Mathematic coupling of data: a common source of error.

The relationship between two variables may be mathematically coupled if either one or both variables are derived and/or calculated, and this can lead to erroneous results and invalid conclusions. The purpose of this report is to identify four types of mathematic coupling of data. Type 1 coupling involves directional changes in two variables which are mathematically coupled. Type 2 coupling is the functional relationship between two calculated variables which have one or more common component variables. Type 3, the most common type of mathematic coupling, is direct algebraic coupling between two variables, when one or more of the variables is derived and/or calculated. Type 4 is indirect coupling or physiologic coupling. The common problem in each type of mathematic coupling is that one variable either directly or indirectly contains the whole or components of the second variable. Statistical techniques, when properly applied to the relationship between the two variables, further obscure the underlying mathematic coupling, and tend to support the erroneous results. Recognition of mathematic coupling is imperative for correct data analysis and accurate interpretation.