3P Sampling

The (Un)Importance of "K" in 3P Sampling

Published April 1994

There is a maximum random number in 3P sampling called "K+Z" or "KZ". It is used to control the number of samples chosen during the cruise. When trees are estimated, these estimates (sometimes called a "KPI") are compared to the random number, and the tree is chosen as a sample tree if the estimate is equal to or greater than the random number.

This comparison step is tedious, and allows a chance for error. One other way to minimize the problem is to know the largest estimate (KPI) you will encounter during the cruise. This is called "K"

Since all random numbers larger than this will always lead to rejection of a tree, these random numbers are noted on the 3P lists with a "rejection symbol" of some type. This was invented as a convenience for field folk. It has caused a great deal of trouble.

The message was supposed to be simple: you would never choose a sample tree with this random number, since there are no trees big enough to be "equal to or larger than" this random number.

Now the trouble began. Once in a while people would actually find a tree larger than they expected. In which case, the probabilities of sampling were upset. This led to "sure-to-be-measured trees", since there was no option for getting a comparison number in the field. Next Column


These "sure-to-be-measured trees" that result from the problem are a bad notion. Now if you want to measure all trees of a specific type, that is certainly OK, but to get it forced on you by the mechanics of the selection process (which are supposed to be a convenience) is really a bad thing.

This was a pain, so people began to worry about the "right" value for the largest tree, with fixed plots being used and other silly adventures.

There are several alternatives:

  1. Choose a value for K larger than you will ever find. You must then do the comparisons, but you can do that without too much extra work.
  2. Carry an additional list of numbers which go all the way up to KZ. Use these when you find a tree larger than the "K" entered in the usual list.
  3. Have the computer people just put a special symbol beside all KPI values larger than the "K" you think is reasonable, but keeping the original number. That way you can always do the comparison when you need it.
  4. Do the selection with a hand-held recorder, which does not care about the "K" value, since it just uses "KZ" as the upper limit and always compares them.

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