Always Need to be "Whole Numbers"?

No. In many cases it is quite wrong to
force them to be "integers" (whole numbers) by rounding them off before using
them. It is never necessary for them to be integers. Rounding often causes a bias when you
are dealing with small numbers. A good example is tree volume in cubic meters, or volumes
that have been scaled way down to make recording easier. When you round the random numbers
before comparison, it changes the probabilities, and introduces a slight error. For
instance, with rounded numbers, a tree with a "KPI" or estimated volume of 7.8
has the same probability as one with a value of 7.1. Worse yet, it encourages people to
round off good estimates to humor the rounded random numbers. There are obvious ways to get around the problem. You can request a set of integer numbers that is 100 times larger than you need, and use the last 2 digits as two decimal points of accuracy. That is the easy solution with most computer programs. Better yet, get the computer program changed. 3P sampling is sometimes used in ways where the computer is the only one to "see" the random numbers anyway. In these cases it is certainly foolish to round them off. . |
This problem has a long history, and probably began with a
statement in a publication by Lew Grosenbaugh (who invented 3P sampling) to the effect
that the numbers should be integers. Now Lew is about the smartest guy who ever dabbled in
forest measurements, and it is just foolish not to take his advice unless you think it out
very thoroughly. The problem is that people didn't check with him to see if he had a
particular reason for saying this. We were not about to give advice on this without
calling Lew, so here is what he told us: According to Lew, his computer facilities made it easy to generate integers, and most people at the time were dealing in board feet. Even when coded to Scribner Decimal C, it wasn't a problem to use integer numbers. They gave plenty of precision under the circumstances. Secondly, it was easier to introduce to the field staff that way. Lew has brought in a number of changes to the US Forest Service and cruising in general, and was well aware that smooth acceptance at the field level is always important. Decimal random numbers would have been slightly more correct, but were unnecessary for practical purposes at the time. Since that time, a number of 3P applications have made use of estimates that naturally fell into the 0-20 range. In such cases the random numbers should not be rounded into integer numbers, or should be coded so that the random numbers have at least the number of digits used in the estimates. If a computer is only using them internally, there is no point in rounding at all. |