Variance analysis of advantages and disadvantages of the service that active financial associations provide their customers solution by the model of hierarchy classification with two factors and an application

 

Doç. Dr. Adnan MAZMANOĞLU

Department of Mathematics

Marmara University.

Göztepe Campus/İstanbul

E-Mail:amazman@marun.edu.tr

           

                Key Word : Linear Models, Two-Way Nested Classification

                V.A.          :  Variance Analysis

 

           

                The “data table” below is formed by the results of analysis made face to face with some customers chosen random and among different geographical regions and different status, to test the advantage of the level of consumer  credit, credit card and commercial credits(level of   to factor  in ) which are not only included in the economical activities of the public and special banks(factor ) but also assumed by our model, provide their customers.

                Table :1: Observation Table                                           

Observation Values

Banks

Bank type

Points

Sum(Observation)

Number

Average

 

Public

 

Credit card        (1)

5, 3

8

2

4

Consumer credit(2)

9, 3

12

2

6

Commercial      (3)

credit

8,8

16

2

8

 

Sum

36

6

6

Special

Banks

Credit card       (1)

9, 9, 6

24

3

8

Consumer credit(2)

9

9

1

9

Commercial      (3)

 credit

3, 8, 10

21

3

7

                                                       Sum               

54

7

8

                                                  General Sum :               90                   13               7            

 

            In this table, having shown the credit card, consumer credit and commercial credits service types among the busiest activities of the public and special banks, and finding out how much the customers are satisfied with this services, have directed us to the two-factored hierarchic(nested) variance analyses model in which the different levels of hierarchicly set two factors will be tested

                       

Model

            Looking at the data table we can understand that the most suitable model is

 

                                             (1)

. Let’s try to explain this parameters:

: is the  k observation value of the i type of bank in the j  service level

 :  is the type of i bank

 :  shows the effect of the i type bank and j type service type

 

The model consist of two factors   and and these are one within the other. The   factor has two levels named public and special banks, and the  factor has six levels, three of them in the first factor of    and three of them in the second factor of .

p=2;     i=1,...p

q1=3;   j=1,...q1

q2=3

Assuming that there are nij observation value j service type of  i bank, and k=1,...nij  such that;

 

, is the error term.

ni. =  and   n..=

            Using the data table easily, for example,

            n1.= ni. = == n11 + n12 + n13 =6

            n2.= = = n21 + n22 + n23  = 7

            n.. = =6+7=13

Let’s write the normal equations of these thirteen observations using the (1) model.

 

y111 =   5= + 1 +  + 111

y112 =   3= + 1 +  + 112

y121 =   9= + 1 +  + 121

y122 =   3= + 1 +  + 122

y131 =   8= + 1 +  + 131

y132 =   8= + 1 +  + 132

y211 =   9= + 2 +  + 211

y212 =   9= + 2 +  + 212

y213 =   6= + 2 +  + 213

y221 =   9= + 2 +  + 221

y231 =   3= + 2 +  + 231

y232 =   8= + 2 +  + 232

y233 = 10= + 2 +  + 233

 

 

 

 

If we write the models consisting of the (1, 0) indicator values of these equations again,

 

 

 

 

 

 

 

y111 =   5+ + 1(1)+2(0) + (1) + (0) +(0) +(0)+(0) +(0)+ 111

y112 =   3+ + 1(1)+2(0) + (1) + (0) +(0) +(0)+(0) +(0)+ 112

y121 =   9+ + 1(1)+2(0) + (0) + (1) +(0) +(0)+(0) +(0)+ 121

y122 =   3+ + 1(1)+2(0) + (0) + (1) +(0) +(0)+(0) +(0)+ 122

y131 =   8+ + 1(1)+2(0) + (0) + (0) +(1) +(0)+(0) +(0)+ 131

y132 =   8+ + 1(1)+2(0) + (0) + (1) +(1) +(0)+(0) +(0)+ 132

y211 =   9+ + 1(0)+2(1) + (0) + (0) +(0) +(1)+(0) +(0)+ 211

y212 =   9+ + 1(0)+2(1) + (0) + (0) +(0) +(1)+(0) +(0)+ 212

y213 =   6+ + 1(0)+2(1) + (0) + (0) +(0) +(1)+(0) +(0)+ 213

y221 =   9+ +