Missing Women and Sex-Selective Abortion 

 The problem of â€śmissing womenâ€? in many developing countries reflects not just the gender inequality but serious violation of human rights, as Amartya Sen reported in his book  Development as Freedom  (1999). It refers to the phenomenon of excess mortality and artificially lower survival rates of women. Particularly disturbing is the practice of sex-selective abortion, which has become quite widespread in China and South Korea.   

 Statistical analysis, in particular examination of anomalies in a distribution of interest, can give compelling evidence of crime or corruption. If nine out of ten babies delivered at a hospital are boys, we must have a strong suspicion that the doctor(s) in the hospital conduct(s) sex-selective abortion. It may not be evidence sufficient for a conviction, but it probably is sufficient grounds for investigation. Then, what will be a good guide to decision for investigation? Applying a threshold of a certain percentage will not be a good idea, because the probability of 6 or more boys out of 10 babies is much larger than the probability of 600 or more boys out of 1000 babies. So, an appropriate guide may be the use of binomial probability distribution. 

 Suppose the probability of producing boy or girl is exactly 50 percent. Then, the probability of producing six or more boys out of ten babies 37.7 percent, while the probability of producing 60 or more boys out of 100 babies is only 2.8 percent in the absence of some explanatory factor (probably sex-selective abortion). The probability of producing 55 or more boys out of 100 babies is 18.4 percent, but the probability of producing 550 or more boys out of 1000 babies is only 0.09 percent in the absence of some explanatory factor (again, probably sex-selective abortion). If the police decide to investigate the hospitals with more than a certain percentage of boy-birth rate, say 60 percent, then many honest small hospitals will get investigation, while large hospitals that really engage in sex-selective abortion may avoid the investigation.