AP Statistics

Suppose that you were asked to design and carry out a study which determines whether divorce rates are linked to religion. What would you do? How would you analyze the resulting data? How would you access the "significance" of your results; more to the point, what does "significance" in statistics mean, after all?

In very crude terms, "probability" can be thought of as the mathematical analysis carried out before an experiment is conducted, whereas "statistics" can be throught of as the analysis carried out after the experiment is conducted. As a simple example, we can make some predictions about the outcomes of tossing a fair coin. However, once we actually toss the coin a number of time, we can revisit—statistically—the assumption of "fairness of the coin. Let me put this slightly differently. Suppose that I toss a fair coin, catching it in my hand, but hiding the result. I then ask an observer, What is the probability that the result is heads? As you might imagine, the naive observer will usually answer 1/2, but this is wrong! Why? Well, the key is that the experiment has already been conducted, removing all randomness. The answer is 0 or 1; it's just that the observer doesn't know which! Probability should not be confused with ignorance!

Anyway, questions such as the above, and many other very interesting scenarios will lend themselves to statistical and/or probabilistic arguments, therefore making this course not only intrinsically interesting but very applicable to what goes on around us. A quote by the famous philosopher Bertand Russell is appropriate here:

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