Basic Statistics Analysis
Paired T-test
Between Groups T-tests
Chi-Squared Significance Test
Frequency
Frequency Counting
Simple Correlation Coefficient
Simple Correlation Coefficient Modified
Regression Analysis
Discriminant Analysis
Anova/Manova
Factor Analysis
BASIC STATISTICS ANALYSIS
Paired t-test
Statistical analysis of print advertisements and brand preferences for the following Vodka products: Absolut, Grey Goose and Skyy. The sample used for this analysis consisted of 60 people. Paired t-Tests were gathered, comparing brand index scores to the ten Likert items.
Brand Index Score
Brand Name |
Mean |
n |
Standard Deviation |
Absolut |
33.0 |
60 |
5.6 |
Grey Goose |
31.0 |
60 |
5.9 |
Skyy |
29.3 |
60 |
5.5 |
Paired Sample Test
Paired Samples |
t |
Absolut |
3.20* |
Grey |
1.67* |
Skyy |
1.59* |
(*p≤ .15)
The three paired t-Tests are statistically significant at a level of .15. lt is expected that the mean scores of Absolut, Grey Goose and Skyy on the Brand Index Score would be about the same in this sample. Therefore, we can project the results for this sample to the population. Overall, the respondents have the most positive perception for Absolut, the second for Grey Goose, and the third for Skyy.
Between Groups t-tests
Between-groups t-tests were conducted for Grey Goose brand, comparing ad pre-to-post exposure with the Brand Index Score and Ad Index Score . The Individuals that moved up against those who moved down.
Changed Brand Index Score for Grey Goose
Change Score |
n |
Mean |
t |
Move-Up |
35 |
33.1 |
3.43* |
Move-Down |
25 |
28.2 |
(*p ≤ 0.15)
Changed Ad Index Score for Grey Goose
Change Score |
n |
Mean |
t |
Move-Up |
35 |
4.3 |
3.11* |
Move-Down |
25 |
2.4 |
(*p ≤ 0.15)
There were 35 individuals who had a change score which moved up from pre-to-post exposure to Grey Goose ad. The Brand Index Score mean for this group was 33.1 and the Ad Index Score mean was 4.3. There were 25 respondents that moved down on pre-to-post exposure after looking at the ad. The Brand Index Score mean for this group was 28.2 and the Ad Index Score mean was 2.4. In 85 or more samples out of every 100 drawn from the same population, as this sample of 60 people, both of the t-ratios for respondents that moved up and down were significant within the brand index score and ad index score. They can be projected to the population of this sample. Individuals who ranked the Grey Goose brand higher before looking at the ad ranked higher after the exposure to the ad than those who ranked lower throughout the survey. Concluding, the majority of the sample will intensify their preference of Grey Goose after looking at the ad
Chi Squared Significance Test
Chi-Square test conducted to determine a significant relationship between "up", "same", and "down" pre-to-post movers on Grey Goose and being above or below the median Brand Index.
-- |
Above Median |
Below Median |
Moved Up
Row %
Column %
% of Total |
22
61.1%
73.3%
35.5% |
14
38.9%
43.8%
22.6% |
Same
Row %
Column %
Total |
5
33.3%
16.7%
8.1% |
9
59.9%
31.3%
16.1% |
Moved Down
Row %
Column %
Total |
3
27.3%
10.0%
4.8% |
7
63.7%
25.0%
12.9% |
(*p ≤ 0.15)
The Chi-Square test resulted significant at a level of .15. In 85 or more samples out of every 100 drawn from the same population, as this sample of 60 people, we would expect that the same percentage of cross tabulation would result in the population as we have found in this sample. The median for Grey Goose Brand Index Score is 30.0. From the sample of 60 respondents, 60% of the respondents felt more favorably about Grey Goose after viewing the ad. Out of the 60% respondents, 38% rated the brand above the median and 22% rated the brand below the median. In other words, Grey Goose was rated more favorably after viewing the ad, and the other half of the respondents rated the same and less favorably in a proportional way.
