In the marketing research the instances when we need to examine the relationship between two variables are frequent. Knowing the relationship between the two variables involves the use of tests that can be parametric and nonparametric. This paper includes the non-parametric tests used in the bivariate analysis. The used tests are: chi square test, the Mann-Whitney test, the Kolmogorov-Smirnov test. Besides these tests, this paper also includes measuring the association between nominal variables using the C contingency coefficient and Cramer's V coefficient and between two metric variables, using the Pearson’s linear correlation coefficient.variables, Chi square test, U test, Kolmogorov-Smirnov test, Cramer's V contingency coefficient, Pearson's linear correlation coefficient,

Assist. Ph.D Kulcsár Erika

English

Research Papers in Economics

 
 
110 
Revista Tinerilor Economi ti (The Young Economists Journal)
THE BIVARIATE ANALYSIS BETWEEN THE VARIABLES THAT DEFINE THE INVESTIGATED 
TOURIST POPULATION IN THE CENTER DEVELOPMENT REGION AND THE OTHER IMPORTANT 
TOURIST VARIABLES  
Assist. Ph.D  Kulcsár Erika 
University “Babe -Bolyai” 
Faculty of Economics  and Business Administrations 
Cluj Napoca, Romania 
  Abstract: In the marketing research the instances when we need to 
examine the relationship between two variables are frequent. Knowing the 
relationship between the two variables involves the use of tests that can be 
parametric and nonparametric. This paper includes the non-parametric 
tests used in the bivariate analysis. The used tests are: chi square test, the 
Mann-Whitney test, the Kolmogorov-Smirnov test. Besides these tests, this 
paper also includes measuring the association between nominal variables 
using the C contingency coefficient and Cramer's V coefficient and 
between two metric variables, using the Pearson’s linear correlation 
coefficient.   
JEL classification: M31, L83 
Key words: variables,  
2  test ,  U test,  Kolmogorov-Smirnov test, Cramer's V 
contingency coefficient,  Pearson's linear correlation coefficient,.  
Introduction 
  The relation between two variables can be measured with the same type of 
scale or, each with a different type of scale. In this case, practically, I plan to analyze 
the link between two questions. Actually I want to know whether the answers given by 
the subjects to a question, is correlated or associated with the answers given to another 
question. 
6 
  The quantitative marketing research took place during 15.05.2009-17.10.2009. 
Over 2,000 questionnaires have been distributed. 410 filled in questionnaires have been 
included in this research. The questionnaires were filled in by both foreign tourists and 
Romanian tourists in: Bra ov, Predeal, Poiana Bra ov, Sfântu Gheorghe, Covasna, 
Miercurea-Ciuc, Gheorgheni, Tu nad, Târgu-Mure , Sighi oara, Sibiu, Alba – Iulia and 
other localities that have linked this route. 
Non-parametric test  used in the bivariate analysis 
2  test (chi-square) 
   The
2   test is used to test the statistical significance of the frequencies 
distribution, as absolute or percentage values from two variables measured with 
nominal scale, having a given number of ways, for a sample of predetermined size. 
                                                      
6 Constantin L.  Marketing Research, Infomarket Printing House, Bra ov, 2004. p. 249  
 
  111
Business Statistics –Economic Informatics 
Also, the chi square test can also be used to measure the differences between two or 
more independent groups when a certain variable is taken into account. The responses 
given by the subjects must be introduced in a contingency table.
7  
Next I will try to highlight the link between the age of the respondents and 
whether they came for the first time or not in the Centre Development Region. 
Table no. 1. The contingency table 
Is this the first time when you come to this region? * Age Crosstabulation
14 44 80 48 28 8 222
14.1 65.0 57.4 52.0 28.2 5.4 222.0
12 76 26 48 24 2 188
11.9 55.0 48.6 44.0 23.8 4.6 188.0
26 120 106 96 52 10 410
26.0 120.0 106.0 96.0 52.0 10.0 410.0
Count
Expected Coun
Count
Expected Coun
Count
Expected Coun
No
Yes
Is this the first time whe
you come to this region
Total
till 25
years old
between
26-35
years old
between
36-45
years old
between
46-55
years old
between
56-65
years old
more than
65 years old
Age
Total
 
Within table no. 1 the distribution of the tourists who came for the first time 
and those who came before in the region according to the six age categories can be 
noticed. 
There are differences between the observed frequencies and the expected 
frequencies in all subgroups formed by crossing the two variables.  
Table no. 2. 
2   test results 
Chi-Square Tests
37.543a 5 .000
38.975 5 .000
3.986 1 .046
410
Pearson Chi-Square
Likelihood Ratio
Linear-by-Linear
Association
N of Valid Cases
Value df
Asymp. Sig.
(2-sided)
1 cells (8.3%) have expected count less than 5. The
minimum expected count is 4.59.
a. 
 
