Box-Cox Variance-Stabilizing Transformations
 
Question--A common assumption in regression,
          ANOVA, etc. is that sd(Y) is constant;
          if sd(Y) is not constant,
          then what transformation T(Y)
          will yield sd(T(Y)) = constant.
 
Answer--T(Y) = integral 1 / sd(Y)
             = integral 1 / (Y*relsd(Y))
 
resd(Y)          sd(Y)            T(Y)
-----------------------------------------
Y                Y**(2)           Y**(-1)
Y**(1/2)         Y**(3/2)         Y**(-1/2)
constant         Y                log(Y)
Y**(-1/2)        Y**(1/2)         Y**(1/2)
Y**(-1)          constant         Y (no trans.)
Y**(-3/2)        Y**(-1/2)        Y**(3/2)
Y**(-2)          Y**(-1)          Y**2
