Table 4.

Results of the linear mixed model predicting the Euclidean distance between dual landmarks with fixed machine and random subject effects (Observer 2)

Landmarka	Machine effect (Type-III tests of fixed effects)			Covariance parameter estimates		Shapiro–Wilk p-valuec	Data transformation
	F	p-valueb	Degrees of freedom	Intercept and subject	Residual
A	2.14	0.1608	18	0.1714	0.3371	0.3911
ANS	3.96	0.0620	18	0.0342	0.1686	0.9436
B point	0.09	0.7736	18	0.0395	0.1800	0.2283	Square root
Condylion	2.01	0.1733	18	0.1316	0.3029	0.2640
Gonion	12.60	0.0023	18	7.3123	0.8913	0.8641
Sella	7.89	0.0116	18	0.0133	0.1088	0.0659
Sigmoid notch	0.14	0.7092	18	0.0132	0.1085	0.9038
Lower molar	0.71	0.4101	18	0.0615	0.2191	0.0001	Subject nine outliers
Md1 root	0.06	0.8127	18	0.1022	0.2727	0.5955	Natural log
Md1 tip	0.09	0.7735	18	0.0951	0.2645	0.0072	Natural log
Me	7.18	0.0153	18	0.0873	0.2551	0.8707	Natural log
Mx1 root	0.08	0.7834	18	0.0537	0.2063	0.1213
Mx1 tip	0.01	0.9443	18	0.0158	0.1181	0.1843
Nasion	0.49	0.4926	18	0.3119	0.4239	0.4269	Natural log
Orbitale	4.20	0.0552	18	0.0339	0.1679	0.9820	Square root
PNS	0.06	0.8048	18	0.3203	0.4280	0.6150	Natural log
Pog	0.27	0.6076	18	0.3309	0.4331	0.3496	Natural log
Upper molar	1.28	0.2726	18	0.0184	0.1267	0.2198

^aSee Table 1 for definitions of the landmarks.

^bSignificance probability associated with the F-test of significance of the machine effect in the mixed model. Highlighting in bold indicates the significance value of <0.05.

^cSignificance probability associated with the Shapiro–Wilk test of normality of model residuals following data transformation if required.