We are using stereo-videos to sample fish populations, we are interested not only in identifying the species that are part of these populations, but we also want to calculate their biomass as a whole and per species. Since stereo-videos allow us to measure fish quite accurately, we use this information to then estimate biomass. However, sometimes we cannot measure all fish present in our surveys because we cannot get a frame where an individual appears clearly in both video cameras. I have read at least three articles where they used the mean length of the species as the length for the individual that could not be measured. There was another publication where the median was used instead. This may be a problem if our method tends tom for example, sample more large individuals, then it will lead to an over-estimation of the size of the individual that could not be measured. Any statisticians have any comments on how to solve this issue?
As I understand your (interesting) data, you would be much better served to use each valid measurement to produce a probability density function (pdf) than to use central tendencies such as means, medians, etc. I would imagine you would do this separately for each species. The pdf of fish length, for example, will allow you estimate the statistics (mean, mod, percentiles, median, distribution) for length and of anything that can be estimated from length (mass, age, etc.). It would have the substantial value of being able to show skewness or other features that make, for example, the probability of observing a large fish much lower than that of observing a small fish an equal distance from the mean. One straightforward way to produce the pdf is to bin a group of measurements into 10 or so length continuous length ranges (0-0.2 ft, 0.2-0.4 ft, etc.). They need not be of equal width (0-0.2 ft, 0.2-0.3 ft, 0.3-0.45 ft, etc.). If you divide the number of observations in each bin by the bin width and plot this as a function of the center of the bin, this provides an experimental estimate of the pdf. It is more accurate the more samples you have. The samples that you cannot measure can be ignored without bias so long as they are not consistently of one size (large, small, medium, etc.). You can fit these data to any number of analytical pdfs or use the data directly as a numerical pdf.
I don't quite understand your question but I think you mean that you cannot measure the length of some species of fish that are present in your stereo videos. If this is the case I can recommend working with the Image J software. Rueden C, Dietz C, Horn M, Schindelin J, Northan B, Berthold M. ImageJ Ops[Internet]. ImageJ. 2016 [cited 2019 Nov 25]. Available from: https://imagej.net/ImageJ_Ops.
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