Basic Statistics

This report compiles the results of basic statistical analyses that were conducted on the data set that was drawn from a consumer brand preference survey on flavored water. The survey employed several copy testing techniques, which allow us to measure the impact advertising has upon the perceptions and preferences of consumers. The survey measured the brand attitudes before and after exposure to the print advertisements of the three brands Dasani, Tropicana, and Kellogg's. This report provides the results of an analysis of the Brand Index Score, which refers to the summation of ten judgments about each brand on a Likert scale and measures the respondent's attitude towards the brand. Moreover, the relationship of the Brand Index Score before and after exposure was measured. The validity of these numbers was examined using t-ratio and chi-squared significance tests.

1) Correlated (paired) t-tests:

A correlated (paired) t-test was conducted using the Brand Index Scores of all three brands. The highest possible Brand Index Score is 50 and the lowest one is 10; a high Brand Index Score indicates a higher opinion of the brand.

Table 1A: Means of the brand index scores of the three brands under consideration

Brand	Mean Brand Index Score	Standard Deviation
Dasani	31.8	4.3
Tropicana	30.9	2.7
Kellogg's	30	3.5
Sample Size: 82

Table 1A shows that there are only very small differences between the brand index scores of all three brands suggesting that respondents expressed almost equally high brand perception and likeability for all three brands. The standard deviation shows how close respondents were to the mean. The results displayed in table 1A demonstrate rather large differences between the standard deviation scores of all three brands. The results show that responses to Dasani Likert items exhibited greater variances from the mean, while responses to the Tropicana items deviated the least.

Table 1B: Paired t-tests of the mean brand index scores for the three brands under consideration

Brand Pair	t-ratio
Dasani and Tropicana	1.78*
Dasani and Kellogg's	3.87*
Tropicana and Kellogg's	2.27*
* p ≤ 0.15

The paired t-tests displayed in table 1B were conducted to determine whether the differences in the means between the brands are statistically significant. Table 1B shows that all three brand pairs are significant and therefore the results of this sample can be projected to the population for this test. In 85 or more samples out of 100 samples drawn from the same population as this sample, it would be expected that the differences in the mean brand index scores between Dasani and Tropicana, Dasani and Kellogg's and Tropicana and Kellogg's would be about what they are here.

2) Between-groups t-tests:

Between-group t-tests were conducted on the Brand Index Scores and Advertising Index Scores for Tropicana. The Advertising Index Score represents the number of positive attributes selected by the respondent as they apply to each ad.

Table 2A: Means of the advertising and brand index scores for Tropicana for respondents whose purchase intention went up or down after viewing the print advertisements

Tropicana purchase intention after exposure to the ads…	Number	Brand Index Score		Advertising Index Score
		Mean	SD	Mean	SD
…went up	33	31.3	2.3	5.8	2.5
…went down	20	30.5	2.9	3.2	2.6

SD= standard deviation

The respondents of the survey were asked to rate their likelihood of purchasing each of the three brands of flavored water on a constant-sum scale before and after viewing the print ads for each of the brands. As shown in table 2A, the constant-sum score of 33 respondents went up after exposure to the ads and it went down for 20 respondents. The mean brand and advertising index scores of the up-movers were higher than those of the down-movers.

Table 2B: Between-groups t-tests for the means of the advertising and brand index scores for Tropicana

	t-ratio
Tropicana Brand Index Score	1.15*
Tropicana Advertising Index Score	3.61*
* p ≤ 0.15

As shown in table 2B, the means the differences in the mean brand index scores and mean advertising index scores between up-movers and down-movers were found to be statistically significant. The results for this sample can be projected to the population for this test.

3) Chi-squared significance test:

This test was conducted to compare respondents' pre-to-post test results to Median Brand Index Scores for Dasani.

Table 3: Relationship between Dasani purchase intent and Dasani's brand index score

Likelihood of purchasing Dasani after exposure to ads

Dasani brand index score above the median

Dasani brand index score below the median

Went up

Row %

Column %

Total %

43.8%

21.9%

9.7%

56.2%

22.5%

12.5%

Stayed the same

Row %

Column %

Total %

38.9%

21.9%

9.7%

61.1%

27.5%

15.3%

Went down

Row %

Column %

Total %

47.4%

56.2%

25.0%

52.6%

50.0%

27.8%

Chi-squared:0.36

* p ≤ 0.15

The chi-squared test is used to determine if there is a statistically-significant relationship between whether a respondent's intention to purchase Dasani went up, went down or stayed the same and whether a respondent's brand index score for Dasani was above or below the median Dasani brand index score of 32. As table 3 shows, no statistically-significant relationship was found.

4) Frequency tests:

Table 4 shows the number of respondents for each brand whose purchase intentions went up, went down or stayed the same after exposure to the ads.

Table 4:

Likelihood of purchasing brand after exposure to ads	Dasani	Tropicana	Kellogg's
Went up	17	33	35
Stayed the same	22	29	37
Went down	43	20	10

Table 4 shows that Tropicana and Kellogg's had an almost equally positive influence on promoting favorable brand attitudes among respondents. Dasani, however, did not do as well; 43 respondents reported feeling less favorable towards the brand after seeing the ad.

5) Brand Index Score Comparison

Table 5: Number of respondents who had a higher perception of the Dasani brand than the Tropicana brand, and vice versa

Brand	Frequency
Dasani brand index score is higher than Tropicana brand index score	40
Dasani brand index score is lower than Tropicana brand index score	42

The results show that out of 82 people 40 respondents had a higher brand index score for Dasani than for Tropicana. The remaining 42 respondents felt slightly more favorable towards Tropicana than they did towards Dasani.

6) Simple Correlation Coefficient:

Table 6:

Correlation between Dasani brand index score and Tropicana brand index score	0.14*
	* p ≤ 0.15

The results presented in table 6 show that there is a weak correlation between the brand index scores of Dasani and Tropicana. Those respondents who reported liking Dasani might exhibit a similar preference for Tropicana. The results of the test are statistically significant and thus can be projected to the population.

7) Simple Correlation Coefficient:

Table 7: Correlation of selected samples - women

Correlation between Dasani brand index score and Tropicana brand index score	0.02
	* p ≤ 0.15

The correlation coefficient shown in table 7 was calculated based on a sample consisting exclusively of women. The correlation coefficient 0.02 suggests an extremely low correlation between the brand index scores of Dasani and Tropicana. However, since these results are not statistically significant, they cannot be used to describe a larger population.