Analysis

	Table of Contents	Executive Summary	Introduction	Methodology	Analysis	Conclusion	Summary	Appendix A	Appendix B

Analysis

Basic Statistics Analysis

Multiple Regression Analysis

Discriminant Analysis

ANOVA/MANOVA

Factor Analysis

Cluster Analysis

Basic Statistics

Introduction

This report is an analysis from the data collected from my imported Mexican beer survey which asked respondents to answer various questions about three different brands of Mexican beer: Corona, Dos Equis, and Negra Modelo. The data includes the respondents' opinions and feelings about the brands before and after reviewing an ad for each beer. One of the main focuses in this report is measuring the Brand Index Score and the Advertisement Index Score for each beer.

Methods

Several statistical tests were used in this report to demonstrate the relationship between different variables. For question 1, a paired sample t-test was used to compare the Brand Index Score of each brand to the other two brands. Question 2 required an independent t-test to compare the Brand Index Score of Dos Equis to the Advertisement Index Score of Dos Equis. Chi Square analysis was then performed on calculations of respondents who changed their opinion about Dos Equis after reviewing the Dos Equis ad. Question 4 required a frequency test to be run to see how respondents opinions waivered after reviewing each brands' ad. Question 5 analyses the preference of Corona over Dos Equis. Question 6 then examines the relationship between Corona's and Dos Equis' Brand Index Score. Finally for question 7, I analyze the opinions of Dos Equis Brand Index Score among women using the Chi Square analysis.

Descriptive Statistics & Results

Table 1: Statistical Information for Paired Sample Two Tailed t-test; n=60

Variable	M	SD
Corona Brand Index Score	33.9	3.6
Dos Equis Brand Index Score	32.7	3.9
Negra Modelo Brand Index Score	31.2	3.5

Pairs of Brand Index Scores	t
Corona & Dos Equis	2.10*
Dos Equis & Negra Modelo	2.52*
Corona & Negra Modelo	4.27*

* p ≤ .15

Table 1 shows the means of the brand index scores for Corona, Dos Equis and Negra Modelo. The Brand Index Score is calculated by taking the average of 10 scores each respondent's gave about each brand on a Likert scale.

Table 2: Statistical Information for Independent Two Tailed t-test

	Dos Equis Brand Index Score		Dos Equis Advertisement Index Score
	*Move Up*	*Move Down*	*Move Up*	*Move Down*
n	13	22	13	22
M	33.3	33.2	7	3.1
SD	4.5	3.4	3.4	3.1


	Dos Equis Brand Index Score		Dos Equis Advertisement Index Score
	*Equal Variences Not Assumed*		*Equal Variences Not Assumed*
t	0.09		3.33*

* p ≤ .15

Before the respondents were asked to view the ads for each brand, they rated the brands on a constant sum scale. Then after reviewing the brand, they rated the brands again using the constant sum scale. After viewing the ads 7 respondents opinion of Dos Equis was heightened while 3.1 respondents' opinions of Dos Equis was lowered. Table 2 shows the results of an Independent Two Tailed t-test was statistically significant between the Dos Equis Advertisement Index Score respondents who moved up and those who moved down. This means that in 85 samples out of 100 samples drawn from the population as this sample, it would be expected that the difference between the mean Advertising Index Score of the respondents who's opinion was raised and those who were lowered would appear about the same as it did in this test.

Table 3: Chi Square Analysis of Respondents Whose Opinion Moved Above or Below Median of Dos Equis Brand Index Scores

Movement of Opinions About Dos Equis After Seeing Ad		Dos Equis Brand Index Score
		Above Median Score	Below Median Score
Opinion Raised	Count	7	7
	% within Movement of Opinion	63.6%	36.4%
	% within Brand Index Score	24.1%	19.0%
	% Total	14.0%	8.0%

Same Opinion	Count	9	11
	% within Movement of Opinion	45.0%	55.0%
	% within Brand Index Score	31.0%	52.4%
	% Total	18.0%	22.0%

Opinion Lowered	Count	13	6
	% within Movement of Opinion	68.4%	31.6%
	% within Brand Index Score	44.8%	28.6%
	% Total	26.0%	12.0%

Chi Squared	2.38

*p ≤ .15

A Chi Square test is used to determine is there is a statistically significant relationship between a respondents' purchase intention for Dos Equis is related to their Bran Index Score for the same brand. This test did not yield a statistically significant result.

