Table 4.

Concentration (upper table) and residual maximum likelihood (REML) analysis (lower table) of the long‐chain n‐alkanes C₂₇, C₂₉ and C₃₁ of soil under long‐term grass, arable (1949–) or fallow (1959–) treatments in 2008, where the interaction of experiment (E) and treatment (T) factors and the depth (D_v) variate was significant with a fitted D_v/T spline model

	n‐alkane
	C27			C29			C31
	Grass	Arable	Fallow	Grass	Arable	Fallow	Grass	Arable	Fallow
Soil depth / m	Concentration (mean; n = 3) / µg g−1 soil
0–0.15	1.20	0.59	0.42	2.11	0.93	0.50	2.62	1.15	0.45
0.15–0.30	0.75	0.42	0.38	1.06	0.77	0.45	1.32	0.90	0.42
0.30–0.45	0.48	0.41	0.67	0.45	0.42	0.58	0.44	0.43	0.48
0.45–0.60	0.57	0.61	0.64	0.61	0.51	0.54	0.60	0.43	0.42
0.60–0.75	0.48	0.24	0.20	0.72	0.16	0.15	0.91	0.23	0.14

REML statistic	REML values
σ 2	0.026	0.073	0.089
SE	0.007	0.020	0.024
Deviance	−47.03	−13.63	−6.31
d.f.	34	34	34
F statistic	6.87	4.15	5.65
d.d.f.	26.3	27.3	27.3
P	0.014	0.051	0.025
SED	0.149	0.215	0.227

The estimate and standard error (SE) of the residual variance (σ ²), the deviance (−2 × log‐likelihood) and degrees of freedom (d.f.) are given with the variance ratio (F) statistic with the denominator d.f. (d.d.f.), the probability level associated with the variance ratio (P), and the average standard error of a difference of means (SED) for the E·T·D_v interaction. Note that the Wald statistic is identical to the F statistic because the numerator d.f. was 1. The REML structures are outlined in models (4), (5), (6).