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Table 4 Estimated variances in populations with a near zero autocorrelation and a strong, a moderate, and a weak global linear trend. All table entries are means across 30 realizations of a super-population and the K possible samples 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)/120452400121.51 (100)2.50 (166)1.46 (97)1.47 (98)1.84 (122)1.48 (98)
   160060.29 (100)0.63 (214)0.36 (124)0.37 (125)0.36 (124)0.37 (126)
Moderate τi, j = (i + j − 241)/240142400122.12 (100)2.49 (117)2.09 (98)2.09 (98)2.28 (107)2.03 (96)
   160060.42 (100)0.62 (149)0.52 (123)0.52 (124)0.52 (124)0.52 (123)
Weak τi, j = (i + j − 241)/48042400122.36 (100)2.49 (105)2.34 (99)2.33 (99)2.41 (102)2.25 (95)
   160060.47 (100)0.62 (133)0.58 (123)0.58 (123)0.58 (122)0.57 (122)