Table 4: Frequency Analysis of Respondents Movement of Opinions for Each Brand

	Corona	Dos Equis	Negra Modelo
Opinion Raised	30	13	10
Same Opinion	19	25	33
Opinion Lowered	11	22	17

Table 5: Frequency of Respondents Who Favored Corona Over Dos Equis

	Respondents
Corona Brand Index Score Higher than Dos Equis	29

Table 6: Correlation between the Corona Brand Index Score and Dos Equis Brand Index Score

Pearson Correlation	0.3*

*p ≤ .15

Table 6 presents the results of the Pearson Correlation between the Corona Brand Index Score and the Dos Equis Brand Index Score. The calculation is statistically significant which means in 85 out of 100 samples taken from the same population as this sample, it would be expected that the correlation between the Brand Index Scores of Corona and Dos Equis would appear about the same as they do here. Which means that this could be projected onto the population.

Table 7: Cross Tabulation of Women who Opinions of Dos Equis Changed

Females Opinions		Dos Equis
Opinion Raised	Count	17
	% within Movement of Opinion	65.4
	% within Brand Index Score	100
	% Total	65.4

Opinion Lowered	Count	9
	% within Movement of Opinion	34.6
	% within Brand Index Score	100
	% Total	34.6
	Chi Square	0

A Chi Square test is used to determine is there is a statistically significant relationship between a respondents' purchase intention for Dos Equis is related to being female. This test did not yield a statistically significant result.

Multiple Regression Analysis

Introduction

Methods

One of the main focuses in this report the scores for ten questions measured on a Likert Scale are subjected to multiple regression analysis for each brand. These scores on the Likert Scale act as the Independent Variables while the change score, a calculation of how their opinions about a brand changed from before and after reviewing the ad, acts as the Dependent Variable.

Descriptive Statistics & Results

Table 1: Multiple Linear Regression of Corona, Dos Equis, & Negra Modelo

	Corona	Dos Equis	Negra Modelo
Multiple Correlation Coefficient (R)	0.5	0.4	0.6
Coefficient of Multiple Determination (R 2 )	24.5%	17.6%	31.0%
Standard Error of the Estimate (s e )	2.1	2.0	1.3
F-Ratio to Test Correlation Coefficient (F)	1.59*	1.05	2.2*
Constant Term (a)	-0.3	-0.8	-4.1

*p ≤ .15

Table 2: Corona's Brand Characteristics

Statement	Unstandardized Regression Coefficients (b)	Standardized Regression Coefficients (ß)	t-Ratio to Test a's & b's (t)

…is a good beer.	-0.3	-0.1	0.51
…tastes good.	0.3	0.1	0.4
…is a high end beer.	0.2	0.1	0.69
…is for people who know a lot about beer.	0.5	0.2	1.24
I would prefer another brand of beer over…	0.1	0.1	0.34
…is too expensive for me.	0.1	0	0.25
…has a bad aftertaste.	1.1	0.4	2.31*
…is a cool/trendy beer.	-0.6	-0.2	1.62*
…is a well established brand of beer.	-0.5	-0.1	0.69
Would consider buying… next time.	0	0	0.03

*p ≤ .15

Important Variables in Regression Analysis are noted in bold.

In 85 samples out of 100 samples drawn from the same population as this sample, it would be expected that the ten brand attitude Likert statements about Corona account for about 24.5% of the variance in the population's change scores for this brand. Because the F-Ratio is statistically significant, the results can be projected onto the population. There were, however, only two statements that had a statistically significant impact: “Corona has a bad aftertaste” & “Corona is a cool/trendy beer.” In 85 samples out of 100 samples drawn from the same population as this sample, it would be expected that these three coefficients would be about what they are here.

