Basic Statistics | Regression Analysis | Discriminant Analysis | ANOVA/MANOVA | Brand Index Scores for each individual brand:
This table expresses the average of the ten Likert items for each brand on the survey. The standard deviations are also represented to show where about 68, 95 and 99 percent of the respondents are from the mean value. As you can see, Sun Chips has the highest average favorability with the respondents. Comparing Brand Index Scores:
*significant at P < or equal to 1.5 Respondents = 68 This graph shows “statistically significant” data, meaning if one was to pull 85 of 100 respondents from the same population as this sample, they would receive similar results allowing this data to be translated to the population as a whole. Wheat Thins Ad Index Score and Brand Index Score post viewing the ads:
This graph shows a slight difference in the respondents’ feelings, while most respondents didn’t favor the brand (brand index score moved down), they thought higher of the brand after seeing the ad (ad index score moved up). To advertisers this would prove to be a favorable outcome of the ad run. In both the brand index score and ad index score there is significance at the P > = .15, this allows for the data to be assumed on the whole population. If one was to pull 85 respondents of 100 from the same population as this sample, one would receive similar results as the table above. Chi-Square test for Wheat Thins with change score Wheat Thins score change Above median Below median Count 5 10 Move up % Row 33.3 66.7 Column 16.7 30.3 Total 7.9 15.9 Count 9 11 No move % Row 45.0 55.0 Column 30.0 33.3 Total 14.3 17.5 Count 16 12 Move down % Row 57.1 42.9 Column 47.6 52.4 Total 25.4 19.0 Respondents = 68 Chi-Square = 3.1* *P < or equal to .15 The results of the chi-square test are mostly to what is expected, the percentages are pretty even except for the move down row percent (57.1%). Respondents who originally started the survey favoring Wheat Thins, thought lower of the brand after viewing the ad. Also, 66.7% of respondents who originally started the survey NOT favoring Wheat Thins thought higher of brand after viewing the ad. These results are significant and can be applied to the population as a whole, meaning if one took a sample of 85 from a random 100 in the same population as this sample, the results would be similar to the ones above. All brand change score frequencies Brand Up Same Down Wheat Thins frequency 16 22 30 percentage 23.5 32.4 44.1 Flat Earth frequency 34 27 7 Percentage 50.0 39.7 10.3 Sun Chips frequency 15 23 30 Percentage 22.1 33.8 44.1 Respondents = 68 This chart shows the movement of respondents’ attitude toward the three brands prior and post ad viewing. Flat Earth has the highest move up score, with respondents commenting excitement for this new brand. Also with Flat Earth, a majority of respondents stayed the same, not being either positively or negatively affected by the ad. Most respondents moved down after seeing the Sun Chips and Wheat Thins ad, this might be because of the excitement for a new brand of chips. Brand Index Score equaling Wheat Thins > Flat Earth
Brand Index Frequency Percent Wheat Thins > Flat Earth 52 76.5 In a brand comparison, 76.5% of the respondents believed that Wheat Thins is a better brand than Flat Earth. This leaves the other 23.5% of the respondents to believe that Flat Earth is a worse or equal brand than Wheat Thins. Correlation between Wheat Thins and Flat Earth Brand Index score (All)
Brand Index Correlation Wheat Thins & Flat Earth .186 Wheat Thins and Flat Earth have a correlated score of .186 (1 is equal to a perfect correlation) meaning when Wheat Thins’ brand index score increases Flat Earth’s brand index score also increases and vice versa. The correlation is also significant so one could pull 85 respondents of 100 in the same population as this and receive similar results.
Correlation between Wheat Thins and Flat Earth Brand Index score (Men)
Brand Index Correlation Wheat Thins & Flat Earth .279 The correlation between Wheat Thins and Flat Earth is even higher when correlated with only the male respondents. Showing when the male respondents perception of one brand goes up or down, the perception of the other brand follows the same pattern.
