There may be 2 reasons for lack of improvement. The sample sizes we determined were close to optimal except for the sampling plans and estimators we evaluated using the Bowman area in 1987. In particular, the sample size results for SRS with the simple estimator indicate that, for these populations, in each stratum the population total is proportional to the population variance of the count. The allocation method we used is strictly appropriate if sampling is SRS with the simple estimator, but it gave good results for all combinations of sampling plans and estimators. Benefits of stratification are known, but little is known about its pitfalls.
Stratification reduces sample sizes within each stratum.
Stratification increased costs in Slope County due to a large difference in transect areas. Because the grassland stratum was sampled more, a greater percentage of the area was sampled than sampling intensity indicated. The estimators we evaluated are widely used, require no assumptions about population distribution, and are easy to calculate, but their precision in simulations was not compelling except when sampling intensity was high. In simulations, transect areas were not equal, but ratio and simple estimators had similar precision and confidence interval coverage with or without stratification. Instead, we considered the pps estimator in association with PPS sampling.