Frequency
Pre to Post exposure measurement
Change Score |
Grey Goose |
Absolut |
Skyy |
Move-Up |
35 |
35 |
10 |
Same |
14 |
14 |
16 |
Move-Down |
11 |
11 |
34 |
Grey Goose and Absolut were the most moving up in favorability with 35 respondents or 58% of the sample in pre-to-post exposure. Skyy had the least moving up in favorability with 11 individuals or 18% of the sample in pre-to-post exposure. Concluding that individuals favor Grey Goose and Absolut ads more than Skyy ad.
Frequency Counting
Brand Comparison |
n |
Percentage of Participants |
Grey Goose > Absolut |
20 |
33.3% |
Grey Goose ≤ Absolut |
40 |
66.6% |
The results indicated that out of the 60 respondents, 40 (66.6%) respondents rated Absolut higher than Grey Goose, and 20 (33.3%) individuals rated Grey Goose lower or equal to Absolut. R espondents preferred or felt more favorably to Absolut than Grey Goose.
Simple Correlation Coefficient
Brand Index Scores Compared |
Correlation (r) |
Grey Goose and Skyy |
-0.03 |
(*p≤.15)
Although there is a very low correlation between Grey Goose and Skyy the brand index scores, this is not significant at a level of .15. In 85 or more samples out of every 100 drawn from the same population. Respondents who may think highly of the grey Goose may tend to have a negative perception of the Skyy.
Simple Correlation Coefficient Modified
The following tables show a simple correlation coefficient tests’ results about the Grey Goose Brand Index Scores and the Grey Goose Ad Index Scores only for respondents of this survey who purchase alcoholic beverages more than one time per a week. The results were obtained via an online questionnaire, 45 people out of the total sample of 60 were used in this analysis.
Comparison |
Correlation(r) |
Grey Goose Ad Index Scores and respondents of this survey who drink alcoholic beverages more than one time per a week |
0.25* |
(*p≤.15)
There is a very low correlation between Grey Goose Brand Index Scores and respondents of this survey who drink alcoholic beverages more than one time per a week, this is not significant at a level of .15 In 85 or more samples out of every 100 drawn from the same population.
REGRESSION ANALYSIS
This regression analysis was conducted for each vodka brand. The Likert items were treated as the independent variables and the pre-to-post change score as the dependent variable.
Brand |
Multiple Correlation Coefficient (R) |
Coefficient of Multiple determination (R2) |
Standard Error of the Estimate (Se) |
F-ratio |
Grey Goose |
0.5 |
26.8% |
2.2 |
1.87* |
Skyy |
0.5 |
24.3% |
2.3 |
1.64* |
Absolut |
0.3 |
8.6% |
2.8 |
0.49 |
Table 1. (*P<=.15)
Likert Items |
Absolut |
Grey Goose |
Skyy |
b |
beta |
t |
b |
beta |
t |
b |
beta |
t |
Constant |
-1.2 |
|
.49 |
-3.2 |
|
1.97* |
-2.4 |
|
1.36 |
This is a good vodka |
.2 |
.1 |
.27 |
-.5 |
.2 |
.93 |
-.1 |
0 |
.27 |
I prefer this vodka over other brands |
-.2 |
-.1 |
.30 |
1.0 |
.4 |
1.79* |
.7 |
.3 |
1.59* |
I would not drink this vodka |
-.2 |
-.1 |
.53 |
1.0 |
.4 |
2.14* |
-.4 |
-.2 |
.82 |
This is the best tasting vodka |
-.5 |
-.2 |
.70 |
.1 |
0 |
.13 |
-.2 |
-.1 |
.49 |
This vodka mix best with my favorite drinks |
-.4 |
-.1 |
.87 |
-.3 |
-.1 |
.67 |
-.1 |
0 |
.29 |
I would quickly grow tired of this vodka |
-.1 |
0 |
.18 |
-.1 |
0 |
.32 |
-.3 |
-.1 |
.79 |
This vodka has a bad after taste |
.5 |
.1 |
.77 |
.2 |
.1 |
.40 |
.5 |
.2 |
.94 |
I like the image conveyed bout me when I drink this vodka |
.5 |
.1 |
.74 |
.2 |
.1 |
.56 |
.5 |
.2 |
1.13 |
This vodka fits my lifestyle |
.3 |
.1 |
.48 |
-.1 |
-.1 |
.36 |
.6 |
.2 |
1.23 |
I would feel good about drinking this vodka |
-.2 |
-.1 |
.45 |
-.1 |
0 |
.18 |
0 |
0 |
.06 |
Table 2. (*P<=.15)
From table 1, we can see from the multiple regression analysis that Grey Goose has a low relationship (26.8%) between how respondents rated the bran on the ten Likert items regarding its attributes and its favorability on the ad. The standard error of estimate is high (2.2). The F-ratio is significant, 1.87 tells that 85 or more samples out of every 100 drawn from the same population, at this sample of 60 people, would expect multiple regression coefficients.
