Basic Statistics | Regression Analysis | Discriminant Analysis | ANOVA/MANOVA | Correlated t-test across Brand Index Scores The respondents showed the most positive attitude toward Sun Chips brand based on the brand index score which is a compilation of the respondents' responses on the ten Likert's items. Sun Chips had a mean of 32.7, while Wheat Thins had a mean of 31.4, and Flat Earth had a mean of 27.6. However, all three mean scores were in the middle range indicating that the respondents, on average, had neutral feelings towards all three brands. Because the t-tests for all three brands were significant, this is true for both the sample and the population. Between-group t-test: Pre-to-post Exposure to Ad For Wheat Thins, about 32% of the respondents gave lower preference score after seeing the ad than before seeing the ad while only 29% gave higher score. The mean brand index score for the respondents who moved down was also higher than the mean brand index score of the respondents who moved up. The decrease of post-exposure preference score among the respondents who viewed the brand more positively might be the result of their negative attitude toward Wheat Thins' ad or the more postive attitude toward other ads resulting in them giving more preference score to other brand than to Wheat Thins. This result is statistically significant and thus could be projected to the rest of the population. While the brand index score indicates how the respondents feel toward the brand, the ad index score, on the other hand, indicates how the respondents feel toward the ad. The up-movers showed higher ad index score than the down-movers indicating that the respondents who increased their preference score after seeing the ad were the respondents who liked the ad. Based on the t-ratio, this was true in both the sample and the rest of the population. Chi-squared Significance Test: Relationship between High/Low Brand Index Scores and Up/Same/Down Movers The greatest number of respondents (n=16) fell within the category of those who gave lower preference score after seeing the ad but had the brand index score above the median. This indicated that for those who had brand index score above the median, more than half gave lower preference score after seeing the ad while the rest were almost equally distributed between non-movers and up-movers. On the other hand, for the respondents who had the brand index score below the median, 11 stayed the same while 10 moved up and 12 moved down. These percentages between the respondents who moved up, stayed the same, or moved down and below and above the brand index score median could be projected to the rest of the population based on a significant result from the chi-squared test. This result implied that Wheat Thins' ad might not be as successful as it should be since after seeing the ad, the respondents who already felt positive toward the brand showed less preference toward the brand while the respondents who had negative attitude toward the brand still retained their original preference rate toward the brand. Pre- and Post-Exposure Change Score Frequencies For Wheat Thins, about 44% of the respondents moved down meaning that the majority of the respondents indicated that they would be less likely to buy the brand after seeing the ad than before seeing the ad. For Flat Earth, the result was the opposite, as high as 50% of the respondents moved up after seeing the ad indicating that the ad was successful in changing the respondents' preference toward the brand. For Sun Chips, 44% of the respondents moved down meaning that the almost half of the respondents indicated that they would be less likely to buy the brand after seeing the ad than before seeing the ad. Based on these numbers alone, Flat Earth's ad was found to be the most successful in changing the respondents' preference. Wheat Thins and Flat EarthBrand Index Score Frequency Counting About 77% of the respondents had more positive attitude toward Wheat Thins brand than toward Flat Earth brand. Correlation between Wheat Thins and Flat Earth Brand Index Scores Wheat Thins and Flat Earth had a moderate linear correlation with each other. The relationship was a positive relationship meaning that the more a person had a positive attitude toward one brand, the more positive one would feel toward the other brand. Correlation between Wheat Thins and Flat Earth Brand Index Score Sub-sample Based on only men respondents, the correlation between Wheat Thins and Flat Earth brand index scores was higher than the result for the entire sample indicating that men respondents' attitude toward the two brands were more favorable than the rest of the sample. Multiple Regression Analysis for Wheat Thins The multiple regression analysis for Wheat Thins reveals a coefficient of multiple determination of nearly 31%. This indicates a weak relationship; only 31% of how much respondents liked the Wheat Thins ad is explained by how much they like the brand. The coefficient of multiple correlations is 0.5 and therefore the data has a moderate correlation. The data is also statistically significant (F-ratio=2.52). In 85 or more samples (of 100) drawn from the same population as this sample, it would be expected that the correlation would be