BRM Project Report

BRM Project - SPSS

Study Based on Cold Drinks

Ankur Gupta - B12072

Shaily Khasgiwala B12-112

Shashank Sharma B12-113

Sumeet Tayal B12-122

Radesh Aggarwal B12102

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Table of Contents Purpose of the Study ............................................................................................................................... 2

Chi Square test ........................................................................................................................................ 2

Cramers V coefficient Test ...................................................................................................................... 3

Cochran Test ........................................................................................................................................... 4

Friedman Two-way ANOVA .................................................................................................................... 5

Dunn’s Multiple Comparison test for K related Samples ........................................................................ 6

Point Bi-serial Correlation ....................................................................................................................... 7

Multiple Regression Analysis .................................................................................................................. 9

Kolgomorov Smirnov One Sample Test ................................................................................................ 10

Kruskal Wallis One way ANOVA ..................................................................................................... 10

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Purpose of the Study The Basic purpose of this survey and analysis is the study of the buying behaviour of the cold drinks.

Since it is believed that soft-drinks are mostly driven by impulse buying behaviour and are

dependent on the season, we think that it is important to understand if this hypnosis is really true.

Further, the independence and dependence on various variables need to statistically study to

conclude whether buying behaviour doesn’t have any pattern and correlation. Following is the

survey that we sent to 100 people across various age groups – Random sampling. Out of these we

received 40 responses. We therefore will conduct the study based on these 40 sample data points.

Chi Square test

Purpose

This test is used to find whether there is a significant difference between the two quantitative

variables that are measured on the nominal scale. In our case the two categories have been the age

group and the most brought (brand) soft-drink.

Requirements

a. Variables should be measured on nominal scale

b. There should be independence among the measures.

c. Test should be conducted on actual frequencies.

Null Hypothesis, H0 = There is no association between the most brought brand and the age group of

respondents.

Alternate Hypothesis, H1 =The two variables are dependent.

Snapshot from SPSS

Case Processing Summary

Cases

Valid Missing Total

N Percent N Percent N Percent

Age * Most_Bought 40 100.0% 0 0.0% 40 100.0%

Age * Most_Bought Crosstabulation

Count

Most_Bought Total

Coke Pepsi Sprite Thums Up Fanta

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Age

18-20 1 0 1 0 1 3

21-23 4 2 3 1 1 11

24-26 8 2 2 8 3 23

Above 26 1 0 0 1 1 3

Total 14 4 6 10 6 40

Chi-Square Tests

Value df Asymp. Sig. (2-

sided)

Pearson Chi-Square 8.709a 12 .728

Likelihood Ratio 10.036 12 .613

Linear-by-Linear

Association

.409 1 .522

N of Valid Cases 40

a. 18 cells (90.0%) have expected count less than 5. The minimum

expected count is .30.

Result

As the P value is greater than 0.5 we do not have enough statistical evidence to reject the null

hypothesis. Hence we can safely say that at 95% confidence level, there is no association between

the age group and the most brought brand.

Cramers V coefficient Test

Purpose

The purpose of this test is to analyse the strength of association between the two nominal variables

– the Gender and the most brought brand. This test is effective in measuring the strength of

association irrespective of the table size and therefore we have conducted this test on the following

categories.

Requirements

a. Data should be measured on nominal variables with each variable having any number of

categories

Null Hypothesis, H0= There is no association between the most brought brand and the gender.

Alternate Hypothesis, H1= There is no association between the two variables.

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Snapshot from SPSS


Cases

Valid Missing Total


Sex * Most_Bought 40 100.0% 0 0.0% 40 100.0%

Sex * Most_Bought Crosstabulation

Count

Most_Bought Total

Coke Pepsi Sprite Thums Up Fanta

Sex Male 10 3 5 9 4 31

Female 4 1 1 1 2 9

Total 14 4 6 10 6 40

Symmetric Measures

Value Approx. Sig.

Nominal by Nominal Phi .208 .786

Cramer's V .208 .786

N of Valid Cases 40

Result

As the P value is greater than 0.5 we do not have enough statistical evidence to reject the null

hypothesis. Hence we can safely say that at 95% confidence level, there is no association between

the gender and the most brought brand.