Absolut shows a very low multiple determinant of 8.2%, which indicates there’s no relationship between how respondents rated the bran on the ten Likert items regarding its attributes and its favorability on the ad. The standard error of estimate is high (2.8). The F-ratio is significant, 0.49 tells that 85 or more samples out of every 100 drawn from the same population, at this sample of 60 people, would not expect multiple regression coefficients.
Skyy has a low relationship (24.3%) between how respondents rated the bran on the ten Likert items regarding its attributes and its favorability on the ad. The standard error of estimate is high (2.3). The F-ratio is significant, 1.64 tells that 85 or more samples out of every 100 drawn from the same population, at this sample of 60 people, would expect multiple regression coefficients.
From Table 2, we can derive the following descriptive equations in terms of how the Brand Index Scores explain their pre-post score change
Grey Goose: Pre-Post Change = -3.2 - 0.5(good) + 1.0(prefer) +1.0(would not drink) +0.1(the best tasting) -0.3(favorite mixers) -0.1(grow tired of) +0.2(bad after taste) +0.2(image conveyed) -0.1(lifestyle) -0.1(feel good)
- The more respondents thought that Grey Goose was a good vodka, the less they liked the ad.
- The more respondents thought that they preferred Grey Goose, the more they liked the ad.
- The more respondents thought that they would not drink Grey Goose, the more they liked the ad.
- The more respondent thought that Grey Goose was the best tasting vodka, the more they liked the ad.
- The more respondents thought that Grey Goose mixed best with my favorite mixers, the more they liked the ad.
- The more respondents thought that they would quickly grow tired of Grey Goose, the less they liked the ad.
- The more respondents thought that Grey Goose had a bad aftertaste, the more they liked the ad.
- The more respondents thought that they liked the image conveyed about me when I drink Grey Goose, the more they liked the ad.
- The more respondents thought that Grey Goose fits their lifestyle, the less they liked the ad.
- The more respondents thought that they would feel good about drinking Grey Goose, the less they liked the ad.
Regression Equations
Absolut: Pre-Post Change = -1.2 + 0.2(good) - .2(prefer) -.2(would not drink) -.5(the best tasting) -0.4(favorite mixers) -0.1(grow tired of) +0.5(bad after taste) +0.5(image conveyed) +0.3(lifestyle) -0.2(feel good)
Skyy: Pre-Post Change = -2.4 - 0.1(good) + 0.7(prefer) -0.4(would not drink) -0.2(the best tasting) -0.1(favorite mixers) -0.3(grow tired of) +0.5(bad after taste) +0.5(image conveyed) +0.6(lifestyle) +0 (feel good)
DISCRIMINAT ANALYSIS
This discriminant analysis was made with two groups and the Likert items taken from Grey Goose vodka, the two groups were up-movers and down-movers from the pre-post test. I used as a dependent variable the groups and as independent variables the Likert items. Due to a big difference on up-movers and down-movers, the non-movers group was added to the down-movers group.
Likert items |
Up-Movers |
Down-Movers |
Mean |
Std. Deviation |
Mean |
Std. Deviation |
Grey Goose is a good vodka |
3.6 |
0.1 |
3.2 |
0.7 |
Prefer Grey Goose over other brands |
3.2 |
0.9 |
2.7 |
0.8 |
I would not drink Grey Goose |
3.5 |
0.8 |
2.7 |
0.8 |
Grey Goose is the best tasting vodka |
3.3 |
0.7 |
2.9 |
0.7 |
Grey Goose mixes best with my favorites drinks |
3.0 |
1.0 |
2.8 |
0.8 |
Grow tired of Grey Goose |
3.2 |
0.7 |
2.8 |
0.9 |
Grey Goose has a bad aftertaste |
3.3 |
1.0 |
2.8 |
0.9 |
I like the image conveyed with Grey Goose |
3.4 |
1.1 |
2.9 |
0.7 |
Grey Goose fits my lifestyle |
3.1 |
0.9 |
2.6 |
1.0 |
I feel good about drinking Grey Goose |
3.4 |
0.7 |
3.0 |
0.9 |
ANOVA MANOVA
The purpose of the two-way factorial analysis of variance (ANOVA) and multivariate analysis (MANOVA) is to see if there are any statistically significant relationships between pre to post ad exposure brand index scores, Level of education and the change score of constant sum scale (up, same, down). The two-way ANOVA test uses only one Likert item (Absolut is a good vodka) for the dependent variable. The MANOVA test uses all ten Likert items.