 
2
calc  value is 37.543, it will be compared with 
2
5 ; 05 , 0 
= 11.071 (table no. 2). 
Since
2
calc  >
2
5 ; 05 , 0 
,  0 H  is rejected in the sense that we can guarantee with a 95% 
probability that at the level of the total population, there will be differences between the 
expected and observed frequencies. In conclusion, there is a correlation between the age 
of the tourists and whether they had been before or not in the Center Development 
Region. 
Analyzing the level of significance I reached the same conclusion. Since it is 
less than 0.05, according to which there is a difference between the two variables,  1 H  
is accepted. 
 
                                                      
7 Constantin L.  Marketing Research, Infomarket Printing House, Bra ov, 2004. p. 250 
  
 
112 
Revista Tinerilor Economi ti (The Young Economists Journal)
Mann-Whitney test (U test) 
The U test allows comparison of the differences in the case when the respective 
populations are not normally distributed and they are not equal in terms of variances. 
The specific of the test is that to quantitative values corresponding to two independent 
groups, ranks are associated which brings to study the distribution of the ranks between 
the two samples. 
8 In this part of the essay I will test the existence of a significant 
difference between the two sex categories with respect to the importance of the level of 
charged tariffs in choosing a hotel. 
Table no. 3 The sum of the ranks for each group 
Ranks
230 214.77 49397.00
180 193.66 34858.00
410
Gender
Male
Female
Total
Level of charged tariffs
N Mean Rank Sum of Ranks
 
After applying the test, I obtained table no. 3 which contains the size of each 
group in the sample, the amount of ranks and average ranks. In another table provided 
by SPSS, the value  obs U is given, together with other sizes used to deciding in the case 
of the U test (table no. 4) 
Table no. 4 Values corresponding to the U test 
Test Statistics a
18568.000
34858.000
-1.861
.063
Mann-Whitney U
Wilcoxon W
Z
Asymp. Sig. (2-tailed)
Level of
charged tariffs
Grouping Variable: Gender a. 
 
  In both cases the sub-samples are large, both exceeding 30 people 
( 230 1  n and  180 2  n ). The decision was taken based on the calculated size  U z =-
1.861, which was compared to the value in the table for a significance level   = 0.05. It 
is noted that  U z =-1.861 >- U z =-1.96. Therefore we accept the null hypothesis, 
according to which we can not guarantee with a 95% probability that, between male and 
female, there are differences in terms of the importance given to the level of prices 
charged, in choosing a hotel. I could have taken this decision also based on the level of 
significance "Asymp. Sig. (2-tailed), which is 0.063, higher than the 0.05 value, which 
leads also to the acceptance of the null hypothesis. 
Kruskal-Walis test 
In the event the comparison of three or more groups of the population is aimed 
at, where data are measured ordinal, then the Kruskal-Walis test is used for the 
statistical significance of the differences.
9  
                                                      
8 Constantin L.  Marketing Research, Infomarket Printing House, Bra ov, 2004. p. 259 
9 Cristinel C. - Marketing information system. Marketing data analysis and processing. 
Applications in SPSS, Publisher Infomarket, Bra ov, 2006, p. 172  
 
  113
Business Statistics –Economic Informatics 
I will test the existence of significant differences between 6 groups of 
population formed according to the age of tourists regarding the importance of prices 
charged to choose a hotel. 
The SPSS system has provided a table containing the size of each group at the 
level of the sample and the mean ranks corresponding to the groups (table no. 5). 
Table no. 5 The mean ranks in the case of the Kruskal-Walis test 
Ranks
26 217.50
120 191.15
106 237.93
96 174.27
52 211.96
10 268.90
410
Age
till 25 years old
between 26-35 years old
between 36-45 years old
between 46-55 years old
between 56-65 years old
more than 65 years old
Total
Level of charged tariffs
N Mean Rank
 
Table no. 6 The calculated values in the case of the Kruskal-Wallis test 
 
Test Statistics a,b
21.220
5
.001
Chi-Square
df
Asymp. Sig.
Level of
charged tariffs
Kruskal Wallis Test a. 
Grouping Variable: Age b. 
 
