brands. Table A also shows the t-ratios. Belong by Celine Dion and In Control by Britney Spears are statistically significant, which means the answers in the sample can be projected onto the population. 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 Brand Index Score for Belong and In Control would be about the same as this sample. However, answers given for Shania can’t be projected onto the population because it is not statistically significant.

 

Problem Two: Between Groups t-test Comparing In Control Movers

Table B: Brand Index Scores for In Control

Table C: Advertising Index Scores for In Control

*p ≤ .15

Table B shows that 13 respondents reacted positively to the ad for In Control and gave it a higher score after seeing said ad. Also 13 respondents out of the 60 in the sample had a negative reaction to the ad and dropped their scores accordingly. The results for the Brand Index Score can’t be projected onto the population because they are not statistically significant.

Table C demonstrates the Advertising Index Score for In Control where out of a sample size of 60, 13 respondents reacted positively and are subsequently called up movers. At the same time 13 respondents exhibited a negative opinion and are referred to as down movers. 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 Ad Index Score for In Control would be about the same as this sample.

 

Problem Three: Chi-Squared Significance Test of Shania Movers

Table D: Chi-Squared Test-Shania

*p ≤ .15

In Table D, only 2 out of 60 (sample size) moved up in their opinion of Shania perfume and was above the median of 30.5. This means that after they viewed the Shania ad in the survey the respondents increased the points awarded to the Shania brand and the sum of their scores resulted above the median. A large 87% went down on their opinion of Shania perfume upon seeing the ad (20 respondents) but remained above the median making up 66.7% despite the negative feelings. Three respondents had a negative reaction and brought their division of points down for the brand and stayed below the median score. Eighteen of the respondents didn’t change their points for Shania (30%) and also were reported below the median. In the sample, eight respondents remained the same for the brand and kept above the median where nine increased opinion of Shania and were below the median.

The Chi-Squared score is statistically significant (20.9*) and therefore can be concluded that the responses for this survey can adequately be projected onto the population which this sample was derived. In 85 or more samples our of every 100 samples drawn from the same population as this sample it would be expected that the movers who changed their minds according to the median for Shania would be about the same as it shows in this sample.

Problem 4: Frequency of Pre-Exposure and Post-Exposure for Each Brand.

Table E: Mover Count for Three Brands

Sample Size = 60

This table demonstrates the number of respondents out of the total sample which moved up, down, or remained the same in their scoring after viewing the ads for each brand. The opinion of Shania was changed by 23 people who went down on their scoring, while 11 and 13 changed their mind negatively on Belong and In Control respectively. The majority of the respondents remained the same in each brand evaluation. In Control has the highest with 56.7% keeping their division of scores the same and Shania the lowest with 43.3%. Belong by Celine Dion had 31 respondents remain the same and 30% of the respondents changed their mind favorably towards the brand. In Control had 13 respondents (21.7%) move up after viewing the ad and Shania has 11 (18.3%) move up.

 

Problem Five: Frequency of Brand Index Score for Shania vs. In Control

Shania proved to have an overall higher Brand Index Score than In Control by Britney Spears. Out of the sample size of 60 respondents, 44 were more favorable to Shania by Shania Twain and only 16 for In Control. This is 73.3 % preferred Shania over 26.7% for In Control according to the Brand Index Scores which was a sum of the Likert questions in the survey.

 

Problem Six: Simple Correlation between Belong and In Control

Table F: Correlation of Brand Index Scores

                                                               Sample Size = 60
                                                                               *p ≤ .15

Table F shows that Belong by Celine Dion and In Control by Britney Spears are moderately correlated. It is also shown to be statistically significant and therefore can be assumed the judgements of the sample are connected to those of the population from which the sample was derived. In 85 or more samples our of every 100 samples drawn from the same population as this sample it would be expected that Belong would be fairly moderately correlated to the brand In Control as it shows the same in this sample.

 

Problem Seven: Simple Correlation between Belong and In Control among daily perfume                       
                           users.

Table G: Correlation of Brand Index Scores of Only Perfume Using Respondents

                                                                Sample Size = 60
                                                                               *p ≤ .15

During the survey, respondents were asked to tell how many times a day they used perfume. If they answered zero(0) then they were eliminated from the sample for this particular correlation test. When the variable is taken out Belong and In Control still have a very moderately correlated Brand Index Score. It is slightly higher at .428 rather than the .408 of total respondents in the sample. This too is statistically significant. In 85 or more samples our of every 100 samples drawn from the same population as this sample it would be expected that Belong would be fairly moderately correlated to the brand In Control as it shows the same in this sample.

