The Numbers Behind NUMB3RS Read Online Free PDF Page B

conducting a randomized, double-blind trial. In such a study, the target population is divided into two groups by an entirely random procedure, with the group allocation unknown to both the experimental subjects and the caregivers administering the drug or treatment (hence the term “double-blind”). One group is given the new drug or treatment, the other is given a placebo or dummy treatment. With such an experiment, the random allocation into groups overrides the possible effect of hidden parameters, so that in this case a low probability that a positive result is simply chance variation can indeed be taken as conclusive evidence that the drug or treatment is what caused the result.
    In trying to solve a crime, there is of course no choice but to work with the data available. Hence, use of the hypothesis-testing procedure, as in the Gilbert case, can be highly effective in the identification of a suspect, but other means are generally required to secure a conviction.
    In United States v. Kristen Gilbert , the jury was not presented with Gehlbach’s statistical analysis, but they did find sufficient evidence to convict her on three counts of first-degree murder, one count of second-degree murder, and two counts of attempted murder. Although the prosecution asked for the death sentence, the jury split 8–4 on that issue, and accordingly Gilbert was sentenced to life imprisonment with no possibility of parole.
    POLICING THE POLICE
    Another use of basic statistical techniques in law enforcement concerns the important matter of ensuring that the police themselves obey the law.
    Law enforcement officers are given a considerable amount of power over their fellow citizens, and one of the duties of society is to make certain that they do not abuse that power. In particular, police officers are supposed to treat everyone equally and fairly, free of any bias based on gender, race, ethnicity, economic status, age, dress, or religion.
    But determining bias is a tricky business and, as we saw in our previous discussion of cigarette smoking, a superficial glance at the statistics can sometimes lead to a completely false conclusion. This is illustrated in a particularly dramatic fashion by the following example, which, while not related to police activity, clearly indicates the need to approach statistics with some mathematical sophistication.
    In the 1970s, somebody noticed that 44 percent of male applicants to the graduate school of the University of California at Berkeley were accepted, but only 35 percent of female applicants were accepted. On the face of it, this looked like a clear case of gender discrimination, and, not surprisingly (particularly at Berkeley, long acknowledged as home to many leading advocates for gender equality), there was a lawsuit over gender bias in admissions policies.
    It turns out that Berkeley applicants do not apply to the graduate school, but to individual programs of study—such as engineering, physics, or English—so if there is any admissions bias, it will occur within one or more particular program. Table 4 gives the admission data program by program:
    Table 4. Admission figures from the University of California at Berkeley on a program-by-program basis.

    If you look at each program individually, however, there doesn’t appear to be an advantage in admission for male applicants. Indeed, the percentage of female applicants admitted to heavily subscribed program A is considerably higher than for males, and in all other programs the percentages are fairly close. So how can there appear to be an advantage for male applicants overall?
    To answer this question, you need to look at what programs males and females applied to. Males applied heavily to programs A and B, females applied primarily to programs C, D, E, and F. The programs that females applied to were more difficult to get into than those for males (the percentages admitted are low for both genders), and this is why it