Table 3: Dos Equis' Brand Characteristics

Statement	Unstandardized Regression Coefficients (b)	Standardized Regression Coefficients (ß)	t-Ratio to Test a's & b's (t)

…is a good beer.	1.1	0.4	1.31
…tastes good.	-0.4	-0.1	0.41
…is a high end beer.	0.7	0.3	1.37
…is for people who know a lot about beer.	-0.9	-0.4	1.89*
I would prefer another brand of beer over…	-0.2	-0.1	0.72
…is too expensive for me.	-0.6	-0.2	1.21
…has a bad aftertaste.	0.5	0.1	0.72
…is a cool/trendy beer.	-0.2	-0.1	0.39
…is a well established brand of beer.	0.2	0.1	0.37
Would consider buying… next time.	-0.6	- 0.3	1.4

*p ≤ .15

Important Variables in Regression Analysis are noted in bold.

In this sample, the ten brand attitude Likert statements about Dos Equis account for about 17.6% of the variance in the respondents' change scores for this brand. Because the F-Ratio is not statistically significant, the results can not be projected onto the population. There was only one statement that was statistically significant: “Dos Equis is for people who know a lot about beer.” In 85 samples out of 100 samples drawn from the same population as this sample, it would be expected that this coefficient would be about what it is here.

Table 4: Negra Modelo's Brand Characteristics

Statement	Unstandardized Regression Coefficients (b)	Standardized Regression Coefficients (ß)	t-Ratio to Test a's & b's (t)

…is a good beer.	-1.4	-0.8	1.84*
…tastes good.	1.7	1.1	2.33*
…is a high end beer.	-0.9	-0.5	1.99*
…is for people who know a lot about beer.	0.2	0.1	0.54
I would prefer another brand of beer over…	0.1	0	0.25
…is too expensive for me.	0.1	0.1	0.35
…has a bad aftertaste.	0.9	0.5	1.77*
…is a cool/trendy beer.	0.5	0.3	1.94*
…is a well established brand of beer.	0.1	0.1	0.38
Would consider buying… next time.	0	0	0.16

*p ≤ .15

Important Variables in Regression Analysis are noted in bold.

In 85 samples out of 100 samples drawn from the same population as this sample, it would be expected that the ten brand attitude Likert statements about Negra Modelo account for about 31.0% of the variance in the population's change scores for this brand. Because the F-Ratio is statistically significant, the results can be projected onto the population. There were, however, five statements that had a statistically significant impact: “Negra Modelo is a good beer.” “Negra Modelo tastes good” “Negra Modelo is a high end beer” “Negra Modelo has a bad aftertaste” & “Negra Modelo is a cool/trendy beer.” In 85 samples out of 100 samples drawn from the same population as this sample, it would be expected that these five coefficients would be about what they are here.

Table 5: Multiple Regression Equation for Corona

Change Score for Corona =	-	0.3
	-	0.3(goodbeer)
	+	0.3(tastesgood)
	+	0.2(highend)
	+	0.5(knowalot)
	+	0.1(pref_other)
	+	0.1(expensive)
	+	1.1(bad_taste)
	-	0.6(trendy)
	-	0.5(est_brand)
	-	0(buy_next)

Multiple Discriminant Analysis

Introduction

This report is an analysis from the data collected from my imported Mexican beer survey which asked respondents to answer various questions about three different brands of Mexican beer: Corona, Dos Equis, and Negra Modelo. The data includes the respondents' opinions and feelings about the brands before and after reviewing an ad for each beer. Multiple Discriminant Analysis was performed on the responses about Negra Modelo and whether the up movers and down movers were classified correctly.

Methods

One of the main focuses in this report are scores for ten questions measured on a Likert Scale for Negra Modelo beer, in particular, the scores for the up-movers and down-movers. Up-movers and down-movers are measured by the respondents' responses to questions about the brand before and after viewing the ads. The responses to the questions on the Likert Scale were then subjected to Multiple Discriminant Analysis. These scores on the Likert Scale act as the Independent Variables while the change score, a calculation of how their opinions about a brand changed from before and after reviewing the ad, acts as the Dependent Variable.