 

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regression

A linear regression analysis was run on each of three brands of perfume: Shania, Belong, and In Control. The results are to determine if the 10 Likert items presented in the survey were positively or negatively related to the brand through a scatter plot. The results are derived from the pre-advertisement viewing minus the post-advertisement viewing scores known as the “change” score. This will conclude whether people who enjoyed the advertisements also enjoy the brand by comparing the Likert items (independent variable) against the change score (dependent variable)

Shania by Shania Twain Analysis

Table A

                                                                                                 *p≤.15
Table B

*p≤.15

Table A gives us the information that there is a moderate to high correlation (.7) between Shania and the Likert items that show how well the respondents agreed with the brand but a not very high percentage to show that correlation (43.8%). The standard error of the estimate (1.0) has an inverse relationship with the R and R-squared, therefore it has a relatively low error because the explain variance is moderately high. The F-ratio is to test the multiple R(R²) and is statistically significant (4.13*). In 85 or more samples out of every 100 samples drawn from the same population as this sample it would be expected that the change score for Shania would be about the same as this sample.           

Table B explains the line that would be drawn around the points on the scatter plot. The unstandardized coefficient is the slope (.1) so it is a positive upward line with a slight degree of slant. The remaining unstandardized coefficients are the dots plotted and if they are negative they are in the negative grid below the x-axis. Betas are the standardized coefficients and important in explaining the correlation of the change score. Those listed in bold are of relative importance: .8(good), .4(smell), .5(price), .4(use). T-ratio is the F-ratio to test “a” and “b’s” or the dependent variable and independent variables which some are noted to be statistically significant. In 85 or more samples out of every 100 samples drawn from the same population as this sample it would be expected that the change score for Shania would be about the same as this sample.

 

Belong by Celine Dion Analysis

Table A

Table B

*p≤.15

In Table A there is 19.6% of variance in the dependent variable explained by the independent variables shown in R². The correlation coefficient (R) is .4 which is a moderate correlation and thus signifies the standard error of the estimate to be moderate at 1.4. These terms show that most respondents either didn’t have a strong opinion (negative or positive) of Belong or didn’t voice their opinions in the Likert questions. The F-ratio is an inferential statistic however it is not statistically significant at 1.29.

The constant in Table B reveals a negative slope (-.4) so the line on the scatter plot would show a downward angle. The remaining unstandardized coefficients point out the other dots on the graph with the standard error from Table A demonstrating the average (mean) distance from the line in which the dots would be found. There are several important betas or standardized coefficients including: .5(good), .6(smell), .4(price), .3(trust), .3(use). Only one t-ratio is statistically 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 change score for “I don’t care for the smell of Belong perfume” question on the survey would be about the same as this sample. Having only seen the advertisement a respondent might not be able to make a valid response to this question if it had not be sampled so the results can be projected onto the population.

 

In Control by Britney Spears Analysis

Table A

There is a very low percentage (7.4%) showing the weak correlation (.3) explaining the relationship between In Control perfume and the Likert items in the survey. It is not statistically significant and can’t be projected to the population. The standard error of the estimate is the mean distance of respondents away from the regression equation line. It’s high in accord to the data and thus bad because the explain variance is low and it goes back to their inverse relationship.

The In Control change score reads: -.2+.0(good)+.5(smell)-.3(price)-.2(better)-.1(brand)+.0(sexy)-.3(in control)+.2(confident)+.1(not)+.1(day)

There are four standard coefficients that are important in explaining the correlated change score. The Betas are .4(smell), .3(price), .3(in control), .2(confident). All of the Betas and t-ratios are found in the following table.

Table B

*p≤.15

The t-ratio which tests the dependent variable (change score) and independent variables (Likert items) shows one statistically significant (1.6, smell). In 85 or more samples out of every 100 samples drawn from the same population as this sample it would be expected that the “I don’t like the smell of In Control perfume” would be about the same as this sample. If the respondent had not tested the perfume before the smell can not be determined from the advertisement and would more than likely have resulted in a “neither agree nor disagree” response with no strong feeling towards either end of the Likert scale. Thus, the answer to this particular question can be projected on to the population from which this sample was derived.
                       

 

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discriminant

In the essence of finding the target audience for In Control by Britney Spears brand of perfume a Linear Discriminant Analysis was performed. The independent variables consisted of the 10 Likert items for this brand and the dependent variable was the “up” or “down” movers. All respondents who stayed the same in their opinion of the brand pre- and post- ad viewing were ignored for this analysis. There was an equal number of “up” movers to “down” movers in this sample for In Control.

Table A: Likert Items – Up Movers

                                             Sample Size = 13
Group Centroid = .7

Table B: Likert Items – Down Movers

                                             Sample Size = 13
Group Centroid = -.7

Tables A and B show us the Mean and Standard Deviation for each of the Likert items asked on the survey for the respondents who moved up in their opinion of In Control via the ad shown and those who moved down, respectively. The sample size for each of these was 13 out of the total of 60 which means that 13 moved up and 13 moved down and the majority (34) stayed the same on their opinion.

Table C: Wilks’ Lambda and Chi-Squared

The Wilks’ Lambda measures the significance of the group centroids (found under Table A and B) in relation to the population in which the sample was derived. This table is used to project the sample data onto the population, however the Chi-Squared is not statistically significant and so the data from the sample can’t be inferred onto the population. The Group Centroids (.7 and -.7) are the averages of the dependent variables or z-scores.