Descriptive Statistics
Level of Education |
Up |
Same |
Down |
High |
Mean=3.6
Std. Dev.=0.5
N=8 |
Mean=4.1
Std. Dev.=0.8
N=13 |
Mean=3.6
Std. Dev.=0.7
N=27 |
Low |
Mean=3.0
Std. Dev.=0.0
N=2 |
Mean=1.5
Std. Dev.=2.1
N=2 |
Mean=2.8
Std. Dev.=0.9
N=8 |
Anova Table
Source of Variance |
Sum of Squares |
Degree of Freedom |
Mean Square |
Fo |
Between - Change Score |
0.94 |
2 |
0.47 |
0.77 |
Between - Level of Education |
12.54 |
1 |
12.54 |
20.49* |
Between - Chg Score |
4.87 |
2 |
2.44 |
3.98* |
Within - Error |
34.27 |
54 |
0.61 |
|
Monova
Likert Items for Absolut |
High Level of Education (N=48) |
Low Level of Education (N=12) |
Up |
Same |
Down |
Up |
Same |
Down |
8 |
13 |
27 |
2 |
2 |
8 |
mean |
SD |
mean |
SD |
mean |
SD |
mean |
SD |
mean |
SD |
mean |
SD |
Absolut is a good vodka |
3.6 |
0.5 |
4.1 |
0.8 |
3.6 |
0.7 |
3.0 |
0.0 |
1.5 |
2.1 |
2.8 |
0.9 |
Prefer Absolut over other brands |
3.3 |
0.7 |
4.1 |
0.6 |
3.6 |
0.9 |
3.0 |
0.0 |
3.0 |
0.7 |
2.8 |
1.0 |
I would not drink Absolut |
3.4 |
0.7 |
3.9 |
1.0 |
3.5 |
1.1 |
3.0 |
0.0 |
3.0 |
0.0 |
3.1 |
1.5 |
Absolut is the best tasting vodka |
2.9 |
0.6 |
3.4 |
0.8 |
3.2 |
0.9 |
3.0 |
0.0 |
3.5 |
0.0 |
2.9 |
1.0 |
Absolut mixes best with my favorites drinks |
3.1 |
0.4 |
3.1 |
1.6 |
3.4 |
0.8 |
3.0 |
0.0 |
3.5 |
0.7 |
2.9 |
1.0 |
Grow tired of Absolut |
3.0 |
0.5 |
3.4 |
0.9 |
3.2 |
0.8 |
3.0 |
0.0 |
3.0 |
0.0 |
3.5 |
0.8 |
Absolut has a bad aftertaste |
3.3 |
0.7 |
3.8 |
0.6 |
3.4 |
0.8 |
3.0 |
0.0 |
3.0 |
0.0 |
2.9 |
0.4 |
I like the image conveyed with Absolut |
3.0 |
1.0 |
3.9 |
0.7 |
3.2 |
0.7 |
3.0 |
0.0 |
3.0 |
0.0 |
2.6 |
0.7 |
Absolut fits my lifestyle |
3.0 |
0.8 |
3.4 |
1.4 |
3.3 |
0.7 |
3.0 |
0.7 |
3.0 |
0.0 |
2.3 |
1.0 |
I feel good about drinking Absolut |
3.1 |
0.4 |
3.2 |
1.7 |
3.3 |
1.0 |
3.0 |
0.0 |
3.0 |
0.0 |
2.3 |
1.3 |
Absolut Vodka |
F |
Wilk’s Lambda |
Between |
Within |
Change Score |
0.99 |
0.68 |
20 |
94 |
Education Level |
0.64 |
0.64 |
10 |
47 |
Change Score Education Level |
0.63 |
0.63 |
20 |
94 |
FACTOR ANALYSIS
A factor analysis was performed for each vodka brand to place related brand attributes into independent groups, also known as factors, for the calculation of a brand attitude score. The 10 Likert items were used as variables. Than a paired t-test was performed to find potential statistical significance for the differences of means between brand attitude scores.
