# 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
• 1st 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?