Fig. 2

Examples illustrating problems with model-assisted estimation. Two examples are shown of second-phase simple random samples, of size 10, chosen from amongst the 5000 simulations done with population example 2, the stocking density of Japanese rainforest, with a first-phase sample size of 30 and where the target-auxiliary variable correlation over the population had been set at r = 0.7. In both cases, the solid line shows the ordinary least-squares straight-line fit to the target-auxiliary variable data, that is, the model used to obtain model-assisted estimates of the population mean using Eq. (6.2). In the case of a the estimates of the parameter values were α = 3533 and β = 0.083, but the correlation level between the target and auxiliary variable data was r = 0.51, which was not significantly different from zero (at p = 0.05). In the case of b, α = 7800, β = 0.604 and the correlation was r = 0.77, which was significantly greater than zero (at p < 0.01 at least)