about the same. Only one of the ten Likert items ("Consider") is important in this analysis because they best explain the variance in pre-to-post change scores compared to the other brand attributes. In regards to this statement, we would NOT expect to find similar results in 85 or more samples out of every 100 samples drawn from the same population as this sample. Multiple Regression Analysis for Flat Earth The multiple regression analysis for Flat Earth reveals a coefficient of multiple determination of 23%. This indicates an even weaker relationship than Wheat Thins had; only 23% of how much respondents liked the Flat Earth's ad is explained by how much they like the brand. The coefficient of multiple correlations is 0.5 and therefore the data has a moderate correlation. The data is also statistically significant (F-ratio=1.70). In 85 or more samples (of 100) drawn from the same population as this sample, it would be expected that the correlation would be about the same. Only one of the ten Likert items ("Healthy") is important in this analysis because they best explain the variance in pre-to-post change scores compared to the other brand attributes. In regards to this statement, we would NOT expect to find similar results in 85 or more samples out of every 100 samples drawn from the same population as this sample. Multiple Regression Analysis for Sun Chips The multiple regression analysis for Sun Chips reveals a coefficient of multiple determination of 22%. This indicates the weakest relationship amongst all three brands; only 22% of how much respondents liked the Sun Chip's ad is explained by how much they like the brand. The coefficient of multiple correlations is 0.5 and therefore the data has a moderate correlation. The data is also statistically significant (F-ratio=1.70). In 85 or more samples (of 100) drawn from the same population as this sample, it would be expected that the correlation would be about the same. Only two of the ten Likert items ("Consider" and "Feel Good" ) are important in this analysis because they best explain the variance in pre-to-post change scores compared to the other brand attributes. In regards to this statements, we would NOT expect to find similar results in 85 or more samples out of every 100 samples drawn from the same population as this sample. Three of the ten attributes for Wheat Thins were found to be important in contributing to the differences in pre-to-post ad exposure scores. As a general interpretation of the meaning of the discriminant function coefficients, we may say the following about the three most important attributes: * The more respondents think Wheat Thins is a good brand of chip, the more they like the ad However, because the Wilk's Lambda and chi-squared tests were not significant, the result found could not be projected to the population. On the other hand, the Classification Matrix showed that it was possible to predict with 80.4% accuracy whether a respondent would prefer the brand based on the attitude that that respondent had toward the brand and because the t-ratio was found to be significant, this accuracy percentage could be projected to the rest of the population. ANOVA The differences between the means in the genders are minimal, however men have slightly higher mean scores across the board. The largest difference sits in the non-movers category with male having a significatly higher mean than females. The group most sensitive to the dependent variable "Wheat Thins tastes good" are male non movers, and the group least sensitive to the same category are female up movers. Nevertheless, none the F-ratios showed significance and thus could not be projected to the rest of the population. MANOVA Several interesting conclusions drawn from the MANOVA analysis were: * When comparing all ten Likert items specific attributes stood out, in the category "Tastes good" female down movers had a much higher mean than male down movers. Meaning that females were more sensitive to taste as an important attribute. The eigenvalues showed that all three brands had three important Eigenvalues. For Wheat Thins, 66% of the variance was explained by these three factors. For Flat Earth, 70% of the variance was explained by these three factors. And for Sun Chips 69% of the variance was explained by these three factors. The attitude scale reveals that this population has a higher opinion of Sun Chips than both Wheat Thins and Flat Earth. Lastly, a t-test showed that the differences in the mean attitude scores between the three brands were significant and could be projected to the population. For Wheat Thins, the respondents should be grouped into two clusters instead of three clusters since the relationship between the cluster in the two-cluster group was much clearer with one cluster consistently having higher mean scores than the other. The two-cluster group also could be identified based on the respondents' gender. Although both clusters had more females, cluster 1 had more males than cluster 2, and cluster 2 had slightly more females than cluster 1. The chi -square test showed that the results from the two-cluster group are significant and could be applied to a larger population than this sample.
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