# Sopher՚s Index Measuring Disparity YouTube Lecture Handouts

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# Title: Sopher՚s Index Measuring Disparity

## Sopher՚s Index

- Developed by Sopher in 1974
- Measures Disparity
- Rural-Urban; Male-Female
- 1974 by David Sopher – generally used to understand relative disparity
- 1
^{st}applied to disparity between rural and urban literates - Measures disparity between 2 groups in their possession of particular property in terms of logarithm of odd ratios
- D = 0 (perfect equality)
- High value of D – higher extent of disparity
- Lower value of D – lower extent of disparity
- Where it is used: rural-urban literacy; rural-urban population; male-female literacy; male-female PCI
- is disparity index
- is percent of rural/female literate
- is percent of urban/male literate
- (if that is not done, we will have same value of disparity index but there will be negative sign)
- Idea of taking log is to reduce the levelling of effect i.e.. , regions with higher literacy rate show lower level of disparity than regions having low literacy rate even though the gap is same for both regions.
- If 2 numbers are big, there difference would be the same but values would be smaller however if 2
- The
**natural logarithm function ln (x)**is defined only for x > 0. So, the**natural logarithm**of a negative number is undefined.

Why we take log?

- Sopher՚s Index modified by Kundu & Rao (1983)
*What if the values are more than 100?*- Additive monotonocity axiom
- 1974 by David Sopher – generally used to understand relative disparity
- Modified in 1983 by Kundu and Rao
- GER: Divide the number of students enrolled in a given level of education regardless of age by the population of the age group which officially corresponds to the given level of education, and multiply the result by 100. A high GER generally indicates a
__high degree of participation__, whether the pupils belong to the official age group or not. A GER value approaching or exceeding 100 % indicates that a country is, in principle, able to accommodate all of its school-age population, but it does not indicate the proportion already enrolled. The achievement of a GER of 100 % is therefore a necessary but not sufficient condition for enrolling all eligible children in school. **Sopher՚s index**would have log of negative number if GER**is more than 100**, so present study**has**used modified**Sopher՚s index**that**is**modified by**Kundu**and Rao- Kundu and Rao (1986) have shown that the Sopher index fails to satisfy the additive monotonicity axiom
- Monotonic implies if x increases, y should also increase but log of negative number is undefined so no monotonicity would exist. There 200 is used rather than 100 to have a positive value for log function.
- The additive monotonocity axiom specifies that if a constant is added to all observations in a non-negative series, ceteris paribus (all other things remain constant) , the inequality index must report a decline. It would reduce the ratio and inequality index would decline.

✍ Manishika