how to demonstrate that stratified random sampling is more efficient than regular grid I have to sample a private forest and the local manager proposed for 1-2 sampling area (SA) per hectare according to the old tradition of cruising the territory using contour lines and establishing one SA every approximately 50-100 metres (and ending up with a semi-regular grid). A good knowledge of the site allows me to 1) divide it into homogenous sub-areas and 2) use a stratified random sampling.
Is there a way to demonstrate a priori (without going in the field) that his number of SA could be lowered with a proper sample stratification still maintaining the estimation quality of the population parameters?
Right now I only found that stratified random sampling is better than plain random but requires not to oversample the small strata (see here).
 A: Stratified sampling is more efficient than systematic sampling only under certain condition. In particular, you want -- as you say -- the strata to be fairly homogenous. More formally, you want the intra-stratum variation to be smaller than the inter-stratum variation.
Without concrete numbers on the variances encountered, it's impossible to show that in this case stratified sampling is more efficient.
However, since the local manager has proposed a particular sampling proportion, maybe they have some numbers on variation in mind that you can base your calculations on? Or are they just guessing at sample size and taking whatever result they get?
Have there been any previous studies on similar topics from which you can draw initial assumptions on variation?
Can you personally run out and do a small preliminary study to get an initial estimation of the variation involved? (I know you say "without going into the field" but sometimes spending a few hours taking matters in your own hand is the quickest way to get the necessary data.)