A regression analysis allows one to see if there is any relationship between the respondent’s opinion of a brand and how a respondent viewed the brand’s print advertisement. The dependent variable is the difference between the post ad score and the pre ad score, while the independent variables are the ten Likert items within the survey. Correlation between change score and brand index score:
Respondents = 68 *p < = .15 The R square means that only 30.7% of the variance in the change score for Wheat Thins is explained by the 10 likert items for Wheat Thins. Because this percentage is low, it shows that there’s not much connection between how people view the brand and how they view the ad. The standard error of the estimate is 2.5; because R square is a low percentage, the standard error of the estimate is high. The F statistic is significant, meaning that in a sample of 85 or more drawn from the same population as this sample, it would be expected that the multiple correlation coefficient would be the same. Standardized and unstandardized coefficients:
Respondents = 68 *p < = .15 The variable “Healthy” is important because it has a Beta at least half the size of the largest Beta of .31 (the Beta of “Taste”). The variables “Taste,” “Healthy,” and “Feel Good” had a t score that proved to be significant to the pre to post change score meaning for these variables in 85 or more samples out of every 100 samples drawn from the same population as this sample, it would be expected that the correlation would be about the same as in this sample. Correlation between change score and brand index score:
Respondents = 68 *p < = .15 The R square means that only 22.9% of the variance in the change score for Flat Earth is explained by the 10 likert items for Flat Earth. Because this percentage is low, it shows that there’s not much connection between how people view the brand and how they view the ad. The standard error of the estimate is 2.2; because R square is a low percentage, the standard error of the estimate is high. The F statistic is significant, meaning that in a sample of 85 or more drawn from the same population as this sample, it would be expected that the multiple correlation coefficient would be the same. Standardized and unstandardized coefficients:
Respondents = 68 *p < = .15 The variable “Healthy” is important because it has a Beta at least half the size of the largest Beta of .32 (the Beta of “Consider”). The variable “Consider” had a t score that proved to be significant to the pre to post change score meaning for these variables in 85 or more samples out of every 100 samples drawn from the same population as this sample, it would be expected that the correlation would be about the same as in this sample. Correlation between change score and brand index score:
Respondents = 68 *p < = .15 The R square means that only 21.9% of the variance in the change score for Sun Chips is explained by the 10 likert items for Sun Chips. Because this percentage is low, it shows that there’s not much connection between how people view the brand and how they view the ad. The standard error of the estimate is 2.7; because R square is a low percentage, the standard error of the estimate is high. The F statistic is significant, meaning that in a sample of 85 or more drawn from the same population as this sample, it would be expected that the multiple correlation coefficient would be the same. Standardized and unstandardized coefficients:
Respondents = 68 *p < = .15 The variables “Feel good” and “Consider” are important because they have a Beta at least half the size of the largest Beta of .25 (the Beta of “Best Brand”). The variables “Prefer” and “Taste” had a t score that proved to be significant to the pre to post change score meaning for these variables in 85 or more samples out of every 100 samples drawn from the same population as this sample, it would be expected that the correlation would be about the same as in this sample. Multiple Regression for Wheat Thins: The general purpose of multiple regression is to learn more about the relationship between several independent or predictor variables and a dependent or criterion variable. Y=a+bx Change score for Wheat Thins = -1.5-.6+.4+.1+1+1+.1+.4-.3-.6-1.4 Change score for Wheat Thins = -1.4
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 Wheat Thins. 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 Wheat Thins brand’s survey section. Results are given below: Up Movers
n=16 Down Movers
n=30 Most of the mean scores for Wheat Thin’s 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. Group Centroids
df = 10 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 1.4, which tells us that there is a moderate level of separation between the two groups. Wilks’ lambda
*p< or equal to .15 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. Discriminant function coefficients
The above coefficients can be used to write the linear discriminant function (the actual line that separates the two groups). Important coefficients, those BOLDED in the “Standardized” 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., 0.6 is the largest value; any coefficient greater than 0.3 is important). For Wheat Thins, “Good brand,” “Well dip,” and “Feel good,” are the largest factors that account for the variance in respondents’ change scores.
This table shows how accurate the discriminant function is in separating the two groups. For this particular analysis, 9 of the up-movers and 28 of the down-movers were correctly categorized, for an overall accuracy of 80.4% percent. To determine the significance of this accuracy, a t-ratio is calculated:
*p ≤ .15 The critical value for t in a one-tailed test at p ≤ .15 is 1.04. Because t-observed (3.23) is greater than t-critical (1.04), the classification accuracy in this analysis is significant, meaning that we can expect a very similar accuracy (80.4%) to occur in at least 85 out of 100 samples from this population.
