When to log?

[MitchG]

Hello all,

I have a dataset which I am using to perform some allometric analyses. It's straightforward enough when taking the log₁₀ of single values to plot against each other, but when using the formula for Fulton's condition factor K=(M_s/L_T³)*100 where M_s is the somatic body mass and L_T is total body length, I am uncertain whether the log transformation should be done on the data being plugged into the formula or on the resulting output from the formula.

Thank you in advance.

[taeto]

Certainly it is suggested to plot \(y = \log(K) \) versus \( x = \log( 100M_s/L_T^3) = \log(100M_s) - 3\cdot \log(L_T). \) The reason being that the latter expression only has linear dependencies, meaning something like \(y = ax+b, \) as opposed to ratios and exponents that appear in your original. You will obtain a graphical representation which is pleasant to look at, and if you need to do a regreession analysis, these are the points you would want to do it on.