Questions from the Field ...

"Let's just check the plots near the road."

Not a good idea, but you could check cruise the convenient ones more often.

 Principles

There are lots of situations where one type of information is ugly, expensive and painful.  There is no problem with sampling that kind of item less often, but you cannot ignore them. 

If you choose some types of plots 1/10th as often, they must have 10 times the effect when they are sampled.   

Mechanics

You could decide to visit the plots based on the effort needed to get to them.  Plots within an hour of the road are sampled at the base rate.  Those that take between 1 to 2 hours will be sampled ˝ as often – those between 2 and 3 hours at 1/3 the rate, etc.  The weightings are arbitrary – choose them to suit yourself.  Using this scheme, we can assign “selection probabilities” to each plot. 

You could select plots using a sorted list at the end of the project.  You could sort that list and take a systematic sample to insure a good distribution of all types of plots. 

As an alternative, you could use the following scheme, which selects plots soon after they are completed.  As an example, the list might look like this: 

     Each time a plot comes in, we would choose a random number between 0 and 5.  If the random number is smaller than the selection probability assigned to that plot, that plot will be chosen to check cruise.  This is the same selection scheme as in 3P sampling.  Plots further from the road are selected less often, but when they are chosen they will carry a heavier weight. 

The combination of initial selection and final weighting gives each plot an equal overall effect.  The field crew will never know when the next check cruise plot will occur. 

Computation

Suppose we have done this for a project, and have the following results, with 6 plots chosen for sampling.  How will the average error be computed?  It is a weighted average. 

 The simple average indicates that the value is overestimated by $8/MBF due to measurement error.  That is incorrect.  This is because you are measuring more plots close to the road, and those plots tend to be over-estimated in this example (for some reason).  The plots farther from the road were under-estimated.  The proper weighted average is slightly negative.  Notice the heavy effect of plot #2, which represents more plots that are selected infrequently. 

This method allows us to check expensive plots less frequently, but still produce a valid sample that leads to a correct result in the long run.  Note that these plots are not in traditional “strata.”  Each could have a different individual selection probability, but they are all computed in the same sample.   

Considerations

There are plenty of other things to consider, of course.  For one thing, what does it say to the field crew when they often drag themselves over the ugly ground, but the big shot check‑cruisers only do it once in a while? 

There are better reasons for doing this kind of selection.  Maybe certain crews with a poor record should be checked frequently, while those with a good record are recognized by checking at 1/3 that rate.  Perhaps that more frequent check is designed into the bidding process and costs the poor crews more money.  That gives people with a good record a bidding advantage. 

In most cases, it would be best to let everyone know how the sample selection works.  Otherwise, they might assume that the selection is incorrect and the people running it are foolish, lazy or unorganized.  That’s never a good message to convey.