Descriptive Statistics & Results

Table 1: Negra Modelo Brand Attitudes

Likert Scale Questions	Up-Movers Respondents = 10		Down-Movers Respondents = 17		Standardized Discriminant Function Coefficient	Unstandardized Discriminant Function Coefficient
	Mean	Standard Deviation	Mean	Standard Deviation
…is a good beer.	3.4	0.8	3.5	0.9	-0.9	-1.1
…tastes good.	3.4	0.8	3.4	1.1	1.3	1.4
…is a high-end beer.	3	0.5	3.7	0.7	-0.9	-1.5
…is for people who know a lot about beer.	3.2	0.6	3.5	0.9	0.2	0.2
would prefer another brand over…	3.3	0.5	3.7	1.3	-0.1	-0.1
…is too expensive.	2.8	0.6	2.6	0.8	-0.2	-0.3
…has a bad aftertaste.	3	0.5	2.7	1.2	0.6	0.7
…is a cool/trendy beer.	2.9	0.3	3.2	1.1	0.2	0.3
…is a well-established brand of beer.	3.3	0.7	3.4	1.1	-0.3	-0.3
would consider buying… next time.	3.3	0.9	3	1.4	0.5	0.4

Important Variables in Discriminant Analysis are noted in bold.

The sample was drawn from a total of 27 respondents: 10 Up-movers and 17 Down-movers. “Negra Modelo is a good beer”, “Negra Modelo Tastes Good”, “Negra Modelo is a high-end beer” and “Negra Modelo has a bad aftertaste” seem to be the most important factors in determining the movement of the respondents' opinions.

Table 2: Negra Modelo Inferential Statistics

	Average Discriminant Score/ Group Centroids
Up-Movers	0.92
Down-Movers	-0.54
---------------	----------------------------
*Wilkes Lambda*	0.65
*Chi-Square*	8.66

*p ≤ 0.15

Wilkes Lambda is not statistically significant. Therefore, we can not be certain if 85 samples out of 100 samples drawn from the same population as this sample, the difference in the group centroids of the Up-movers and the Down-movers would be what it is here. The group centroids can not be projected onto the population.

Table 3: Negra Modelo Classification Matrix

Actual Membership	Predicted Membership
	Up-Movers	Down-Movers
Up-Movers	8	2
Down-Movers	2	15

Twenty-three out of 27 respondents fell into the predicted membership groups, thus creating 85.2% of the original grouped cases being correctly classified.

Table 4: Significance of Classification Matrix

t o =	(.852)-(.500)
	√{[(.852)(.148)/27]+[(.500)(.500)/27)]}

t o =	50.54*

*t o ≥ t c (t c = 1.04 when a = 0.15 in a one-tailed t-test)

85.2% is a pretty good classification accuracy. The original grouped cases are correctly classified and are statistically significant. In 85 out of 100 samples drawn from the same population as this sample, it would be expected that the percentage of cases correctly classified as Up-movers and Down-movers would be about what it is here.

ANOVA/MANOVA Analyses

Introduction

This report is an analysis from the data collected from my imported Mexican beer survey which asked respondents to answer various questions about three different brands of Mexican beer: Corona, Dos Equis, and Negra Modelo. The data includes the respondents' opinions and feelings about the brands before and after reviewing an ad for each beer. Both the ANOVA and MANOVA analyses were performed on the Corona up-movers, down-movers and non-movers and the gender of the respondents.

Methods

One of the main focuses in this report are scores for ten questions measured on a Likert Scale for Corona beer, in particular, the scores for the up-movers down-movers and non-movers. “Movement” of the respondents is measured by the respondents' responses to questions about the brand before and after viewing the ads. The responses to the questions on the Likert Scale were then subjected to ANOVA and MANOVA analyses taking into account each respondents' gender. These scores on the Likert Scale act as the Dependent Variables while the change score, a calculation of how their opinions about a brand changed from before and after reviewing the ad along with the gender, act as the Independent Variables.

Descriptive Statistics & Results

ANOVA

Table 1: Mean Scores of Males & Females on "Corona Has a Bad Aftertaste."

	Males	Females
Up-Movers (N)	14	16
Mean (M)	2.9	3.1
Standard Deviation (SD)	1.0	0.7

Non-Movers (N)	11	8
Mean (M)	2.2	2.5
Standard Deviation (SD)	0.6	0.5

Down Movers (N)	4	7
Mean (M)	2.8	2.0
Standard Deviation (SD)	0.5	0.0

Table 2: Between Groups Effects

Between Group Variation:	Sum of Squares (SS)	Degrees of Freedom (df)	Mean Square (Xbar)	F-ratio
Gender	0.04	2	2.98	5.79
Up/Down/Non Mover	5.97	1	0.04	0.07*
*Gender Up/Down/Non Mover**	2.27	2	1.14	2.20

*p ≥ 0.15

In 85 samples out of 100 samples drawn from the same population as this sample, it would be expected that the difference in the mean Likert scores of “Corona Has a Bad Aftertaste” between the Up-Movers, Down-Movers, and Non-Movers groups would be about what it is here. The results of this analysis can be projected onto the population, unlike the comparison between genders or the comparison between the movers and gender.

