Estimating Uncertainty of Economically Optimum N Fertilizer Rates

Table 2

Comparing point estimate 𝑁_optand confidence sets at different confidence levels when considering the different designs of 𝑁 levels, where the ratio between 𝑁 fertilizer price 𝑟 and crop price 𝑝 is𝑟⋅𝑝⁻¹=5.4545, for example, 𝑟=0.60 €kg⁻¹ and 𝑝 = 110 €Mg⁻¹.

	Without max. 𝑁 rate^1		All Nlevels^2		Without zero 𝑁 rate^3)
	kg ha^−1
	High yield zone
𝑁opt	226		240		249
80% CI and length^4	[199,278]	79	[214,284]	70	[213,440]	227
90% CI and length	[193,304]	111	[208,305]	97	[208,1066]	858
95% CI and length	[188,335]	147	[204,328]	124	(−∞,−657]∪[203,∞)	∞
99% CI and length	[180,449]	269	[196,402]	206	(−∞,7]∪[196,∞)	∞
	Low yield zone
𝑁opt	195		199		227
80% CI and length	[173,238]	65	[181,230]	49	(−∞,82]∪[183,∞)	∞
90% CI and length	[168,260]	92	[177,244]	67	(−∞,130]∪[175,∞)	∞
95% CI and length	[164,288]	123	[173,260]	87	(−∞,155]∪[162,∞)	∞
99% CI and length	[157,404]	247	[167,312]	145	(−∞,∞)	∞

1The confidence sets are based on all measured yields at the 𝑁 rates𝑁₁-𝑁₁₀ according to Table 1.
2The confidence sets are based on all measured yields at the N rates𝑁₁-𝑁₁₁ according to Table 2.
3The confidence sets are based on all measured yields at the 𝑁 rates 𝑁₂-𝑁₁₁ according to Table 1.
4Single numbers behind intervals denote of the preceding confidence set.