This is not due to random error, the two CVs are two different things. Look at the dataset below, %CVs are 80 and 113, very different. There is no proof that the two values should be similar.   I don't think you understand my question. If you are a staff in SAS, could you please refer me to the right team? Thanks.   Original Scale Ln scale     Original Scale (Assuming Normal) Original Scale (LogNormal) Ln scale 0.182934103 -1.698629283   n 47 47   0.335884261 -1.090988639           1.768862198 0.570336514   GM   0.921088052   0.322330226 -1.132178713   Mean 1.300955496   -0.0822 1.869962942 0.625918614   GSD   2.482316779   4.092048456 1.40904569   SD 1.039364637   0.909192 1.615234314 0.479480032   %CV 80 113   0.586349193 -0.533839775           0.854526206 -0.157208108           0.368046246 -0.999546681           1.92127702 0.65299008           0.694299929 -0.364851237           0.062064248 -2.779585165           0.522980221 -0.648211634           1.603548144 0.472218764           0.495035732 -0.703125334           3.263487488 1.182796405           0.991658216 -0.008376771           0.807604862 -0.213682372           2.166518473 0.773121489           0.367439171 -1.001197496           0.796960379 -0.226950314           0.437185347 -0.827398039           1.649246645 0.500318605           0.28163224 -1.267153174           3.533515975 1.262293402           1.850595694 0.615507584           0.50108275 -0.690984021           0.578666907 -0.547028257           2.031517886 0.708783241           1.004733644 0.004722476           1.748168892 0.558568893           0.727650154 -0.317934903           1.325797122 0.28201388           0.242380432 -1.417246756           0.843038824 -0.170742268           2.131842779 0.75698676           1.011822918 0.011753574           4.396706363 1.480855707           2.611930193 0.960089486           0.961948844 -0.038794006           2.065023208 0.725141465           0.251275204 -1.38120651           0.792867525 -0.232099127           0.426753947 -0.851547668           2.196685175 0.786949486           1.853787599 0.617230897           ... View more

Thanks for taking the time to create an example.   1.  x1+x2+...+xn = exp(log (x1+x2+...+xn)) , which are not equal to exp(log(x1)*log(x2)*....*log(xn)), as log (x1+x2+...+xn) is not equal to log(x1)*log(x2)*....*log(xn)   2. As you mentioned, in your example, the two CVs are "almost the same value", meaning they are different, no matter how similar they are in this particular example. For a statistical software like SAS, I do believe we should aim at an accurate result, instead of some results similar. Even a small difference could mean a lot in different industries/context.   3. The key is to understand how SAS uses this CV value at the back end to calculate the sample size/power.  I'm hoping the SAS team that wrote the SAS documentation can answer my question.      ... View more

I don't understand what you meant by "valid". CVs calculated from these two formulas are different, both can be entered in Power Procedure, and get different results. As a SAS user, I want to know which is the right one. ... View more

Yes. That's why I think CV=sqrt(exp(SDlog2)-1) should be entered in the CV option, instead of the ratio of SD and Mean of original scale data, as in SAS documentation. ... View more

  CV=sqrt(exp(SDlog2)-1) CV2=exp(SDlog2)-1 CV2+1= exp(SDlog2) log(CV2+1)= SDlog2 SDlog=( log(CV2+1))1/2 Note "2" is referring to square and "1/2" represents square root. This window does not allow me to type it.   which is the same as in SAS documentation       ... View more

Thanks Jill for your reply. This reference is for correlation conversion, I don't have it now, will appreciate if you can share the part for derivation.   Regarding my original question about CV, it makes more sense if CV=sqrt(exp(SDlog2)-1) where SDlog is the SD from natural Log scale data. I suspect it is a mistake in SAS documentation to indicate it as the ratio of the standard deviation to the mean on the original data scale, but I want to get the confirmation from the experts in SAS.   ... View more