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Table 2 Estimated variances in populations with spatial autocorrelation and a strong, a moderate, and a weak global linear trend. All table entries are means across 30 realizations of a super-population with autocorrelation and a linear trend, and the K possible sample for a given sampling interval (d). Variances in parentheses are relative variances with the DES variance fixed at 100. τi, j is the trend component for unit in row i and column j (i, j = 0.5, 1.5, …, 239.5)

From: Comparison of estimators of variance for forest inventories with systematic sampling - results from artificial populations

TrendTrend variance (%)Site effect variance (%)Sample size (units)Sample interval (units)Variance estimator ×  103
DESSRSMATSDRRIPDOR
Strong τi, j = (i + j − 241)/1204525400120.88 (100)2.52 (288)1.04 (119)1.15 (131)1.58 (180)1.20 (137)
  160060.24 (100)0.62 (262)0.25 (104)0.26 (107)0.21 (88)0.26 (110)
Moderate τi, j = (i + j − 241)/2401635400121.50 (100)2.56 (171)1.51 (101)1.64 (109)2.06 (138)1.65 (110)
  160060.34 (100)0.62 (182)0.34 (101)0.35 (104)0.35 (105)0.36 (106)
Weak τi, j = (i + j − 241)/480440400121.71 (100)2.56 (150)1.67 (98)1.81 (106)2.20 (129)1.81 (106)
  160060.38 (100)0.62 (162)0.38 (100)0.39 (105)0.40 (103)0.39 (103)