IIBMS ANSWER SHEETS – 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.
IIBMS ANSWER SHEETS – 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.
IIBMS ANSWER SHEETS – 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.
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.
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
Chi-square test has been used to cross-tabulate and to understand the relationship between the independent and the dependent variable.
Calculation of contingency coefficient and the lambda asymmetric coefficient is done to find the strength of the association between the two variables.
Sample size is taken as thirty.
Analysis of cross-tabulation.
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%
0
0
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%
0
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%
0
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
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 associationbetween the two variables. Take Sample size as thirty. Analysis of cross-tabulation using SPSS software package would be required.
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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