SAMPLING VEGETATION ATTRIBUTES - New Mexico NRCS - US ...

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APPENDIX D
The formula for using these decimal random numbers for selecting a sampling unit or
point is:
[u x N] + 1
Where: u = random number (expressed as decimal)
N = total population size
[ ] = used to indicate that only the integer part of the product is used in the
calculation
To illustrate how this formula works, let’s say that our baseline is 200 meters long. Here
we need to select numbers between 0 and 200 as points along a baseline. Consider
these points as a “population” of 200 possible points. Using the first of the six random
numbers we came up with above, 0.32978, we calculate:
[0.32978 x 200] + 1
= [65.956] + 1
= 65 + 1
= 66
Thus, 66 is the first point. Using the second random number we have:
[0.59902 x 200] + 1
= [119.80400] + 1
= 119 + 1
= 120
Now we have the second point, 120. We continue in this manner until we have the five
points we need. Although the formula may look difficult, a hand-held calculator or
computer program with a random number generator makes it easy.
The reason for adding the 1 to the integer of the product of the random number and N
is that only whole numbers will be used. Without adding 1, it would be impossible to
obtain the number 200. Consider the highest possible random number we could obtain,
0.99999. If we multiply this number by 200, we obtain 199.99800; taking the whole
integer of this number yields the number 199. Adding 1 makes it 200.
As a rule of thumb, you should make sure the random numbers have more digits on the
right side of the decimal point than the number of digits in N. In the example above, N
is 200 and we are using random numbers with five digits to the right of the decimal
point, so we are okay.
Note that this process is much more efficient than the first method because we do not
need to reject any numbers. Given the fact that there is only a 1 in 5 chance of any
three-digit number falling between 1 and 200, we would—on the average—have to
examine 25 three-digit numbers to come up with five points under the first method.
Using the second method, on the other hand, we can use the first five random numbers
from the table to select the same five points.