Assessing biological and technical variation in destructively measured data

Abstract

The majority of experimental data are obtained by destructive measuring techniques. Inevitably, in all these data variation is present, sometimes small and negligible, sometimes large, preventing proper analysis and extraction of meaningful information by traditional statistical techniques altogether. In this paper, three systems are presented to analyse destructive (cross-sectional) data, including biological as well as technical variation. The first system involves ranking the data per measuring point in time which provides a pseudo fruit number that can be used in non-linear indexed regression analysis similar as for non-destructive (longitudinal) data. The rationale behind this is that the individual with the highest value at some point in time will resemble the most another individual with the highest value at previous or future times, and the second highest the second highest at previous times, and so on. The second system also relies on this ranking number, but is now converted into a probability, which is used in non-linear regression analysis with quantile functions. The third system is based on optimising the log likelihood of the density function derived from the applied model (i.e., the expected distribution) over the measured data. Simulated data are used to elucidate the power of the three systems. A dataset on mango colour is used to validate the systems on a real-world data set. Although all three systems perform satisfactorily with percentages variability accounted for (R2adj) well over 90%, a clear preference cannot be given since the choice of the proper analysis system depends on the experimental conditions (number of data, individuals and sampling points in time). Non-linear indexed and non-linear regression with quantile functions delivered the most reliable estimates. The three systems open up the possibility to analyse and reanalyse destructively measured data providing a sufficient large number of individuals and a clear indication of the kinetic model is available.