One of the interesting examples of PPS, probability proportional to sampling, is the use of the angle gauge. This is a single device. It has an arm with a gap at the end of it. The other end of the arm is brought up to the eye. The gap forms an angle. At a sampling site the person doing t he sampling simply turns in a circle and counts how many trees are larger than the observed angle. If the tree fits inside of the gap, then the tree is too small to count. The goal in this type of sampling is to estimate the total volume of wood in the forest.

Think about it. A small tree can be very close and not counted, yet a large tree some distance away is counted. Does that make sense? Does it appear that this is biased sampling? It turns out that the sampling is not biased.

What is clear is that the trees are sampled with different probabilities. The difference is probability is due to a characteristic of the tree. In this case the characteristic is a physical characteristic – the diameter of the tree.

The importance of this sampling technique is that the person doing the sampling is doing a small amount of work relative to a typical quadrat sampling technique.

A quadrat is a sampling site. It is often a rectangular area. Stopping laying out a rectangle at place in the forest is often slow and not without its complications. There are all sorts of impediments from bushes, cliffs, mud, and water courses to whatever that make it hard to lay out a quadrat.

With the angle gauge there is no quadrat layout step. There are no tree diameter measurements to take. Its turn, count, and go. What a sweet advance. What a huge gain in efficiency!

The proportionator also uses PPS to increase the efficiency of counting. Anyone looking at a vast number of slides to process can only hope that a better way of counting is just around the corner. Now it is here.

Count less, count better, and use the proportionator.