A fictitious data set consisting of thirty respondents was created. The data was mainly constructed to find the relationship between the dependent and independent variable.

A fictitious data set consisting of thirty respondents was created. The data was mainly constructed to find the relationship between the dependent and independent variable.

 

A fictitious data set consisting of thirty respondents was created. The data was mainly constructed to find the relationship between the dependent and independent variable.

 

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Marketing Research

 

CASE – 2   Chi-square Test

 

Methodology

  1. A fictitious data set consisting of thirty respondents was created. The data was mainly constructed to find the relationship between the dependent and independent variable. Age was taken as the independent variable and choice of a drink as dependent variable. Six brands of soft drinks were considered as the different choices for the respondents.

  2. The age group coded into six categories as 1 to 6 and the brands of soft drinks were coded into six categories and the codings are as follows:

    (a) Independent variable
              Age                         Coding

             <15                               1

            16 – 25                          2

            26 – 35                          3

            36 – 45                          4

            46 – 55                          5

             >55                               6

     (b)  Dependent variable
           Different brands          Coding

               Coke                           1

               Pepsi                           2

               Mirinda                       3

               Sprite                          4

               Slice                            5

               Fruit Juice                   6

  3. Chi-square test has been used to cross-tabulate and to understand the relationship between the independent and the dependent variable.

  4. Calculation of contingency coefficient and the lambda asymmetric coefficient is done to find the strength of the association between the two variables.

  5. Sample size is taken as thirty.

  6. Analysis of cross-tabulation.

  7. SPSS software package for the cross tabulation analysis.

Problem

This is a bivariate problem. The basic intention of the problem is to understand the relationship between AGE and BRAND PREFERENCE of different brands of soft drinks.

Input Data Table

Serial No.

Age

AGECODE

SOFT DRINK

DRINK CODE

1

<15

1

FRUIT JUICE

6

2

<15

1

SPRITE

4

3

<15

1

MIRINDA

3

4

<15

1

PEPSI

2

5

<15

1

FRUIT JUICE

6

6

16-25

2

COKE

1

7

16-25

2

SLICE

5

8

16-25

2

COKE

1

9

16-25

2

PEPSI

2

10

16-25

2

MIRINDA

3

11

26-35

3

SLICE

5

12

26-35

3

SPRITE

4

13

26-35

3

FRUIT JUICE

6

14

26-35

3

PEPSI

2

15

26-35

3

SLICE

5

16

36-45

4

MIRINDA

3

17

36-45

4

FRUIT JUICE

6

18

36-45

4

FRUIT JUICE

6

19

36-45

4

SLICE

5

20

36-45

4

PEPSI

2

21

46-55

5

COKE

1

22

46-55

5

SPRITE

4

23

46-55

5

SLICE

5

24

46-55

5

FRUIT JUICE

6

25

46-55

5

SLICE

5

26

>55

6

MIRINDA

3

27

>55

6

COKE

1

28

>55

6

COKE

1

29

>55

6

PEPSI

2

30

>55

6

FRUIT JUICE

6

Output Data

Age by Drink Preference

                                                  Age

Drink Preference

Code

<15

16-25

26-35

36-45

46-55

>55

Total

Coke

1

0

2

  33.32% 

1

  20% 

 1

  40%

     5

  16.67%

Pepsi

2

1

  20%

1

  16.67% 

1

  25% 

 1

  20%

 0

 1

  20%

      5

  16.67%

Mirinda

3

 1

  20%

 1

  16.67%

 0

 1

  20%

 0

 1

  20%

     4

  13.33%

Sprite

4

1

  20% 

 1

  25%

 0

1

  20% 

0

    3

   30%

Slice

5

 0

1

  16.67% 

 2

  50%

 1

  20%

     2

   40%

0

6

40%

Fruit Juice

6

     2

40%

1

  16.67%

     2

40%

 1

  20%

 1

  20%

   7

  23.33%

Total

    5

100%

    6

100% 

    4

100%

   5

100%

   5

100%

   5

100%

  30

100%

Chi-Square

Value

DF

Significance

Pearson

18.22857

25

.08325

Likelihood Ratio

25.52646

25

.04332

Mantel-Haenszel test for linear association

.13961

1

.07086

             Minimum Expected Frequency ─.500

             Cells with Expected Frequency <5─36 of 36 (100.0%)

Approximate Statistics

Value

ASE 1

VAL/ASE 0

Significance

Contigency Coefficient

.61479

.08325*1

Lambda:

Symmetric

.18750

.08892

1.99754

With ‘DRINK CODE’ dependent

.21739

.12757

1.56813

With ‘AGE CODE’ dependent

.16000

.07332

2.14834

Goodman & Kruskal Tau:

With ‘DRINK CODE’ dependent

.12432

.03912

.08412*2

With ‘AGE CODE’ dependent

.12152

.02580

.08580*2

   *1  Pearson Chi-square probability

   *2  Based on Chi-square approximation

         Number of Missing Observations: 0

Analysis

In a Chi-square test, for a 90 per cent confidence level, if the significance level is greater than or equal to 0.1, it signifies that there is no association between the two variables in the cross-tabulation and if significance level is less than 0.1, then it signifies that there is a significance relationship between the selected variables.

 A fictitious data set consisting of thirty respondents was created. The data was mainly constructed to find the relationship between the dependent and independent variable

A fictitious data set consisting of thirty respondents was created. The data was mainly constructed to find the relationship between the dependent and independent variable.

A fictitious data set consisting of thirty respondents was created. The data was mainly constructed to find the relationship between the dependent and independent variable.

 

The result of the cross-tabulation

From the output tables, the Chi-square test read a significance level of 0.08325 at 90 percent confidence level. For 90 per cent, significance level is 0.1, that is (1─0.9), so the above result shows that at 0.08 (which is less than 0.1), there is a significant relationship between the two variables. At 95 per cent confidence level, significance level being 0.05, and the above output giving a significance level of 0.08 which is greater than 0.05, there is no relationship between the variables:

If contingency coefficient value is greater than +0.5 then the variables are strongly associated. In the above case the contingency coefficient value being 0.6 which is greater than 0.5, hence the variables are strongly associated.

The asymmetric lambda value (with DRINKCODE dependent) 0.21739 means that 21.7% of error is reduced in predicting brand preference when age is known.

From the above result we can conclude that there is a significant relationship between AGE (independent variable) and BRAND PREFERENCE (dependent variable), of the respondents.

Thus we can conclude that the age of the respondent plays an important role in the purchasing intention of a particular brand of soft drink.

Question

Case 2:  Conduct Chi-square test to cross-tabulate and to understand the relationship between the independent and the dependent variable. Also calculate contingency coefficient and the lambda asymmetric coefficient to find the strength of the association between the two variables. Take Sample size as thirty. Analysis of cross-tabulation using  SPSS software package would be required.

 

 

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