Factor |
Grey Goose |
Skyy |
Absolut |
Eigen Value |
% of Variance |
Cum. % |
Eigen Value |
% of Variance |
Cum. % |
Eigen Value |
% of Variance |
Cum. % |
1 |
4.8 |
47.7 |
47.7 |
4.0 |
40.0 |
40.0 |
4.0 |
39.8 |
39.8 |
2 |
1.4 |
13.8 |
61.5 |
1.6 |
16.3 |
55.9 |
1.8 |
18.1 |
57.9 |
3 |
0.9 |
8.8 |
70.3 |
1.2 |
11.7 |
67.6 |
1.0 |
10.4 |
68.3 |
4 |
0.7 |
7.3 |
77.7 |
0.8 |
7.8 |
75.4 |
0.9 |
9.1 |
77.4 |
5 |
0.6 |
5.9 |
83.5 |
0.7 |
7.1 |
82.5 |
0.7 |
6.6 |
84.0 |
6 |
0.5 |
5.0 |
88.5 |
0.6 |
5.6 |
88.1 |
0.5 |
4.7 |
88.7 |
7 |
0.4 |
3.8 |
92.3 |
0.4 |
4.1 |
92.2 |
0.4 |
4.3 |
93.0 |
8 |
0.3 |
3.3 |
95.6 |
0.3 |
3.2 |
95.5 |
0.3 |
3.9 |
96.4 |
9 |
0.3 |
2.5 |
98.1 |
0.3 |
2.6 |
98.1 |
0.2 |
2.1 |
98.5 |
10 |
0.2 |
1.9 |
100.0 |
0.2 |
1.9 |
100.0 |
0.2 |
1.5 |
100.0 |
GREY GOOSE Vodka
Attribute |
Communalities |
Factor Matrix |
Verimax Rotated Matrix |
1 |
2 |
1 |
2 |
Grey Goose is good vodka. |
0.6 |
0.7 |
-0.2 |
0.7 |
0.2 |
I prefer Grey Goose over other vodka. |
0.7 |
0.8 |
-0.3 |
0.8 |
0.2 |
I would not drink Grey Goose vodka. |
0.6 |
0.7 |
0.3 |
0.4 |
0.6 |
Grey Goose is the best tasting vodka. |
0.7 |
0.8 |
-0.3 |
0.8 |
0.2 |
Grey Goose mix best with my drinks. |
0.5 |
0.5 |
-0.5 |
0.7 |
-0.1 |
I will quickly grow tired of Grey Goose |
0.7 |
0.4 |
0.7 |
0.0 |
0.8 |
Grey Goose has a bad aftertaste. |
0.7 |
0.6 |
0.6 |
0.2 |
0.8 |
I like the image conveyed when I drink Grey Goose vodka. |
0.6 |
0.8 |
0.2 |
0.6 |
0.5 |
Grey Goose fits my lifestyle. |
0.5 |
0.7 |
-0.1 |
0.7 |
0.2 |
I feel good about drinking Grey Goose. |
0.7 |
0.8 |
-0.1 |
0.7 |
0.3 |
For Grey Goose brand can be said that 61.5% of the variance can be explained by two factors, which were the only ones that have the Eigen value greater than one. And only those items greater than 0.5 on the varimax rotated matrix were used in computing the attitude score for Grey Goose.
