Common Errors in Statistics (and How to Avoid Them), 4th Edition

FUNDAMENTAL ASSUMPTIONS

Most statistical procedures rely on two fundamental assumptions: that the observations are independent of one another and that they are identically distributed. If your methods of collection fail to honor these assumptions, then your analysis must fail also.

Independent Observations

To ensure the independence of responses in a return-by-mail or return-by-Web survey, no more than one form per household should be accepted. If a comparison of the responses within a household is desired, then the members of the household should be interviewed separately, outside of each other’s hearing and with no opportunity to discuss the survey in between. People care what other people think and when asked about an emotionally charged topic may or may not tell the truth. In fact, they are unlikely to tell the truth if they feel that others may overhear or somehow learn of their responses.

To ensure independence of the observations in an experiment, determine in advance what constitutes the experimental unit.

In the majority of cases, the unit is obvious: one planet means one position in space, one container of gas means one volume and pressure to be recorded, one runner on one fixed racecourse means one elapsed time.

In a clinical trial, each individual patient corresponds to a single set of observations, or does she? Suppose we are testing the effects of a topical ointment on pink eye. Is each eye a separate experimental unit or each patient?

It is common in toxicology to ...