Hi everyone. Let's suppose that we have an index which summarizes an event of a real-life situation. Let's suppose then that we want to compare the same index of two patients and one index is way bigger than the other one (crude ratio around 200). If we do the ratio between the inverse log10 of the index (1/Log10(index)) of the two patients we obtain a 10-fold ratio, which might be easy to "handle" and to understand in a publication. Would it be better to run statistical analysis with the crude ratio, the ratio of inversed log10, or both? Which other transformation would you suggest for presenting and working with such data? Thank you in advance for your time and suggestions.
It's hard to say anything concrete without knowing the subject matter, the scientific background and the aim of the statistical analysis.
To my experience, many variables from biological systems have an approximate log-normal distribution. Notably, ratios of log-normal variables again have a log-normal distribution. Thus, it often makes sense to analyze changes or differences in geometric means or "log fold-changes". This is done easily with the standard models (mean values, t-test, ANOVA, linear regression etc.) that are all based on the assumption of normal distributed data when the logarithms of the raw data are used in the analysis.
What usually make no sense is to use ratios of logarithms. This would mean that you analyze some rational root of the raw values, and it's hard to explain what this should represent. Differences of logarithms, in contrast, are log fold-changes - something that is well understandable.
It is a bit hard to understand the distribution of your data. However, most of times statistical analysis is improved by transormation of the variables towards approximate normality. The Box-Cox transformation is one powerful option, see eg:
https://www.statisticshowto.datasciencecentral.com/box-cox-transformation/
It's hard to say anything concrete without knowing the subject matter, the scientific background and the aim of the statistical analysis.
To my experience, many variables from biological systems have an approximate log-normal distribution. Notably, ratios of log-normal variables again have a log-normal distribution. Thus, it often makes sense to analyze changes or differences in geometric means or "log fold-changes". This is done easily with the standard models (mean values, t-test, ANOVA, linear regression etc.) that are all based on the assumption of normal distributed data when the logarithms of the raw data are used in the analysis.
What usually make no sense is to use ratios of logarithms. This would mean that you analyze some rational root of the raw values, and it's hard to explain what this should represent. Differences of logarithms, in contrast, are log fold-changes - something that is well understandable.
Thank you for your answers. Unfortunately it is not a concrete case, but a speculation on an interesting topic, since it is a situation that I often have to deal with. Using a difference instead a ratio of logarithms is surely more understandable.
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