As before,
a dummy alternative,A4 is included to preclude the net assignment of a value
of 0 to any of the basic alternatives (A1, A2 and A3). Once the process of
assigning relative desirability is completed, the alternative choice coefficient
(ACC) is determined. ACC is equal to the sum value for an individual alternative
divided by the sum for all the alternatives. Thus ACC for the alternative
Ai (i=1,2,3) may be expressed as
Where
i = 1,2,3 ..... M-1;
and M = number of alternatives including the dummy alternative.
It can be seen from Table 5.2 that for the decision factor F4 alternatives A2 and A3 are of equal importance. A value of 0.5 is therefore assigned to both A2 and A3 in the pair A2-A3 in Table 5.6
As may be seen from the ACC column of Table 5.3, alternative A1 is the most desirable relative to decision factor F1.
The next step is to develop a decision matrix. The decision matrix displays the products of the importance weights and the alternative scales. In the example being cited, the importance weights of the decision factors and the alternative choice coefficients of the alternatives relative to each of the decision factors may be presented in a summarised form (Table 5.7).
Table 5.7 FIC and ACC Values
From the total score obtained for each alternative it may be observed that alternative A3 would be the best choice followed by A1 and A2. Table 5.8 Presents the Final Product Matrix
Table 5.8 Final product Matrix
The above example, though very simple, elucidates the concepts of unranked pair-comparison technique and how it can be used for environmental decision making using weighting scaling checklists.
It has already been brought to focus that the scale used in unranked paired-comparison techniques is an ordinal scale. This precludes their averaging, linear transformation and analysis by parametric statistics (e.g., standard deviation, t-test, F-test etc.). Consequently ordinal values must be analysed by non-parametric techniques.
Need for such analyses arises because of the fact that the final scores obtained in the product matrix do not indicate the statistical significance of the differences between the scores.
Though unranked paired-comparison technique or its minor variants are by far the most popular technique used in weighting-scaling checklists there are many other techniques which have been successfully used for ranking of alternatives. Such techniques include
1. alternative-profile concept;
2. use of a reference alternative;
3. linear scaling based on maximum change;
4. letter or number assignment designating impact categories;
5. evaluation guidelines,
6. functional curves; and,
7. predefined impact rating criteria.
These techniques have been reviewed in details in a number of publications. Among these are Solomon (1974), Bisset (1980a 1988), Clark et al (1978 1980), Nichols and Hyman (1980 1982), Rau (1980), Duke et al (1977), Odum et al (1976) and O'Banion (1980).
'Functional graphs' or 'value function curves' have gained wider acceptance as a tool for 'commensuration' (O'Banian 1980). The term commensuration refers to measuring different things by a single standard or measure. Commensuration, as applied to EIA, involves the development of common units of measurement for various environmental attributes, with these units serving as the basis for assessing environmental quality.
Principle of commensuration has been utilised for the development of a number of weighting-scaling checklist methodologies. Canter (1996) described four such methodologies developed for environmental impact assessment of water-resource development projects.
A value function relates the various levels of parameter estimates to the appropriate levels of environmental quality. For every parameter to be considered a value function is developed. A parameter estimate may then be transformed into environmental quality value through the use of the value function developed for the parameter (Dee et al. 1972).
Value function curves are mostly used to transform the impact magnitude into a value scale (e.g., a scale representing environmental quality). The value scale for each type of environmental impact may then be transformed into a composite score representing the total environmental impact due to an alternative.
Where
i = 1,2,3 ..... M-1;
and M = number of alternatives including the dummy alternative.
It can be seen from Table 5.2 that for the decision factor F4 alternatives A2 and A3 are of equal importance. A value of 0.5 is therefore assigned to both A2 and A3 in the pair A2-A3 in Table 5.6
As may be seen from the ACC column of Table 5.3, alternative A1 is the most desirable relative to decision factor F1.
The next step is to develop a decision matrix. The decision matrix displays the products of the importance weights and the alternative scales. In the example being cited, the importance weights of the decision factors and the alternative choice coefficients of the alternatives relative to each of the decision factors may be presented in a summarised form (Table 5.7).
Table 5.7 FIC and ACC Values
|
Decision factor
|
FIC values
|
ACC values, by alternative
|
||
|
A1
|
A2
|
A3
|
||
|
F1
|
0.40
|
0.50
|
0.17
|
0.33
|
|
F2
|
0.20
|
0.33
|
0.17
|
0.50
|
|
F3
|
0.10
|
0.17
|
0.33
|
0.50
|
|
F4
|
0.30
|
0.16
|
0.42
|
0.42
|
From the total score obtained for each alternative it may be observed that alternative A3 would be the best choice followed by A1 and A2. Table 5.8 Presents the Final Product Matrix
Table 5.8 Final product Matrix
|
Decision factor
|
FIC x ACC by alternative
|
||
|
A1
|
A2
|
A3
|
|
|
F1
|
0.200
|
0.068
|
0.132
|
|
F2
|
0.066
|
0.034
|
0.100
|
|
F3
|
0.017
|
0.033
|
0.050
|
|
F4
|
0.048
|
0.126
|
0.126
|
|
Total Score
|
0.331
|
0.261
|
0.408
|
The above example, though very simple, elucidates the concepts of unranked pair-comparison technique and how it can be used for environmental decision making using weighting scaling checklists.
It has already been brought to focus that the scale used in unranked paired-comparison techniques is an ordinal scale. This precludes their averaging, linear transformation and analysis by parametric statistics (e.g., standard deviation, t-test, F-test etc.). Consequently ordinal values must be analysed by non-parametric techniques.
Need for such analyses arises because of the fact that the final scores obtained in the product matrix do not indicate the statistical significance of the differences between the scores.
Though unranked paired-comparison technique or its minor variants are by far the most popular technique used in weighting-scaling checklists there are many other techniques which have been successfully used for ranking of alternatives. Such techniques include
1. alternative-profile concept;
2. use of a reference alternative;
3. linear scaling based on maximum change;
4. letter or number assignment designating impact categories;
5. evaluation guidelines,
6. functional curves; and,
7. predefined impact rating criteria.
These techniques have been reviewed in details in a number of publications. Among these are Solomon (1974), Bisset (1980a 1988), Clark et al (1978 1980), Nichols and Hyman (1980 1982), Rau (1980), Duke et al (1977), Odum et al (1976) and O'Banion (1980).
'Functional graphs' or 'value function curves' have gained wider acceptance as a tool for 'commensuration' (O'Banian 1980). The term commensuration refers to measuring different things by a single standard or measure. Commensuration, as applied to EIA, involves the development of common units of measurement for various environmental attributes, with these units serving as the basis for assessing environmental quality.
Principle of commensuration has been utilised for the development of a number of weighting-scaling checklist methodologies. Canter (1996) described four such methodologies developed for environmental impact assessment of water-resource development projects.
A value function relates the various levels of parameter estimates to the appropriate levels of environmental quality. For every parameter to be considered a value function is developed. A parameter estimate may then be transformed into environmental quality value through the use of the value function developed for the parameter (Dee et al. 1972).
Value function curves are mostly used to transform the impact magnitude into a value scale (e.g., a scale representing environmental quality). The value scale for each type of environmental impact may then be transformed into a composite score representing the total environmental impact due to an alternative.