Table 7.

Results of the linear mixed model predicting the Euclidean distance between dual landmarks with fixed machine and observer, and random subject within machine, effects

Landmarka	Machine effect (Type-III tests of fixed effects)			Observer effect			Covariance parameter estimates		Shapiro–Wilk p-valuec	Data transformation
	F	p-valueb	Degrees of freedom	F	p-value	Degrees of freedom	Intercept and subject	Residual
A	0.35	0.5602	18	3.17	0.0911	19	0.0000	0.1170	0.9807	Square root
ANS	0.36	0.5547	18	3.30	0.0850	19	0.0000	0.3361	0.6003	Natural log
B point	0.05	0.8341	18	0.19	0.6657	19	0.0614	0.1214	0.3513	Square root
Condylion	1.29	0.2718	18	0.07	0.7948	19	0.0279	0.2261	0.2694	Natural log
Gonion	0.04	0.8476	18	1.23	0.2812	19	0.0000	0.3191	0.0324	Square root
Sella	19.72	0.0003	18	39.24	<0.0001	19	0.0068	0.1319	0.1076	Natural log
Sigmoid notch	2.22	0.1537	18	4.22	0.0539	19	0.0000	0.0907	0.5152
Lower molar	0.15	0.6998	18	5.12	0.0355	19	0.0000	0.4252	0.0006	Natural log
Md1 root	0.76	0.3942	18	9.91	0.0053	19	0.0000	0.1196	0.0043	Square root
Md1 tip	3.87	0.0649	18	7.57	0.0127	19	0.0163	0.4233	0.0046	Natural log
Me	2.03	0.1718	18	23.01	0.0001	19	0.0393	0.0660	0.7453	Square root
Mx1 root	0.13	0.7272	18	21.08	0.0002	19	0.0510	0.1105	0.6495
Mx1 tip	0.00	1.0000	18	6.67	0.0183	19	0.0000	0.0893	0.2746
Nasion	0.19	0.6674	18	1.10	0.3080	19	0.1852	0.4615	0.0795	Natural log
Orbitale	2.78	0.1125	18	0.08	0.7804	19	0.0625	0.1061	0.0614	Square root
PNS	0.30	0.5920	18	3.53	0.0758	19	0.0520	0.1704	0.0845	Square root
Pog	0.71	0.4090	18	0.97	0.3382	19	1.1316	0.9534	0.0735
Upper molar	5.83	0.0266	18	11.88	0.0027	19	0.0231	0.0791	0.0835

^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.