## Questions from the field:

### How can I choose a 10% “package” of the land base to sample?

Your boss wants you to “sample 10% of the land base”. By this he means that he wants to install sample plots into stands, and those stands added up to 10% of the land base. How could these stands be chosen from an overall total of N acres?

First or all, let’s be clear. This 10% does not imply “how good” the answer will be. It might be comforting to know you traveled over 10% of the land base, but that is just good psychology – not good sampling theory. Psychology, of course, is not to be discounted in an inventory business that provides comfort and security of action. The precision of the work is given by the correct Sampling Error of that inventory. Nothing else. Repeat – nothing else. (The correct sampling error for a systematic sample is almost sure to be smaller than what is computed with the usual random sampling formula, as noted our earlier article “Sampling from a List - a Big Improvement”).

Some companies want to put in grid samples that cover entire stands. They might have a budget for 500 plots. At 1 plot per acre, this means covering 500 acres. The Sampling Error will not be as good as 500 individual plots spread over the entire ownership, but it will also not be as expensive. How can they choose polygons adding up to this 500 acres ? One valid way to do this is to divide the entire area into X “packages” of stands, each of which totals to about 500 acres. Then sample one package.

You could sample randomly until you put together 500 acres, then start to put together another package. Continue doing this for the entire ownership. You now have X packages of approximately 500 acres apiece. If you have 4,859 acres to work with, you can divide them into 10 packages with about the right number of acres. You can also divide them into 20 packages and choose 2 of them, but let’s just use 10 for the moment.

What do you conclude after you sample that package ? If that package averages 60,000 BF/acre, you would conclude that the whole ownership has about that average volume. This method could also be done by strata, of course.

How do you properly select one of these packages ? The best way to do that is to choose a random number between 0 and N. That random number indicates a particular acre. The stand that acre falls into also indicates which package to sample1. Determine that by looking at the running average of all the acres in your area (illustrated in the spreadsheet you can download). In this way, each package is chosen proportional to its total area, even when the packages do not have exactly the same acres.

Are there better ways to put the packages together? Certainly so. If you have a rough idea of the volume per acre, “balance” the packages so they have a variety of volumes/acre. Like any systematic sample, this will almost certainly produce a better average than a random selection. If you sort the acres by volume, then choose every 10th stand, you will get a good initial mix inside the packages. Each package will not be exactly 485.9 (= 4,859/10) acres when you are done.

Can you shift acres to equalize the packages ? You can. You can arbitrarily shift acres from one of the packages with too much area into one with less (this is before you choose the package to sample, of course).

How about really large stands ? You should probably break them up into smaller ones by the use of roads or other visible features such as streams. You do not want just a few stands to dominate the results in your sample package.

The Sampling Error of such a process is only going to be approximate, since it is a systematic sample, but there is such a large advantage over a random sample that you probably do not want to sacrifice a better answer for more appropriate statistics. One of the advantages of sampling 3 small packages instead of one large one is that you can get a valid sampling error using the 3 averages from the packages (if you are really fixated on this sort of thing). These are just 3 observations, and you do the standard statistics to get a valid Sampling Error.

Why not just randomly choose stands until you get enough acres ? You could, but with this system you can insure that the packages have a good mix by approximate volume, cost to sample, rough site index and any other characteristic you want before you choose the final package. This kind of process is not hard to do with a simple spreadsheet. You can download a spreadsheet showing an example of this process HERE .

This is not particularly a sampling system we like, but it did come up as a practical question, and we thought it illustrated some interesting points. The reason that it is not efficient is that the samples are not spread out, but highly clustered into a few stands. Good for travel cost and efficiency (and for the answer in those stands), but not as good for estimating the overall inventory total.

This technique would be much more efficient if you were sampling “to correct” an initial estimate of the stands in the sample package, such as a photo-interpretation or a previous estimate from an older inventory. As we have pointed out in the past, how you use the data is just as important as the number of plots and expense you apply to the problem.

Like so many things in forest inventory, sample design is a balancing act.

1 You could also choose a random point in a rectangle surrounding your property. If the point falls into your land it also chooses a stand (and therefore a package) with the correct probability.

Originally published March, 2005