The value H = 
2
calc   of the analysis table is equal to 21.220 (table no. 6).Since 
H = 21,220 > 11.071, which means that I accept the alternative hypothesis. Therefore, 
between the 6 groups of the population there are differences in terms of the importance 
given to the levels of prices charged in choosing a hotel. 
Kolgomorov-Smirnov test 
The test is used to test the differences between two independent samples, the 
same as with Mann-Whitney test. Test analyses the existence of significant differences 
between the two groups in terms of evaluations or attitudes towards a product, service 
or marketing phenomenon, based on a specific criterion. 
10 
Based on Kolmogorov-Smirnov, I shall test if the views on the statement "The 
gentleness of the staff can make this hotel to become one of the favorite places of 
tourists" are different depending on the gender of the respondents. 
Out of the 180 female respondents 43.3% have chosen the "totally agree", 4.4% 
opted for "totally disagree". 39.1% of male opted for the variant “totally agree" (table 
no. 7). 
 
                                                                                                                                              
 
10 Cristinel C. - Marketing information system. Marketing data analysis and processing. 
Applications in SPSS, Publisher Infomarket, Bra ov, 2006, p. 166 
  
 
114 
Revista Tinerilor Economi ti (The Young Economists Journal)
he gentleness of the staff can make this hotel to become one of the favorite places of tourist
* Gender Crosstabulation
6 8 14
2.6% 4.4% 3.4%
8 8 16
3.5% 4.4% 3.9%
58 22 80
25.2% 12.2% 19.5%
68 64 132
29.6% 35.6% 32.2%
90 78 168
39.1% 43.3% 41.0%
230 180 410
100.0% 100.0% 100.0%
Count
% within Gender
Count
% within Gender
Count
% within Gender
Count
% within Gender
Count
% within Gender
Count
% within Gender
totally disagree
disagree
neither agree
nor disagree
agree
totally agree
The gentleness of
the staff can make
this hotel to become
one of the favorite
places of tourists
Total
Male Female
Gender
Total
 
Table no. 8 Distribution of responses on groups formed according to the gender 
Frequencies
230
180
410
Gender
Male
Female
Total
The gentleness of the
staff can make this hotel
to become one of the
favorite places of tourists
N
 
Out of the total of 410 tourists who have expressed their opinion on this 
question, 180 are female and 230 male (table no. 8) 
Table no. 9. The values calculated for the Kolmogorov-Smirnov test 
Test Statistics a
.102
.102
-.028
1.024
.245
Absolute
Positive
Negative
Most Extreme
Differences
Kolmogorov-Smirnov Z
Asymp. Sig. (2-tailed)
The
gentleness of
the staff can
make this
hotel to
become one
of the favorite
places of
tourists
Grouping Variable: Gender a. 
 
The maximum difference between the cumulated frequencies is 0.102.  calc D  = 
0.102 (table no. 9) I compared the value of for   D    180 , 230 2 1   n n . I calculated 
Table no.7. Relative frequencies n percentages and columns  
 
  115
Business Statistics –Economic Informatics 
this value according to the formula:
180 230
180 230
36 , 1 36 , 1
2 1
2 1






n n
n n
D = 0,135. 
Since  calc D <  D , the alternative hypothesis is accepted.   
Conclusion: Between the two groups there are no differences in terms of their 
opinions regarding the gentleness of staff. 
Measuring the association between nominal variables 
The 
2  test only proved me the existence of links between the nominal 
variables analyzed without indicating their intensity. In order to measure the association 
between nominal variables I used the C contingency coefficient and Cramer's V 
coefficient. 
Next I will try to highlight the intensity of the relationship between age and 
whether respondents had been to this region of the country before or not.  This 
relationship had been previously examined, through the 
2   test, the result being the 
fact that we can accept with a 95% probability that the two variables are related.  
290 . 0
410 543 . 37
543 . 37
2
2





n
C
calc
calc


 
From table no. 2 I extracted the value 
2
calc    which is 37.543 and with its help I 
can calculate the coefficients that measure the association between the two variables.  
Independent variable is age, which has 6 categories. Therefore the basic value 
to which  max C is calculated is k = 6.  91 . 0
6
1 6 1
max 




k
k
C  
Next I shall calculate also the value of the Cramer’s V coefficient.  
1 410
543 . 37
2




t n
V
calc 
=0.303 
In table no. 10 the measuring coefficients of the association between the 
nominal variables provided by the SPSS system are presented.   
Table no. 10 The measuring coefficients of the association between the nominal 
variables 
Symmetric Measures
.303 .000
.303 .000
.290 .000
410
Phi
Cramer's V
Contingency Coefficient
Nominal by
Nominal
N of Valid Cases
Value Approx. Sig.
Not assuming the null hypothesis. a. 
Using the asymptotic standard error assuming the null
hypothesis.
b. 
 
