The paradox in which considering the rates of occurrence in a two-way table of the characteristics in two groups separately can lead to the opposite conclusion from when the two groups are combined. For this to occur, it is necessary that there be a substantial difference in the proportions of one category within two groups. For example, if 80% of students applying for science are accepted and 40% of students applying for arts are accepted, irrespective of sex in both cases, then there is no discrimination. However, if 75% of boys apply for science courses and only 30% of girls apply for science, the overall success rate of applications for boys and girls would look very discriminatory. With the above proportions, and 1000 boys and 1000 girls altogether the two-way tables would be:That is, overall 70% of boys would be accepted compared with only 52% of girls, but the rates of acceptance from each group by type of course were identical.
http://exploringdata.cqu.edu.au/sim_par.htm Examples of Simpson's paradox.