Questions from the Field ...

"Can't I adjust the sample size if I encounter practical problems? I don't know how long the field season will be next year!"

Good question. There are always problems that occur – snow, budget crunches, short flying days, etc, etc. The general trick is to make sure that you complete one sample, and then add other small (also complete) independent samples to that data if you have the time.

For instance, if you have laid out a grid you can’t just do the plots starting from one corner and finish the project when the weather shuts down the field season. An appropriate sample has to be installed across the entire area, and yours has been stopped before producing a valid sample. You would be forced to finish it next year, and cannot compute the average from the partial sample you have.

As long as you finally complete the work, of course, it is perfectly OK to do the high elevations when they are snow-free, or in some convenient order, but you do have to get them done or the sample is biased. Any systematic sample has to be completed.

People just hate to wait until the process is done to get an answer, especially if it runs into the next field season, and you are never really sure about next year’s budget (ask any company that has been taken over recently).

The crews, on the other hand, want to visit plots in a sensible order that minimizes their pain. They cannot control the weather, and travel time and costs are never a sure deal – which means that the sample size is likely to be variable because of these uncertainties. Something has to give. There are a couple of useful approaches.

If you might run short ...

First: You could take a random approach (at least a random order to the sampling) Suppose you lay out a grid of 300 plots over the area as your intended project, to be completed if possible. You are not sure how long the field season (or budget) will last. When you have to stop you want the sample to be valid at that point. Put in one plot at a time, randomly chosen from the grid.

With this system, you can stop because of time or budget problems and have a valid sample (but you can’t stop because you like the average). With luck, you might complete all 300, and you would then have a good coverage of the area and the intended number of plots. During the process, however, you have a form of insurance against unforeseen problems. The drawback is that the method might involve a lot of extra travel when you visit the plots in a random order.

Another advantage to a completely random sequence is that you can use a statistical method called "sequential sampling," and stop when the sampling error is small enough to suit you. This will not be discussed here, but you can check it out from other sources. Sequential Sampling requires a random sequence of observations.

Second: Consider this more reasonable approach that should suit both field and office staff. Lay out a complete sample plan that you know you can finish, then add other small valid samples to it if you have extra time. Independent samples can always be combined in some way.

Perhaps you know for sure that you can do 200 plots, but any additional amount is hard to predict and would not exceed 100. Set up a systematic sample of 300. Randomly start the process, but skip every 3rd plot. Visit the first 200 plots in any convenient order. When the 200 are done you have gathered a valid systematic sample. You can do the statistics and report the results. If necessary, you can stop the project at that point.

If time and budget permit, start measuring the remaining 100 plots. You can do them randomly as individuals, or in systematic groups of a weeks work at a time (to gain a bit of travel efficiency). This data can be added to what you have already, and the process can stop whenever time, money or weather run out.

What if one of your plots cannot be visited due to snow? Then the process stops right there (even if you can get to some of the others). If you are doing a set of 5, and 3 are already done when the project must stop, you should technically throw away those 3 in the uncompleted set. As the time to shut down get close, you should obviously use smaller sets.

Stratification

If you know that some geographic area is likely to be a problem, you might consider making it a strata. A strata is just an independent sample. Use one of the methods just described to get an answer for this troublesome part of the inventory. When it gets shut down, you can continue working on the other parts of the inventory.

This works because these are separate strata, and do not need to be sampled at the same rate, so you can use any remaining time to "oversample" in the other strata that are still operable.

Adding Plots

If things go very well, and you have extra time, you can do something similar. Add random plots (or randomly chosen plots from a large systematic sample) until you are forced to stop. You can also add small systematic samples which cover the entire area. Here again, you might be able to add plots in groups to cut the travel time and hassle. These additional plots can be added to your existing set, and the process can be terminated at any time.

You might want to consider this issue when you set up your next inventory. One of the main problems with a large sample size is in the last stages, when it has to be completed and quality control starts to suffer. It’s better to have fewer plots than questionable data. These techniques let you use the available time and budget without causing this "end of project stress" to the system.