25 Technique of Computing the Composite Score for Socio- Economic Development

Prof Bimal Kar

Introduction

Socio-economic development, social well-being, human development, quality of life, agricultural development, agricultural productivity, infrastructure development, etc are all multi-dimensional concepts. Each of these is the combined performance or effects of a number of related attributes. Depending on the varying nature of differentattributes their units of measurement also vary. For instance, computation of Human Development Index as per UNDP involves combining the performance of GNP per capita, educational status in terms of adult literacy rate and gross enrolment ratio, and life expectancy at birth. The units of their measurement in this case are dollar, percentage and year respectively. It may be mentioned here that while finding out the cumulative result of these three attributes with different units of measurement, viz. dollar, percentage and year, it is necessary to make them unit-less by applying certain data standardization or transformation techniques. As discussed under Data Transformation, the standardization or transformation of data with different units of measurement, viz. percentage, number, year, monetary value, km per km2, number per unit area, number per lakh population, production per unit area, etc, can be done through ranking, simple ratio, simple quotient and Z-value. Such techniques of data standardization help computing composite score by adding the unit-less transformed values. This is very much important in geography for the purpose of areal classification of various phenomena of multi-dimensional nature, as already mentioned, and to undertake phenomenal patterning based on the principle of relative degree of homogeneity or heterogeneity.

With this background, an attempt is made here to apply the techniques of data standardization like ranking, simple quotient and Z-value for computing composite score. For this purpose the attributes like literacy rate (in per cent), proportion of urban population (in per cent), proportion of population in age group 0-6 (in per cent), proportion of households with electricity (in per cent), proportion of non-agricultural workers (in per cent), road density (km per km2) and proportion of hospital beds (number of beds per lakh population have been considered at district level for the state of Assam for the year 2011 (Table 1). These attributes constitute some of the indicators of socio-economic development. A meaningful computation of composite score combining the performance of these indicators in standard form gives us the relative position of each district in respect of socio-economic development, and choropleth mapping of the same gives the picture of spatial variation in socio-economic development in the state of Assam.

Table 1: District level data of selected socio-economic development indicators for Assam, 2011

Such indicatorsmay be expressed in quantitative manner as ith that shows a particular indicator is expression of i=1,2,3,…,nwhile areal units, districts are expressed as jth, j=1,2,3,…,m. Say i=2  represents the percentage of urban population in a particular district. Likewise, i=4 represents the percentage of HH having electricity connections, while j=8 represents Lakhimpur district.

It may be mentioned here that out of 7 indicators of socio-economic development (X1 to X7) as given in Table 1, excepting X3, all are positive indicators of development. It means X3, i.e. proportion of population in age group 0-6 is a negative indicator. In this case, the higher value is indicative of lower development level. Hence, in the midst of a large number of positive indicators, the negative indicator should be taken all necessary care while transforming its value so that it is compatible with the values of positive indicators.

Let us now consider the application of three different simple techniques of calculating composite score of socio-economic development level for the data given in Table 1.

1. Ranking Method

It is one of the simplest and quickest methods of computing composite score involving multivariate data with different units of measurement. Kendall (1939) used this technique for finding out agricultural efficiency in England and Wales using productivity data of different crops. The standardization of productivity data was done through ranking, giving rank 1 to the highest productivity, rank 2 to the next highest productivity, and so on. It means conversion of the value of interval or ratio data into ordinal data makes it scale free. The composite score, called ranking coefficient, in this case is found out for each spatial unit by simply adding the corresponding rank values of allthe indicators (e,g, productivity of different crops). Here, as the highest value of an indicator refers to Rank 1 and next highest value to rank 2, higher value of composite score of ranks is indicative of lower level of productivity.It can be expressed as

Where Cj is composite rank value of jth district and Ri is rank of an indicator of development in the State of Assam.

In the present case (Data Table 1), the rank value of literacy rate is 1 for Kamrup Metropolitan district with highest literacy rate of 88.71 per cent, 2 for Jorhat district with second highest literacy rate of 82.15 per cent, and 27 for Dhubri district with lowest literacy rate of 58.34 per cent (Table 2). But, in the case of negative indicator ‘proportion of population in age group 0-6’ the lowest value of 9.99 per cent in Kamrup Metropolitan district is given rank 1, least but 1 of 11.41 per cent in Jorhat district is given rank 2, and the highest value of 18.89 per cent in Dhubri district is given rank 27 (Table 2). It may be mentioned here that although the rank value corresponds to the absolute value for each indicator, the rank difference is same for two adjoining values irrespective of their difference in absolute term. This is considered as one of the limitations of the ranking method.

