Linear Rescaling to Accurately Interpret Logarithms

Abstract

Abstract The standard approximation of a natural logarithm in statistical analysis interprets a linear change of p in ln(X) as a (1 + p) proportional change in X, which is only accurate for small values of p. I suggest base-(1 + p) logarithms, where p is chosen ahead of time. A one-unit change in log1 + p(X) is exactly equivalent to a (1 + p) proportional change in X. This avoids an approximation applied too broadly, makes exact interpretation easier and less error-prone, improves approximation quality when approximations are used, makes the change of interest a one-log-unit change like other regression variables, and reduces error from the use of log(1 + X).