## Is it true that ...## Changing the prism factor from plot to plot in a stand in order to "optimize" the number of trees per plot gives just as reliable and unbiased an answer as using the same prism factor within a stand?In short –
The "optimum" prism size works just like it
does in fixed plots. Larger plots are less variable
(smaller coefficient of variation, CV) and so you need For old growth in the Northwest they decided many
years ago that this would be around ¼ acre and adopted
that size widely.
There is a second reason not to get a high tree count
– you start missing trees (personal error),
particularly fallen trees, and it makes any "edge
effect" problems worse. Above 10 trees seems to be
where these problems begin to occur – with
Would you be better off getting 4-8 trees on every The second reason is that it is
*It can be somewhat biased under practical conditions.**It has no statistical advantage.*
In addition, the chance of messing up the paperwork and writing down the wrong prism is pretty high, and it is nice to use the same prism all the time so you get a feel for which trees to check.
To do this you need to get coefficients of variation (CV) of tree count for a cruise using various basal area factors. This is easily done in two ways: (1) Measure the diameters and distances to all trees at each point and use various plot radius factors to simulate tree counts for different BAF prisms, or (2) use a range of prisms to get tree counts at many points. Use the tree counts from the various prisms to compute the CV [CV = Standard Deviation of tree count / Average tree count] and then plot the CV against the average tree count and smooth out the curve. This will tell you how CV relates to average tree count. Next, use the CV to calculate how many sample points would be needed for a fixed sampling error [n = (CV/SE)2]. Last, work out the cost of doing that number of trees on that many plots. Plot the cost against the average number of trees, and see where it is minimized. Or, you can just go along with the conventional wisdom. All of the calculations are easily done on most calculators with statistics functions or in a computer spreadsheet. Let us know if you try it, particularly if you get a surprising result.
For those interested in the history of this problem, it runs something like this – the exact details of disasters are always rather muddied, for obvious reasons: The 4-8 rule has been published in books on sampling for some time. The standard, Bell and Dilworth Variable Plot Sampling book, has had it for years. The USFS and at least one company decided that if the range was good, getting an exact number was even better, and settled on 7. Field crews were told to get 7 every time, and switched prisms to do so. Eventually, people got nervous, and the first widely
published account was ["Selection of basal area
factor in point sampling" by Wensel A second publication ["Ensuring an adequate
sample at each location in point sampling",
Schreuder The last chapter in the saga appears to have been
["Changing angle gauges in variable plot sampling:
Is there a bias under ordinary conditions?", Iles
& Wilson, Canadian Journal of Forest Research, 1988,
Volume 18, pages 768-773]. This showed that switching
prisms could be unbiased, under a |

*Originally published October
1994*