1) A researcher studying correctional treatment on 192 sex offenders composed of 10 females and 182 males finds that 11 males along with 1 female had reoffended. He then calculates the percentages and finds that 10% of females and 6% of males had reoffended and concludes that female sex offenders were more likely to reoffend than male sex offenders. What is wrong with his conclusion?
2) A researcher evaluating a gun training program in a large American city found that rapes dropped by 90% in the year following the training. Researchers looking at the same data but expanding the time frame to include 5 years before the training and 5 years after the training found that the rape rate in the same city had fluctuated wildly over that decade including zero rapes being recorded in the city two years before the gun training was implemented. Thirty years after this research advocates still cite the first study and ignore the second study. What's the moral of this story?