The composite score value, the sum of rank values of all the indicators corresponding to one district, is indicative of overall relative level of socio-economic development in a district. For instance, the composite score value for Kokrajhar is found to be 133, which is the sum of corresponding rank values of 23, 24, 17, 25, 22, 13 and 9 (Table 2). Accordingly, among the 27 districts of Assam, Kamrup Metropolitan district occupies the top position in respect of socio-economic development with composite score value of 20, followed by Jorhat with 32, Sivasagar with 39 and the lowest in Chirang with 155 (Table 2). It thus shows a marked spatial disparity in the levels of socio-economnic development in Assam. It is also clearly visible in the choropleth map (Fig. 1).

In fact, ranking method calculates the relativity of areal units based on their composite rank scores. However, the inter value difference is not visible accurately in this method. For instance, the actual data value- difference between the disrticts of rank 1 and 2 (Kamrup and Jorhat) in literacy rate is 88.71-82.15=6.56 %. The same difference we would not find in another set of subsequent rank differences. It means this method does not follow objective relative principle of data transformation to rank.

Fig. 1

2. Simple Quotient Method

It is another simple but meaningful method of interval or ratio data transformation and computation of scaled free composite score. In this method, individual values of various indicators with different units of measurement are converted into unit-less value by dividing an individual value of an indicator by the corresponding mean value of that indicator.It is notated as

Where Xi represents ith value of variable X and X*i is mean of the same varaible.

For instance, in the case of Kokrajhar district, its literacy value of 65.22 per cent is divided by the mean literacy value of 72.25 per cent to get a value of 0.90 (Table 3). This is not only a unit-less value, but also a measure of literacy value by times of mean literacy value. In other words, if the resultant value is 1.0, it means equal individual and mean values; if the resultant value is 0.5, it means individual value is half that of mean value; and if the resultant value is 2.0, it means individual value is double that of mean value. But, in the case of negative indicator like proportion of population in age group 0-6, the individual quotient value is found out by dividing mean value of the indicator by an individual value of the same indicator for an area (Table 3).

Table 3: Quotient values of selected development indicators for the districts of Assam and composite quotient index using Simple Quotient Method

• # Individual Quotient Value= Individual attribute value/ Mean attribute value
• * Individual Quotient Value =Mean attribute value/Individual attribute value (in the case of negative indicator)

Composite Quotient Index= Summation of individual quotient values (higher the score, higher is the level of development)

The composite score value is found out by adding the quotient values of all the indicators corresponding to one district. For instance, the composite score value for Kokrajhar standsat5.79, which is the sum of corresponding quotient values of 0.90, 0.45, 0.96, 0.63, 0.74, 0.93 and 1.18 (Table 3). Accordingly, among the 27 districts of Assam, Kamrup Metropolitan district records the highest position in respect of socio-economic development with composite score value of 15.63, followed by Jorhat with 9.03, Sivasagar with 8.65 and the lowest in Chirang with 4.88 (Table 3). The spatial variationin the levels of socio-economic development is presented in a choropleth map (Fig. 2).

Fig. 2

Quotent method is of course simple to calculate. Ratio-based transformation is used for the calculation of composite scores of many variables. No doubt, it creates mean-free platform for the conversion of variables. However, there is another dimension of variability of distribution that is different Standard Deviations for different variables. It is not considered in this method of variable transformation.

3. Z-Score Method

It is statistically a standard method of data transformation and computation of composite score involving a large number of indicators, both positive and negative. This method is also used for finding out composite score in the sophisticated Principal Component Analysis and Factor Analysis. In Z-score method of computation of composite score, two steps are involved, that are:

negative indicators compatible with positive indicators while finding out the composite Z-score meaningfully (Table 4).

Table 4: Z-Values of selected development indicators for the districts of Assam for computation of Composite Z-Score

# Individual Z-value (for positive indicator) = Individual attribute value – Mean attribute value/Standard Dev *Individual Z-Value (for Negative Indicator) =Mean attribute value – Individual attribute value / Standard Deviati Composite Z-Score= Summation of individual z- values (higher the score, higher is the level of development)

For instance, in the case of Kokrajhar district, the composite Z-score value of -3.34 is found out by adding the individual Z-values of all the 7 indicators like -1.0, -0.5, -0.32, -0.92, -0.80, -0.20  and 0.40 (Table 4).Accordingly, among the 27 districts of Assam, with composite Z-score value of 17.06 the Kamrup Metropolitan district records the highest position in respect of socio-economic development, followed by Sivasagar with 6.47, Jorhat with 6.29 and the lowest in Dhubri with -6.16 (Table 4). The spatial variation in the levels of socio-economic development is presented in a choropleth map (Fig. 3).

Fig. 3

Conclusion

All the three methods of computing composite scores to understand the relative position of different spatial units in respect of development level have their own merits and demerits. Among them, composite Z-score method is statistically sounder.It may be mentioned here that one common limitation of all the three methods discussed above is that equal weightage has to be given for all the seven indicators irrespective of their varying degree of contribution to the level of socio-economic development. This limitation can be overcome by giving meaningful weightage to different indicators through justification and through principal component or factor analysis technique.

References

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