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

MODEL SELECTION

Limited Scope

Almost every relationship has both a linear and a nonlinear component with the nonlinearities becoming more evident as we approach the extremes of the independent (causal) variable’s range. One can think of many examples from physics, such as Boyles Law, which fails at high pressure, and particle symmetries that are broken as the temperature falls.

Almost every measuring device—electrical, electronic, mechanical, or biological—is reliable only in the central portion of its scale. In medicine, a radioimmune assay fails to deliver reliable readings at very low dilutions; this has practical implications as an increasing proportion of patients will fail to respond as the dosage drops.

We need to recognize that although a regression equation may be used for interpolation within the range of measured values, we are on shaky ground if we try to extrapolate, to make predictions for conditions not previously investigated. The solution is to know the range of application and to recognize, even if we do not exactly know the range, that our equations will be applicable to some but not all possibilities.

Ambiguous Relationships

Think why rather than what.

The exact nature of the formula connecting two variables cannot be determined by statistical methods alone. If a linear relationship exists between two variables X and Y, then a linear relationship also exists between Y and any monotonic (nondecreasing or nonincreasing) function of X. Assume X can only take positive ...