Hello potential heroes,
Currently I am assessing data from a mass-spectrometry experiment and I try to figure out whether my measurements are good enough for the purpose and how many runs of each sample I would need to get a reasonable estimate. To do so I wanted to calculate the coefficient of variation or standard error or something of the sorts, but here is where the following conceptual problem arose.
My measurements are originally ion-intensities and my error around these measurements is suspected to be normally distributed, this would lead me to think that standard error and coefficient of variation are good measurements for my purpose. However, my interest is in log-fold change of my samples, so I would want to log-transform the obtained sample mean intensity. Thus, I am interested in what the repercussions of my standard error are on the estimate of log-transformed mean ion-intensity.
Is it valid to take the obtained standard error of the untransformed data, use it to calculate a confidence interval on that data, and then transform these limits to the log scale to get an estimate on the precision of my log-transformed variable? While it might seem reasonable, I am afraid to do so since small deviations in the lower limit of the interval would have far more drastic consequences on the log-transformed estimate than deviations in the upper limit (logarithms asymptotically approach infinity as the intensity approaches zero). Therefore, it seems to me that the "certainty" on the lower limit is rather low and that my log-transform of the mean and its confidence interval is rather fishy. Does someone has any suggestion on how to tackle this issue? Infinite gratitude in advance!