Problem with the Proportionator

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Proportionator may have Difficulty Increasing Efficiency due to Transverse Sections

The idea behind the proportionator (Gardi et al., 2008) is to search where the object you are studying is most prevalent to increase efficiency. Unlike the old joke, ‘Did you lose your keys where you are searching for them?’ whose punch line is ‘No, but the light is much better here’; the proportionator guides the sampling to where the object is actually more likely to be found. The bias is resolved by taking into account the increased probability of sampling when extrapolating to arrive at the total estimate. The concept is sound in theory, but in practice it is difficult to come up with criteria that will instruct the software where the object is more likely to be found.

A characteristic used to guide the sampling is color. For example, to estimate the number of Purkinje Cells in Cerebellum, the proportionator can be trained to be more likely to look at light blue stained areas that are ‘close to the border of a more densely stained region’ (see step ‘2’ of the proportionatorfact sheet: In other words, sample in the light blue region where Purkinje cells are more likely to exist, and then weight the extrapolation inversely to the amount of light blue in that field, i.e. the probability that field will be presented for sampling. Another way to say this is make it less likely to visit the regions that are not light blue, including the adjoining more densely stained granule cell layers.

Gains in efficiency can be lost however, when the object whose number is being estimated does not always correlate with the color. In the case of an orthogonal section, the Purkinje Cells may be seen with a background of granule cells (Skefos, et al., 2014, Figure 7); but the proportionator sampling protocol would make it less likely to visit this region due to its non-light-blue staining. Still unbiased since the extrapolation is weighted; but the increase in efficiency is negated for this region that is not light blue but does have many Purkinje cells present.


Gardi, J.E, Nyengaard, J.R. and Gundersen, H.J.G. (2008). Automatic Sampling for Unbiased and
Efficient Stereological Estimation Using the Proportionator in Biological Studies. J. Microsc. 222:
242 – 250.

Skefos, J., Cummings, C., Enzer, K., Holiday, J.,Weed, K., Levy, E., Yuce, T., Kemper, T., and Bauman, M. (2014). Regional Alterations in Purkinje Cell Density in Patients with Autism. PLOS One,



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