Cochran Test

Purpose

This test is used to measure responses to dichotomous which have responses such as yes or no.

Requirements

a. Data to be measured on dichotomous scale

b. Number of treatment should be greater than two

c. All the respondents should have responded to all the treatments.

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We have applied this test to observe whether or not increase in the price of cold drink has any effect

on its purchase

Null Hypothesis, H0= the change in price does not have any effect on the buying behaviour.

Alternate Hypothesis, H1= There is relation between the prices and the buying behaviour

Snapshot from SPSS

Cochran Test

Frequencies

Value

0 1

Cold_Drink_12 8 32

Cold_Drink_14 16 24

Cold_Drink_16 30 10

Result

It is clearly visible that we can safely reject the null hypothesis to accept the alternate hypothesis

and therefore we can say that buying behaviour change with the change in prices.

Friedman Two-way ANOVA

Purpose

This test is done to find out consistency of ranking the cold drinks by the students. We cannot use

any other rank correlation test here as we have more than 2 students and more than 2 cold drinks.

We cannot use Kruskal-Wallis One-way ANOVA because the rankings are done by the same

individuals across the attributes. Hence the only option is to use Friedman Two-way ANOVA

Null Hypothesis, H0= There is no significant difference in the ranking of cold drinks.

Alternate Hypothesis, H1= There is a significant difference between the ranking of cold drinks.

Snapshot from SPSS

Ranks

Mean Rank

Coke 2.45

Pepsi 3.10

Thumsup 2.65

Fanta 3.88

Test Statistics

N 40

Cochran's Q 33.818a

df 2

Asymp. Sig. .000

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Sprite 2.93

Test Statisticsa

N 40

Chi-Square 19.300

df 4

Asymp. Sig. .001

Result

Since the asymptotic significance is 0.001 and it is less than α=0.05, we reject the null hypothesis.

Hence we conclude that there is a significant difference between the ranks of cold drinks, Coke being

ranked 1

Dunn’s Multiple Comparison test for K related Samples

Purpose

Whenever Friedman’s test reveals a significant difference in the mean ranks, then it becomes

mandatory to check which sample group is different from which other sample group. This is done

with the help of Dunn’s Multiple Comparison test.

Null Hypothesis, H0= The rank preference of ith and jth cold drink is same.

Alternate Hypothesis, H1= There is a difference in the rank of ith and jth cold drink

Snapshot of testing

The sum of ranks R1 = 98, R2 = 124, R3 = 106, R4 = 155, R5 = 117

The absolute difference between these sum of ranks across all categories is as follows:

D12 26

D13 8

D14 57

D15 19

D23 18

D24 31

D25 7

D34 49

D35 11

D45 38

The largest absolute difference is 57.

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Standard Deviation for the data set = Square root of (n*k*(k+1)/No. of pairs), where n = 40 and k =5.

Hence SD = 10.95445

The critical Z value for a single tailed probability = α/k(k-1) = 2.32 taking alpha as 20%

Now Tij=Dij/SD which is calculated for all values.

T12 2.373464

T13 0.730297

T14 5.203364

T15 1.734455

T23 1.643168

T24 2.8299

T25 0.63901

T34 4.473068

T35 1.004158

T45 3.46891 When Tij >= Critical Z, we reject the null hypothesis and hence establish that there is no significant

difference between ith and jth cold drink.

Result

1. Coke is the most preferred cold drink while Fanta is the least.

2. The absence of a significant difference between Thumsup and Sprite signifies that they are

tied for the second most preferred cold drink.

Coke Thumsup Sprite Pepsi Fanta

Point Bi-serial Correlation

Purpose

The test is used to analyse the correlation between two variables which are on different categories.

Requirements

a. There should be two variables of measurement. One variable on interval scale and other on

a dichotomous scale

b. It is mandatory that nominal scale independent variable should have two categories. We

have applied this test to observe whether or not increase in the price of cold drink has any

effect on its purchase

Null Hypothesis, H0= There is no significant correlation between the gender of the respondent and

the number of cold drinks bought.

