. 2021 Aug 18;16(8):e0255256. doi: 10.1371/journal.pone.0255256

Table 2. The variances of $\hat{τ}$ , $\tilde{τ}$ , ${\hat{τ}}_{t s}$ and ${\hat{τ}}_{S R S}$ are computed with the same effective sample sizes for the buttercups population when the population was partitioned into 12 PSUs.

The relative efficiencies and the efficiencies of both estimators of ATIS are computed where m = 12.

c	k	$var (\tilde{τ})$	$var (\tilde{τ})$	$var ({\hat{τ}}_{t s})$	$var ({\hat{τ}}_{s r s})$	$RE (\hat{τ})$	$EF (\hat{τ})$	$RE (\tilde{τ})$	$EF (\tilde{τ})$
0	2	7173.01	7173.01	8865.71	11186.62	1.24	1.56	1.24	1.56
	3	3944.57	3944.57	5569.68	7027.74	1.41	1.78	1.41	1.78
	4	2506.73	2506.73	3924.37	4951.71	1.57	1.98	1.57	1.98
	5	1730.62	1730.62	2937.95	3707.07	1.70	2.14	1.70	2.14
	6	1226.99	1226.99	2278.44	2874.90	1.86	2.34	1.86	2.34
	7	876.13	876.13	1807.45	2280.62	2.06	2.60	2.06	2.60
	8	617.47	617.47	1454.91	1835.79	2.36	2.97	2.36	2.97
	9	426.84	426.84	1180.89	1490.04	2.77	3.49	2.77	3.49
	10	269.05	269.05	961.19	1212.82	3.57	4.51	3.57	4.51
1	2	8170.04	8307.66	9723.35	12268.78	1.19	1.50	1.17	1.48
	3	4666.58	4708.53	6145.24	7753.97	1.32	1.66	1.31	1.65
	4	3078.24	3097.05	4356.06	5496.41	1.42	1.79	1.41	1.77
	5	2176.36	2191.40	3281.63	4140.72	1.51	1.90	1.50	1.89
	6	1600.59	1608.72	2566.13	3237.90	1.60	2.02	1.60	2.01
	7	1173.07	1181.01	2053.86	2591.53	1.75	2.21	1.74	2.19
	8	883.24	887.22	1670.80	2108.19	1.89	2.39	1.88	2.38
	9	664.54	668.13	1372.46	1731.75	2.07	2.61	2.05	2.59
	10	485.49	488.18	1133.74	1430.53	2.34	2.95	2.32	2.93
2	2	9549.18	10242.79	10636.93	13421.52	1.11	1.41	1.04	1.31
	3	5733.32	5950.00	6755.19	8523.60	1.18	1.49	1.14	1.43
	4	3876.63	3980.21	4810.68	6070.05	1.24	1.57	1.21	1.53
	5	2856.13	2924.76	3645.15	4599.39	1.28	1.61	1.25	1.57
	6	2152.17	2194.61	2869.08	3620.16	1.33	1.68	1.31	1.65
	7	1656.64	1685.76	2315.14	2921.21	1.40	1.76	1.37	1.73
	8	1328.43	1352.29	1898.54	2395.55	1.43	1.80	1.40	1.77
	9	1054.40	1071.50	1574.72	1986.96	1.49	1.88	1.47	1.85
	10	845.48	859.13	1316.13	1660.68	1.56	1.96	1.53	1.93

Table 2. The variances of τ^, τ˜, τ^ts and τ^SRS are computed with the same effective sample sizes for the buttercups population when the population was partitioned into 12 PSUs.