You'd think so but try reading "Freakonomics". The connection is clear and well made. They look at times when abortion rates are low (because of low gov support from Repub presidents), and then see crime rise decades later when those unwanted children come of age (teenagers) and commit crimes.
By using statistics the authors even figured out that there are a certain number of sumo matches that have been fixed.
Take a poll of the number of people who eat ice cream in the summer and crime rate in the summer. Now take a poll of the number of people who eat ice cream in the winter and the crime rate in the winter.
The results will show that the crime rate in the summer is higher and the number of people who eat ice cream is higher. So higher ice cream consumption will produce more crime?
You can basically do this with anything and find correlations. People do it all the time and make connections between things that have no scientific merit. Also there are so many variables unless you conduct a control experiment your results will be skewed.
Maybe the rise in crime rate a decade later was due to something else? You can't just take statistics of abortion rate 10 years ago and go "oh look, crime rate has gone up 50% since then." It must be because of the low abortion rate?