Investigation of Some Sector Sampling Statistical Properties

Sector sampling is designed to sample objects in clusters or small, irregularly shaped polygons, such as variable retention patches and associated harvested areas. A number of statistical aspects of sector sampling were examined by using real data and a resampling framework. When the sector angle is selected at random, the probability of sampling each tree is the same; thus, a simple expansion factor method is all that is required to calculate tract totals and mean tree values. Standard variance formulas can then be used. For unit area estimates (such as basal area per hectare) a ratio-of-means estimator balances the areas in different-sized sectors. However, both the ratio-of-means mean and variance may be underestimated. An empirical correction to the biased variance estimator was derived. Alternatively, an unbiased and also more efficient unit area estimate can be made using a random point sector angle selection with a mean-of-ratios method. In this case standard variance formulas can again be used. A systematic sector arrangement reduced variance under an expansion factor but did not reduce variance using a ratio-of-means approach where sector area was already considered.