3P Sampling

1. The "expected" sample size is never quite what you actually get.
2. You can't guess the CV correctly in any sampling situation, and you may need extra trees to get the sampling error you want.
3. The buyer of the sale may want a tighter answer than you got, and may want more measured trees.

These trees are usually called "reserve" or "insurance" trees. It is much easier to choose the trees during the cruise than to do the whole cruise over again.

Suppose you chose 60 trees in the areas, measuring 25 of these as you do the cruise. The other 35 trees are marked and mapped, but not measured during the cruise. Later in the month you decide that you need 15 more trees measured (for a total of 40) in order to satisfy some sampling error requirement.

How should you pick the 15 trees you need out of the 35 reserve trees? First of all, there are some ways NOT to do it. You do not pick the ones nearest the road, next to the nice lunch spot, the best looking trees, the ones you think are most "typical" or anything like that.

Would those trees automatically be a "bad" sample and give you a wrong answer ? We will never know. Will this lose you the case if you go to court? – count on it! It is almost as easy to do it correctly.

What, then, are some appropriate ways to choose the extra measured trees? The first principle is that all of the trees must have an equal long run chance to be chosen. They were selected by the 3P rule because they each represented the same amount of estimated

.

Since much of this work is done on handheld data recorders, the random number generators in these can also be used.

In the 3P program that we use for short courses the selection process is very simple. The handheld simply randomly sorts the reserve trees. You can then take as many trees as you need in the order they are listed.

Can this procedure be improved upon? Yes, it can. As we have often emphasized, systematic samples are nearly always preferable to random ones. Sort the trees into an order of interest to you (for instance, by DBH). You can then choose a random starting point, and pick the trees systematically from there on.

In this case we list the 35 trees in DBH order, pick a random number from 1 to 35, and start with that tree. From then on we will pick every second tree until we get 15 trees. If we start at 30, we would pick 30,32,34,1,3 ... etc. The fact that we do have a small series of unselected trees will not cause a bias.

This process will insure that we have a set of sample trees which cover the DBH range "well", and you can also examine the ratios over that sequence after the cruise.

Once these are chosen, make a map of them and visit them in the order that is best for minimizing travel effort.