Is it true that ...

Lines of plots should be run at right angles to the slope?

A good question – this is one that has been around a long time. The answer is "no – it does not have to be done this way – but the intent is correct."

A random sample gives you the same answer (in the long run) as any other proper sample, but the rate at which it converges on the final answer is well known. Most other sampling systems converge at an unknown rate – or at least one which is a devil to calculate. You can get a better answer by treating the data differently, and sometimes by laying out the plots differently.

If you are putting out a set of plots that is not random then you would like the data to be at least as well distributed as a random sample. In this case "well distributed" means that you get a wide range of values on the plots – not that they are widely spaced. A wide range of values means that the average from that set of data moves toward the final answer more quickly than a random sample would.

If you can artificially insure that the distribution is "better" than a random sample, the answer will be better than a random sample. Systematic samples are all designed to do this. In this case, putting the plots up and down the slope is such an attempt.

In statistics there is a thing called a "sorted list sample" where you line up all the items from large to small, then take a systematic sample of them. This insures that you get a better distribution than you would normally find (although it looks even more variable) and the average is better than a random sample. This is a good system if you can do it.

Putting your plots up and down the slope is an attempt to take advantage of a set of plots that have already been "sorted" by nature, with smaller more separated trees on the ridge and larger ones down in the valley.

Running your lines along the slope would have the opposite effect. They would tend to give you the same answers, and the statistics would look good, but the averaging process would not be as efficient.

So – putting your line of plots up at right angles to the topography is a generally good idea because it gives a sample sorted by nature.

Running straight up the slope, however, is not always a good idea. What if you hit a creek? Do you go up it, or avoid it? There is no choice – you have to go up it, otherwise you are biasing the sample. In doing so you also get a poor sample of the area. A much better layout would be to go up and down the slope with your plots, but do it at a slight angle so as to cross the creeks. You will cover just a bit more ground, but will get a better distribution.

If you happen to be using a grid sample where the plots are spaced an equal distance apart then for heavens sake do not feel obliged to travel between them by going up and down the slope – go whatever way is easiest for you.