A machine measures the height of some plants. In the context of industrial quality procedures, we repeat the same measurement
Hi 10 times and expect the repeatability errors
Ei to follow a gaussian law around their mean. however, it appears that the measurement error is proportional to the measure itself (the machine makes bigger mistakes for higher plants). Something like that:
To account for this when assessing global repeatability error, we compute these errors in relative by dividing each single measurement by the average of the 10 (similar to a "CV%").
My question is, suppose we test different plants that are randomly selected from the stock (so their true heights follows a uniform distribution). The procedure asks to check the normality of all the residuals (taken from all the plants samples). My intuition is that since there is this dependancy of the deviation to the measurement level, there is no way that the raw residuals would globally follow a gaussian, so I suggested to test the normality of the "CV%" residuals instead. Is that right in your opinion?
Thanks for your help.