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Snapshot from SPSS

Correlations

Frequency of

Purchase

Sex

Pearson Correlation Frequency of Purchase 1.000 -.058

Sex -.058 1.000

Sig. (1-tailed) Frequency of Purchase . .360

Sex .360 .

N Frequency of Purchase 40 40

Sex 40 40

Variables Entered/Removed

Model Variables

Entered

Variables

Removed

Method

1 Sexb . Enter

a. Dependent Variable: Frequency of Purchase

b. All requested variables entered.

Model Summary

Model R R Square Adjusted R

Square

Std. Error of the

Estimate

1 .058a .003 -.023 5.19713

a. Predictors: (Constant), Sex

ANOVAa

Model Sum of Squares df Mean Square F Sig.

1

Regression 3.513 1 3.513 .130 .720b

Residual 1026.387 38 27.010

Total 1029.900 39


b. Predictors: (Constant), Sex

Result

It is clearly visible that the regression coefficient is equal to -.058 which is very low, indicating a weak

correlation between the two variables. Also the p value is .720 which is greater than .05 indicating

that there is not enough evidence to reject the null hypothesis. So there is no correlation between

the two variables.

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Multiple Regression Analysis

Purpose

We are trying to find the correlation between one independent and two independent variables.

Hence, we are using multiple regressions. As we have two independent ordinal variables, we have

recoded them into dummy variables keeping the lowest value as reference.

Null Hypothesis H0: There is no significant correlation between age of the respondent/climate of the

region where he stays and the number of cold-drinks bought per week.

Multiple Regression Analysis

Coefficients

Model Unstandardized Coefficients Standardized

Coefficients

t Sig.

B Std. Error Beta

1 (Constant) 5.419 2.547 2.128 .040

Sex -.710 1.968 -.058 -.361 .720


Model Summary

Model R R Square Adjusted R

Square

Std. Error of the

Estimate

1 .201a .040 -.101 5.39147

a. Predictors: (Constant), cool, age greater than 26, age between 18

and 20, age between 21 and 23, moderate

ANOVAa

Model Sum of Squares df Mean Square F Sig.

1

Regression 41.589 5 8.318 .286 .917b

Residual 988.311 34 29.068

Total 1029.900 39


b. Predictors: (Constant), cool, age greater than 26, age between 18 and 20, age between 21

and 23, moderate

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Because, significance level is way high than .05, we can say there is not enough statistical evidence

to reject the null hypothesis. So, we can infer that there is no correlation between age of the

respondent/climate of the region where he stays and the number of cold-drinks bought per week.

Kolgomorov Smirnov One Sample Test

Purpose

We have used this test to evaluate to see if the customers are indiscriminate in their perception

about the fizz impact of a cold-drink

Null Hypothesis: There is no difference in the proportion of the respondent’s perception about the

fizz impact.

Snapshot from SPSS

Kolmogrov Smirnov Test


Cases

Valid Missing Total


Fizz_Impact 40 97.6% 1 2.4% 41 100.0%

Tests of Normality

Kolmogorov-Smirnova Shapiro-Wilk

Statistic df Sig. Statistic df Sig.

Fizz_Impact .269 40 .000 .868 40 .000

a. Lilliefors Significance Correction

Results

As the p-value is less than 0.05, we have enough statistical evidence to reject the null hypothesis.

This means that there is a difference in the proportion of fizz impact.

Kruskal Wallis One way ANOVA

To find out whether the average number of cold drinks bought is the same across regions of

different climate we perform the Kruskal Wallis One way ANOVA.

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H0: The average number of cold drinks is the same across regions of different climate

Ha: The average number of cold drinks is not same across regions of different climate

Ranks

Climate N Mean Rank

Frequency of Purchase

Warm 19 19.92

Moderate 15 21.30

Cool 6 20.33

Total 40

Test Statisticsa,b

Frequency of

Purchase

Chi-Square .123

df 2

Asymp. Sig. .940

a. Kruskal Wallis Test

b. Grouping Variable: Climate

Since the asymptotic significance is less than alpha, the null hypothesis cannot be rejected. Hence

the average number of cold drinks bought is not dependent on climate.

If this result had come out significant, then to find the reason for significance we would perform

Wilcoxon Multiple Comparison Test.

BRM Project Report

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