ABSOLUT Vodka
Attribute |
Communalities |
Factor Matrix |
Varimax Rotated |
1 |
2 |
3 |
1 |
2 |
3 |
Absolut is good vodka. |
0.7 |
0.8 |
0.0 |
-0.3 |
0.8 |
0.3 |
0.1 |
I prefer Absolut over other vodka. |
0.8 |
0.8 |
-0.1 |
-0.3 |
0.8 |
0.3 |
0.1 |
I would not drink Absolut vodka. |
0.6 |
0.3 |
0.7 |
0.1 |
0.1 |
0.1 |
0.8 |
Absolut is the best tasting vodka. |
0.7 |
0.8 |
-0.2 |
0.1 |
0.6 |
0.6 |
0.0 |
Absolut mix best with my drinks. |
0.5 |
0.5 |
0.1 |
0.4 |
0.1 |
0.7 |
0.2 |
I will quickly grow tired of Absolut. |
0.8 |
0.1 |
0.8 |
0.3 |
-0.2 |
0.1 |
0.8 |
Absolut has a bad aftertaste. |
0.8 |
0.4 |
0.7 |
-0.4 |
0.5 |
-0.2 |
0.7 |
I like the image conveyed when I drink Absolut vodka. |
0.7 |
0.7 |
-0.2 |
-0.4 |
0.8 |
0.2 |
0.0 |
Absolut fits my lifestyle. |
0.7 |
0.8 |
-0.2 |
0.3 |
0.4 |
0.7 |
-0.1 |
I feel good about drinking Absolut. |
0.6 |
0.6 |
0.0 |
0.5 |
0.2 |
0.8 |
0.1 |
For Absolut brand can be said that 68.3% of the variance can be explained by two factors, which were the only ones that have the Eigen value greater than one. And only those items greater than 0.5 on the varimax rotated matrix were used in computing the attitude score for Absolut.
SKYY Vodka
Attribute |
Communalities |
Factor Matrix |
Varimax Rotated |
1 |
2 |
3 |
1 |
2 |
3 |
Skyy is good vodka. |
0.6 |
0.6 |
-0.2 |
-0.5 |
0.8 |
0.0 |
0.1 |
I prefer Skyy over other vodka. |
0.7 |
0.7 |
-0.2 |
-0.4 |
0.4 |
0.8 |
-0.1 |
I would not drink Skyy vodka. |
0.8 |
0.6 |
0.5 |
-0.5 |
0.5 |
0.0 |
0.8 |
Skyy is the best tasting vodka. |
0.5 |
0.5 |
0.3 |
0.4 |
0.0 |
0.7 |
0.3 |
Skyy mix best with my drinks. |
0.5 |
0.6 |
-0.1 |
0.4 |
0.3 |
0.6 |
0.0 |
I will quickly grow tired of Skyy |
0.6 |
0.3 |
0.6 |
0.4 |
-0.3 |
0.5 |
0.5 |
Skyy has a bad aftertaste. |
0.9 |
0.4 |
0.8 |
-0.2 |
0.1 |
0.1 |
0.9 |
I like the image conveyed when I drink Skyy vodka. |
0.7 |
0.8 |
-0.2 |
0.1 |
0.6 |
0.6 |
0.1 |
Skyy fits my lifestyle. |
0.7 |
0.8 |
-0.3 |
-0.1 |
0.8 |
0.4 |
0.0 |
I feel good about drinking Skyy. |
0.7 |
0.8 |
-0.2 |
-0.2 |
0.8 |
0.3 |
0.1 |
For Skyy vodka brand can be said that 67.6% of the variance can be explained by two factors, which were the only ones that have the Eigen value greater than one. And only those items greater than 0.5 on the varimax rotated matrix were used in computing the attitude score for Skyy vodka.
Attitude Statistics
Vodka Brand |
Mean |
Std. Deviation |
Grey Groose |
3.1 |
0.7 |
Absolut |
3.3 |
0.7 |
Skyy |
2.9 |
0.6 |
Absolut had the most favorably attitude score 3.3, meaning that Absolut is the vodka brand liked the most. Coming in second place is Grey Goose with a 3.1 and thirdly Skyy with 2.9.
Paired T-test
Vodka Brand |
t |
Grey Groose - Absolut |
.90 |
Grey Goose - Skyy |
2.00* |
Absolut - Skyy |
2.74* |
(*p≤.15)
The t-test showed significance in two pairs, Grey Goose-Skyy and Absolut-Skyy, meaning that in 85 or more samples out of 100 taken from the same population as these 60, we are able to expect to find a difference between mean of attitude scores of about the same. However difference between mean cannot be projected for Grey Goose and Absolut.