The calculated coefficients indicate an average association between the two variables. 
 
  
 
116 
Revista Tinerilor Economi ti (The Young Economists Journal)
Measuring the association between two metric variables 
The intensity of the relationships between two variables metrically measured is 
measured based on the Pearson’s linear correlation coefficient. It is based on the co-
variation between the two variables, being a parametric coefficient since it is calculated 
as the mean of the two variables.
11  
Table no. 11 Pearson’s linear correlation coefficient 
Correlations
1 .017
.729
410 410
.017 1
.729
410 410
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
How many days did you
plan to stay in this region?
Estimation of the expenes
incurred in the Center
Development Region
(including the residence
country - EUR-)
How many
days did you
plan to stay in
this region?
Estimation of
the expenes
incurred in the
Center
Development
Region
(including the
residence
country -
EUR-)
 
The correlation coefficient between the two variables is r = 0.017 (table no 11), 
this indicating that there is no significant link between the expenditure incurred in the 
Centre Development Region and the number of days planned for this region. For the 
test I calculated the critical report: 
2 2
017 , 0 1
2 410 017 , 0 2

 




r n
n r
RC =0.343 
RC=0,343<1.96, which means that the two variables are not correlated. This decision 
can be taken also based on the level of significance which is higher than 0.05.  
 
By processing the primary data I obtained the following results:  
-  There is a link between the age of respondents and whether they had been or 
not in the Center Development Region before. Most of those respondents who 
had been in this part of the country before fall within the age group 26-35 years 
category followed by tourists with ages between 46-55 years.  
-  The results obtained based on the U test surprised me, namely that there is no 
difference between male and female regarding the importance given to the level 
of prices charged, in choosing a hotel. I was very convinced that there is a 
connection between the two groups and the importance given to charges of the 
hotel. But on the one hand, these results underline the fact that the behavior of 
services consumer differs from that of the products consumers, others than 
services.  
                                                      
11 Cristinel C. - Marketing information system. Marketing data analysis and processing. 
Applications in SPSS, Publisher Infomarket, Bra ov, 2006, p. 203 
  
 
  117
Business Statistics –Economic Informatics 
-  Between the six age groups there are differences in the importance given to the 
levels of charged in choosing a hotel which actually explains the existence on 
the tourist market of different categories of hotels.  
-  With respect to the statement "Gentleness of staff makes this hotel to become 
one of the favorite places of tourists" , the opinion of female respondents and 
that of male respondents was similar, i.e. there is no difference between the two 
groups and their evaluations on the gentleness of staff  hotel.  
-  Although I expected that after the application of the Pearson's linear correlation 
coefficient to discover a relationship between the costs incurred in the Center 
Development Region and the expected number of days in the area, following 
the interpretation of the results obtained I found that there is no significant 
relation between the two mentioned variables.  
As a final conclusion of this paper I can mention that the behavior of the tourist services 
consumer requires further research.  
REFERENCES  
1.  Cristinel, C.  Marketing information system. Marketing data analysis and 
processing. Applications in SPSS, Infomarket Press, 
Bra ov, 2006.  
2.  Constantin,  L.  Marketing Research, Infomarket Printing House, Bra ov, 
2004.  
 

Marketing information system. Marketing data analysis and processing.

Marketing Research, Infomarket Printing House,

THE BIVARIATE ANALYSIS BETWEEN THE VARIABLES THAT DEFINE THE INVESTIGATED TOURIST POPULATION IN THE CENTER DEVELOPMENT REGION AND THE OTHER IMPORTANT TOURIST VARIABLES

THE BIVARIATE ANALYSIS BETWEEN THE VARIABLES THAT DEFINE THE INVESTIGATED TOURIST POPULATION IN THE CENTER DEVELOPMENT REGION AND THE OTHER IMPORTANT TOURIST VARIABLES

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