Table D: Discriminant Function Coefficients

Discriminant Function Coefficients are the Likert items from the survey. The important standardized and unstandardized discriminant function coefficients are in bold to show the difference in up and down movers. These were determined significant by taking the absolute value of the highest coefficient and dividing by 2. If the number was larger than the outcome then it is deemed important. The unstandardized coefficients are the “b’s.”

Table E: Classification Results

Table E shows the number of respondents who were predicted to be up movers and actual were up movers (10) and the same for the down movers (11). It’s near perfect because only 2 or 3 were out of place in the prediction to what actually happened. Ten people were correctly predicted to be up movers and 11 people were correctly predicted to be down movers. The classification matrix states 80.8% of original grouped cases were correctly classified. [10+11=21/26=.808, where 26 is the number of cases considered up or down movers.]

Lastly, for the Discriminant Analysis is an inferential statistic. The t-ratio to test classification accuracy must be hand calculated as follows:
t-observed data =√[(.808)(.192)/60] + [(.5)(.5)/60]
                                                        = √[.003] + [.004]
                                                        = √[.007]
                                                        = .08

Since this t-ratio measure the accuracy of the classification matrix (80.8%) it can be proved statistically significant if the t-observed data is ≥ 1.04. This being false the classification matrix can’t be projected onto the population.

In conclusion, this is not a good discriminant analysis from many factors. The group centroids are close and the Wilks’ Lambda is not statistically significant which says this sample can’t be projected onto the population. The means for the two groups of Likert items are very close in number as well, which doesn’t conclude a strong connection on how well respondents perceive the brand. The classification results were strong and the groups had hardly any mixing, but are not statistically significant either. The rest of the analysis doesn’t show a good example from the population and only slightly discriminates.

 

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anova/manova

ANOVA
An analysis of variants, ANOVA, is where two or more independent variables are compared with one dependent variable. The independent factors were the move scores for Up, Down, and Same as well as Region split into East and West. The dependent factor was from the Likert question: Britney Spears is not a brand I trust. The test was conducted in order to find any significant relationship between the variables; such as if respondents didn’t respond well because they don’t like Britney Spears not necessarily the ad and if the part of the country makes a difference. The sample size was 60 and near even split across the country with 29 from the West and 30 from the East assuming one person didn’t answer the question.

Table A: Descriptive Statistics

The data previously stated shows the majority of respondents in East and West stayed the same and equal numbers moved up or down. The overall mean score for the East is slightly higher than the West but the numbers are all reflective and therefore similarly correlate. The highest mean score were the respondents who changed their score positively after viewing the ad and who also feel most strongly about the Britney Spears brand.

Table B: Inferential Statistics

*p≤.15

There is no significant difference between which region of the country and trusting the Britney Spears brand. There is also no significance if all boxes are added together (Move by Region). Therefore the sample can’t be projected onto the population.

MANOVA
A multivariate analysis (MANOVA) is where two or more independent variables are compared with two or more dependent variables. The independent variables stayed the same as in the ANOVA analysis but the dependent variables included all 10 of the Likert items in the survey. The sample size and region breakdowns are the same (60,29,30). This study also tests any significance between variables so if the manner in which the respondents answered the Likert questions had anything to do with how the ad was perceived or which part of the country they reside.

Table C: Descriptive Statistics

Table C reflects the descriptive statistics for the analysis of all 10 Likert items versus the change score for West and East regions of the country. Each cell shows the mean and standard deviation for the Up, Same, or Down Movers pre-to-post exposure of the ad for In Control. The sample size for the West was 6 Up, 17 Same, and 6 Down Movers. The East sample size was 7 Up, 16 Same, and 7 Down. Overall the mean scores from the East tended to be slightly higher than those from the West meaning they felt more positively toward In Control perfume or the Britney Spears brand.

The second to last question, In Control is not like any other perfume was left blank by almost everyone in the survey except respondent(s) from the East who didn’t change their opinion of the brand after seeing the ad. The greatest mean score was 3.7 reflecting that respondents from the East who increased their score after viewing the ad felt that In Control was a good brand of perfume. The lowest mean scores accounted for were 2.3 on non-moving respondents both from West and East who weren’t as sure about using In Control.

Table D: Inferential Statistics

*p≤.15

In the table the F-ratio is the determinant if the statistics are significant for the MANOVA test and can thus be projected onto the population. However as shown none of the results for Move, Region, or Move by Region were significant and therefore this sample can’t be projected onto the population from which it was derived. This was the same results found in the ANOVA analysis as well.

 

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factor

A Factor Analysis is conducted to make sure a scale is efficient according to EPA (Evaluative, Potency, Activity). This Factor Analysis will tell which of the three brands were preferred in regards to their Likert items(like/disklike). Using the 60 respondents in the sample an attitude score was organized for each brand based on an attitude scale using the 10 Likert items of each brand. These were subsequently compared by three paired t-tests to determine the brand that was perceived in the highest favorability.

Table A: Communalities and Factor Matrices for Shania

Table B: Total Variance for Shania

Table B shows us the two factors that were used in Table A because the first two factors were the only Eigenvalues greater than or equal to 1 or had the most explained variance. Table A takes these factors and compares them by absolute value to determine which factor the Likert item “loads” on. As the c