Variation—The Underlying Phenomenon
For more than 200 years people have been quoting variations on this adage. As discussed in Section 1.6, variation is the underlying reason for the existence of statistics. It comes in many forms and the purpose of probability and statistics is to describe it in meaningful ways. Probability distributions exist, for example, to describe the theoretical random variation that occurs when trials of random generators are carried out many times. This might be called the expected variation from an expected value. There is also the issue in statistics of unexpected variation, that is, variation that does not fit an expected distribution. Unexpected variation may be caused by nonrandom behavior, or perhaps variation is related to an identifiable cause such as a treatment or an association among measured characteristics (or variables). When students reach formal statistics courses they will use hypothesis testing or confidence intervals to assist in making decisions about how extreme the difference or variation is in problem situations and whether a particular conclusion is acceptable or not. These formal procedures are based on rules related to probabilities, for example, “Is there an overlap of two 95% confidence intervals?” or “Is the probability of this outcome less than 1 in 20 or 1 in 100?” Teachers have observed, however, that often students in beginning formal statistics courses rely so heavily on the
Question Interpretation of Media Reports
FIG. 7.1. ation.