Questions from the field:

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 –

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
sample^{1}.
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 10^{th}
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*