A survey of 68 respondents, where over half of the surveys were completed by females, was conducted to determine the perception of three different chips and the effects that print advertising has on that perception. In the two way factorial ANOVA test the dependent variable used was “Tastes good” for Wheat Thins. Here we attempt to determine a relationship between the two independent variables 1. Gender and 2. Wheat Thin’s movement score. This factorial analysis allows one to conclude results based on the independent variables, whereas the MANOVA analyzes the ten Likert items as dependent variables in the same manner. Two way factorial analysis of variance:
n = 68 The differences between the means in the genders are minimal though the largest difference sits in the non-movers category with the male mean at 4.7 and the female mean at 3.9. The group most sensitive to the dependent variable “Wheat Thins tastes good” are male non movers with a mean of 4.7 and the group least sensitive to the same category are female up movers with a mean of 3.7. Analysis of variance (ANOVA):
n = 68 *p < or equal to .15 Because none of the F-ratios proved to be significant, we can make the following statements: 1) in 85 or more of 100 samples drawn from the same population as this sample, we could not apply mean scores of the same magnitude among the change score groups (up/same/down). 2) In 85 or more of 100 samples drawn from the same population as this sample, we could not apply mean scores of the same magnitude among the gender groups (male/female). 3) in 85 or more of 100 samples drawn from the same population as this sample, we could not apply mean scores of the same magnitude among the change score groups by sex groups (up/female; same/female; down/female; up/male; same/male; down/male). Two way factorial multivariate analysis of variance:
When comparing all ten Likert items specific attributes stood out, in the category “Tastes good” female down movers had a mean of 4.1 whereas male down movers only had a mean of 2.0. In the “Well w/ dip” category male down movers mean is a very low 1.0 while the female mean for down movers is 3.5. Within the male gender the biggest difference lies in the “Well w/ dip” between the up movers with a mean of 3.5 and down movers with a mean of 1.0. Multivariate analysis of variance (MANOVA):
n = 68 *p < or equal to .15 With the F-ratio for the Wilks’ lambda, testing the significance of the change score, gender and the interaction between the two we can make the following statements 1) in 85 or more of 100 samples drawn from the same population as this sample, we would not expect to find mean scores of the same magnitude among the change score groups (up/same/down). 2) In 85 or more of 100 samples drawn from the same population as this sample, we would expect to find mean scores of the same magnitude among the sex groups (male/female). 3) in 85 or more of 100 samples drawn from the same population as this sample, we would not expect to find mean scores of the same magnitude among the change score groups by sex groups (up/female; same/female; down/female; up/male; same/male; down/male).
This procedure is used identify underlying factors that explain the correlations among a set of variables. Its purpose is often to summarize a large number of variables with a smaller number of factors. A factor analysis was performed on each brand of chips using the 10 Likert items of brand attributes to develop an attitude scale base. A paired t-test was then used to determine if these results could be used to predict the attitudes of the larger population.
For Wheat Thins, three of the factors had Eigenvalues greater than or equal to 1, indicating that each of these factors explained the variance of one of the Likert items. 66.1% of the variance can be explained by these three factors. Leaving 43.9% of the variance unexplained. For Flat Earth, three of the factors had Eigenvalues greater than or equal to 1, indicating that each of these factors explained the variance of one Likert item. 70.0% of the variance can be explained by these three factors. Leaving 30% of the variance unexplained. For Sun Chips, three of the factors had Eignenvalues greater than or equal to 1, indicating that each of these factors explained the variance of one of the Likert items. 68.6% of the variance can be explained by these three factors. Average Attitude Scores
Paired t test
n=68 *p< or equal to .15 The attitude scale reveals that this population has a higher opinion of Sun Chips (avg score 3.6) over both Wheat Thins and Flat Earth. Wheat Thins is close behind however with a score of 3.2. The paired t-test showed significance in all three paired samples, thus it can be concluded that in 85 or more samples of every 100 samples drawn from the same population as the 100 respondents, we can expect to find brand attitude scores similar to those of the respondents.
The following report contains a cluster analysis for Wheat Thins based on online surveys of three brands of chips, Wheat Thins, Flat Earth, and Sun Chips completed by 68 respondents. The purpose of this analysis was to group the respondents together into two and/or three clusters based on their responses on the ten Likert's items. The clusters would be validated by a crosstab analysis on the clusters and the gender of the respondents. The Two-cluster Group was used for analysis because it showed more even sample sizes than the Three-cluster Group. Descriptive Statistics and F-ratio for Two-cluster Group
The F ratios indicate that all but two of the mean scores are significant meaning that in 85 or more samples out of every 100 samples drawn from the same population as this sample of 64 people, it would be expected that the mean scores would be the same magnitude as in this sample. The attributes “well w/dip” and “healthy” do not have significant F ratios meaning that in 85 or more samples out of every 100 samples drawn from the same population as this sample of 68 people, it can NOT be expected that the mean scores would be the same magnitude as in this sample. Crosstab for Two-cluster Group
*p less than or equal to .15 A cross tab analysis was ran between the Clusters and whether or not the respondent was male or female. It was found that Cluster 2 contained more male and female respondents than Cluster I. The Chi-Square value was 2.36, showing significance, which means that in 85 or more samples out of 100 drawn from the same population as this sample of 68 people, we could project these numbers to that population.
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