Linear Rescaling to Accurately Interpret Logarithms (2106.03070v3)

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 (\log_{1+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)).