MANOVA

Table 3: Multivariate Analysis of Variance where N=60

		Males	Females
Up-Movers
…is a good beer.	Mean (M)	4.0	3.8
	Standard Deviation (SD)	0.7	0.8
…tastes good.	Mean (M)	3.9	3.5
	Standard Deviation (SD)	0.5	1.0
…is a high-end beer.	Mean (M)	3.1	3.4
	Standard Deviation (SD)	1.4	0.6
…is for people who know a lot about beer.	Mean (M)	2.9	2.9
	Standard Deviation (SD)	1.2	0.6
would prefer another brand over…	Mean (M)	4.1	3.8
	Standard Deviation (SD)	1.2	0.8
…is too expensive.	Mean (M)	2.8	2.9
	Standard Deviation (SD)	1.1	0.6
…has a bad aftertaste.	Mean (M)	2.9	3.1
	Standard Deviation (SD)	1.0	0.7
…is a cool/trendy beer.	Mean (M)	3.3	3.8
	Standard Deviation (SD)	1.2	0.8
…is a well-established brand of beer.	Mean (M)	4.1	3.9
	Standard Deviation (SD)	0.4	0.4
would consider buying… next time.	Mean (M)	3.4	3.1
	Standard Deviation (SD)	1.0	1.0

Non-Movers
…is a good beer.	Mean (M)	3.9	4.1
	Standard Deviation (SD)	1.0	0.6
…tastes good.	Mean (M)	4.2	4.0
	Standard Deviation (SD)	0.8	0.5
…is a high-end beer.	Mean (M)	2.7	3.0
	Standard Deviation (SD)	1.0	0.8
…is for people who know a lot about beer.	Mean (M)	2.5	2.4
	Standard Deviation (SD)	1.0	1.1
would prefer another brand over…	Mean (M)	3.3	3.7
	Standard Deviation (SD)	1.3	0.7
…is too expensive.	Mean (M)	1.9	2.4
	Standard Deviation (SD)	0.7	0.7
…has a bad aftertaste.	Mean (M)	2.2	2.5
	Standard Deviation (SD)	0.6	0.5
…is a cool/trendy beer.	Mean (M)	3.6	3.5
	Standard Deviation (SD)	0.7	0.5
…is a well-established brand of beer.	Mean (M)	4.2	3.9
	Standard Deviation (SD)	0.6	0.4
would consider buying… next time.	Mean (M)	3.7	3.9
	Standard Deviation (SD)	1.3	0.6

Down-Movers
…is a good beer.	Mean (M)	4.3	4.4
	Standard Deviation (SD)	0.5	0.5
…tastes good.	Mean (M)	4.3	4.1
	Standard Deviation (SD)	0.5	0.4
…is a high-end beer.	Mean (M)	4.0	3.4
	Standard Deviation (SD)	0.8	1.1
…is for people who know a lot about beer.	Mean (M)	1.8	2.6
	Standard Deviation (SD)	1.3	1.1
would prefer another brand over…	Mean (M)	3.5	4.0
	Standard Deviation (SD)	1.3	1.0
…is too expensive.	Mean (M)	2.8	2.1
	Standard Deviation (SD)	0.5	0.4
…has a bad aftertaste.	Mean (M)	2.8	2.0
	Standard Deviation (SD)	0.5	0.0
…is a cool/trendy beer.	Mean (M)	3.3	3.7
	Standard Deviation (SD)	1.0	0.5
…is a well-established brand of beer.	Mean (M)	4.5	4.1
	Standard Deviation (SD)	0.6	0.4
would consider buying… next time.	Mean (M)	4.3	3.4
	Standard Deviation (SD)	0.5	1.1

Table 4: Wilkes' Lambda