These values were determined as the difference between the mean of the simulation standard error estimates of the population mean for each double sampling estimator and the mean of the simulation standard error estimates obtained using simple random sampling, expressed as a proportion of the mean obtained using simple random sampling.
For each of the five example populations, the average deviation from this expected value of the actual standard error of the 45,000 simulation estimates of the population mean obtained using simple random sampling is shown in the second column of Table 3.
However, whilst the square of the estimate of the standard error of the estimate of the population mean obtained using a simple random sample, that is ( widehat{sigma}{left overline{Y}right)}^2 ) from Eq. (3.2), is an unbiased estimator of the square of the standard error of the population true mean (its variance), that is σ 2 in Eq. (9), its square root is not.
where N and M are the numbers of rows and columns respectively, g c (i,j) is the centre pixel at position (i,j), g c (i,j) is the neighbourhood of g c (i,j) lying along the orientation 2p π/P with the radius R and μ p is the oriented mean obtained using the following: μ p = ∑ i = 1 N ∑ j = 1 M | g c ( i, j ) - g p ( i, j ) | / ( M · N ) (5).
In this case, 88.07% was the highest accuracy mean obtained using forward selection (±4.99) and backward elimination (±8.27).
The analyses of variance (ANOVA) were used for calculating significant differences among the means and the comparisons between 2 means were obtained using the modified t-test (Bonferroni method).
Mean haemoglobin concentration was compared using a t-test, and an adjusted difference between means was obtained using normal regression.
Age- and sex-adjusted percentages and means were obtained using logistic regression and ANCOVA, respectively.
Means were obtained using LSMEANS with Tukey adjustments for the degrees of freedom and P < 0.05 default separation.
