Chapter IV Date analysis and suggestions from the result
Altogather we received 55 copies of questionnaire on an investigation visit. Our discription will be divided into 3 parts in this chapter: First, introduce the data analysis methods we are using; Secondly, do further data analysis on respondents’ 3 aspects:the age scale, education, and geographic location on the basis on a comprehensive analysis of all the questionnaires; Finally, offer suggestions from the results of data processing.
4.1 Introduction of data processing method
It involves complex social and economic problems in education system.In the past,the design and system analysis mainly relied on experience and subjective judgments,lacking of proper science,which often resulted in major mistakes. Analytic Hierarchy Process (AHP) is a new kind of system analysis method combined qualitative analysis and quantitative analysis, in which subjective judgment is expressed and processed in quantity method. In recent years, the AHP is paid more and more attention in the education system of system analysis, design and decision-making. The advantage of the method is very obvious, but because of high requirement on mathematics knowledge, there is still certain difficulties on practical application.
4.4.1 Basic methods and steps of AHP
AHP is to break down complex issues into the various constituent elements, and then group these elements into recursion class times structure by dominating relations. By pairwise comparison method to determine the relative importance of each element , and then integrated decision-maker’s judge, to determine the total order of the relative importance of the decision-making program. There are four steps of AHP in system analysis, design, decision-making ;
(1)Analyse the relationship between the various elements ,establish the recursion class times structure in the system.
(2) Conduct pairwise comparison of various elements on the same level about the importance of a criterion in the upper level, form judgement matrix of pairwise comparison.
(3) Calculate the ralative weight of the compared element to this criterion by judgment matrix .
(4) calculate the complex weight of each level’s elements to system target,and reorder.
4.1.2 Establishment of recursion class of times
First,systemize and methodize the system problem,construct a clear hierarchical structural model. In the model, the complex problem is broken into different compoments, these components called elements are classified into different groups,according to their own property,and form different levels. The same hierarchy elements play a dominent role to certain elements in the next level,as the standard.At the same time, it is also dominated by the top level elements. Levels can be divided into three groups:
(1) The top layer: There is only one element in this level ,which is the intended target or desired results.therefore, it is called the target layerof the problem.
(2) The middle layer: This level includes some criteria need to be considered in the intermediate links of the goal achieving. This level is composed by several layers, which can be divided into criteria and sub-criteria . So,this level is also called the criteria level;
(3) The bottom layer: This level includes options of a variety of measures, decision-making programs to achieve the target, and therefore, it is called the measure level or plan level.
The hierarchical structure formed by the dominating relationship between the upper layer elements and the lower layer elements is called the recursion class times structure. Of course, the upper layer elements may dominate all the elements, but sometimes it only dominate certain elements. The number of the level in recursion class times is unrestricted because it is related to the complexity of the problem and how detail the analysis needs to be. Generally, no more nine elements are dominated by each element in each level, because too much domination will bring difficulty on pairwise comparison judgement. The hierarchical structure for problem solving, of course, is very important. Certainly, to establish good hierarchical structure depends on decision makers’ deep and comprehensive understanding of the problems.
4.1.3 Introduction of specific algorithm
The importance of the criteria could be approximated by the AHP using pairwise comparisons [1]:
Suppose that the value function has the form
If , the corresponding outcome can be deleted from consideration. Thus, we shall assume that .
Define the weight ratio by
.
Note that, for any indexes
Define the matrix of weight ratios as :
The matrix W is called consistent if its components satisfy the equalities for any i, j and k.
Observe that: Since each row of W is a multiple of the first row, the rank of W is one, and thus there is only one nonzero eigenvalue which is q.
This due to the fact that =1 and that the sum of all eigenvalues is equal to the trace of W (i.e. ).
We can easily check that therefore w must be the eigenvector of W corresponding to the maximum eigenvalue q.
As a living system, human perception and judgment are subject to change when the information inputs or psychological states of the decision maker change. A fixed weight vector is difficult to find.
Saaty proposed the following to overcome this difficulty: Estimate or elicit the weight ratio by and let be the matrix of components . Note that as each > 0, we expect and shall assume that all > 0.
Furthermore, as Saaty suggested that in practice, only , j > I need to be assessed.
Since A is found as an approximate for W, when the consistency conditions are almost satisfied for A, one would expect that the normalized eigenvector corresponding to the maximum eigenvector of A, denoted by , will also be close to w.
Note that the above observation is valid for any matrix which is consistent. The next thing is to inform the “Intensity of relative importance”:
Intensity of
relative importance Definition
1
3
5
7
9
2,4,6,8 equal importance
weak importance (of one over the other)
strong importance
demonstrated importance over the other
absolute importance
intermediate values between
Table 1. Saaty’s scale of relative importance.
4.2 Data processing
4.2.1 The overall analysis
First,we made an overall statistic over all the questionnaires. All the surveyed teachers, according to the teaching location to distinguish: teaching is located in the city take up 45.5%, teaching is located in districts and counties were 34.5%, teaching is located in rural areas, 20%; according to the teacher's school to distinguish, the teacher who come from provincial and municipal key secondary schools accounted for 81.8%, from the ordinary schools accounted for 16.4%, and from town’s key schools, 1.8%;
[1]T. L. Saaty, The Analytic Hierarchy Process: Planning, Priority Setting, Resource
Allocation, McGraw-Hill, New York, 1980.
先是这个样子,你先看看,下面就准备根据AHP写程序