American Journal of ORTHODONTICS Volume 52, Number 9, S E P T E M B E R , 1966

ORIGINAL ARTICLES

An investigation into the reproducibility of some points, pZanes, and lines used in cephalometric analysis

ANDREW RICHARDSON, Bl.Sc., B.D.S., D.P.D., ~.ORTH.*

Belfast, Iveland

WITH the advent of x-ray cephalometry, there arose the necessity of defining, on lateral skull films, a number of points, planes, and lines which could be used as landmarks for measurements or for the superimposition of films in a serial study.

A multitude of anteroposterior lines and planes have been described. Most of these are geometric constructions suitable either as base lines for measure- ments or for the registration of superimposed films; others are anatomic outlines and can be used for superimposition only.

Many planes are obvious geometric representations of an anatomic part, but, especially in and about the skull base, some planes have been selected for less obvious reasons. De Coster,3 rejecting sella-nasion because appositional growth occurs in the region of nasion, recommended the use of the endocranial outline of the anterior cranial fossa which is unaffected by growth changes after the age of 7 years. Sassouni8 proposed the optic plane on the grounds that it most accurately approximated the horizontal when the head was in its natural upright position.

Apart from Bolton point2 and articulare,l few landmarks have been proposed on the grounds that they can be located accurately on lateral skull films, and it seemed possible that features which are excellent from the standpoint of being immune from growth changes or of closely approximating the horizontal may be difficult to define on x-ray films and may thus give rise to fallacious cephalo- metric analyses.

*Lecturer in Orthodontics, The Queen’s University of Belfast.

637

It has long been appreciated that variability in locating repha.lomctric points may occur. De Caster” criticized Bolton point because its position is often oh scured by superimposition of the mastoid process of the temporal bone : Moorrces” commented on the difficulty in locat,ing potion and orbitale; and GrabeP rejeetcd Bolton point, t,he spheno-occipital suture, the pterygomnsil iary tissure. orbitalc, porion, and the anterior nasal spine on the same grounds. Qassounib expressed the opinion that even the best cephalometric points CWL~I~~ not be located with an error of less than t 1 mm. B&irk, ’ in his classic study entitled The Fucc in Profile, fully investigated the discrepancies which oceurrcd when two observers measured the distances between selected cephalornetric points on replicate pairs of films of the same subjects. By comparing the variability of a number of measurements made from one point wit#h the variability of t,hose from another, it was possible to deduce which points were the more reproducible, although the absolute inaccuracy in reproducing each point could not be determined because all points were subject, to some degree of inaccuracy. Nstrepancies in reproducing the angles between planes were also considered, but here again it was impossible to ascribe the variability to one plane or another since all angles showed appreciable variations.

As Bjiirkl has pointed out, there are three sources of discrepancy in re- producing cephalometric measurements :

1. Differences between two films of the same subject

Fig. 1. The lines and planes studied in the investigation.

Volume 52 Number 9

Reproducibility of cephdometric landmarks 639

2. Observer differences in locating the points 3. Differences in measuring the distance between two marked points In the present study, observer differences have been selected for investigation.

An attempt has been made to estimate the variability in locating each point in the vertical and horizontal directions, to measure the attendant angular varia- tions in lines and planes, and to include anatomic outlines, such as De Coster’s line and the ethmoidal triad.

The lines and planes included in the study are illustrated in Fig. 1. They were defined as follows : Sella-no&on (S-N)--Joining sella and nasion Frankfort (F)-Joining porioa and orbitale Hazillary (MazFJoining posterior nasal spine and anterior nasal spine Mandibular (Ma&.)-Joining gonion and menton Hiis--Joining opisthion and anterior nasal spine Bolton (B.PZ.hJoining Bolton point and nasion De Coster (De C.)--“The anterior lip of the sella turcica, the upper line of the sphenoid

masses, the sphenoido-ethmoidal suture, the lateral masses of the ethmoid, and the lamina cribrata, the encephalic face of the frontal cells and the foramen caecum, the internal osseous line of the frontal bone until above the crista frontalis “3

Optic (O.PZ.)-“The bissectrice of the angle formed by the supra-orbital plane (tangent to the anterior clinoid and the roof of the orbit) and the infra-orbital plane (tangent to the floor of the orbit and the posterior contour of sella tureica) “8

Ethmoidal triad (E.Tr.)--The sphenoid plane, cribriform plate of ethmoid, ethmoid registra- tion point, and the great wings of the sphenoids

Fig. 2. The points studied in the investigation.

640 Richardson

The points marking the ends of these lines and planes at’v illrvkmtcd in E’ig. _. ‘) They were defined as follows : Sella jS)-The center of sclla t,urcica, located by taking the midpoint of the grcat~rst diametrrr Nasion (X)-The junction of the nasal and frontal bones in the midline Porion (I’)-The highest point of the margin of the external auditory mratus Orbit& (O)-The lowest point on the rim of the orbit I’ostf’??or nasal spine (F.W.R.)--‘l’hc most pesterior point of the post&or nasal spine shown in

the radiograph Anterior nnsal spine (A.N.A’.~The most, anterior point of t,he a.ntcrior nasal spine shown in

the radiograph Gonion (G~Thc lowest most posterior point at the angle of the mandible Be~ton (MFThc lowest point on the outline of the mandibular syrnphysis Opisthiom (Op.kTho lowest most posterior point of the foramen magnum Bolton (B.kIIighest point of the notch posterior to the occipital rondylc Cli%oidaTc (CL-The uppermost point of the anterior c,linoid Xoof of orbit (E.O.kThe uppermost point on the roof of the intraorbital surface IWwnoid registwctio?~ point (E.E.P.~Thc point. where the greater wing of the sphenoid crosses

the louver outline of the skull baso

In cases in which bilateral struct,ures were shown as double images, the midpoint was used.

MATBRIAL

Ten 90 degree lateral cephalometric roentgenograms from a survey of under- graduate students were used for the investigation.

METHOD

On each film, an arbitrary horizontal was defined by joining the uppermost point of the image of the earposts to the image of a lead spot which had been placed on the skin over the lowest point on the rim of the right orbit. This horizontal was transferred to the upper margin of t,he film by means of a T square, and the extremities of the line at the top of the film were marked with pin holes. At the right-hand edge of the film, a second line at right angles to the horizontal was defined by making a third pin hole in the bottom right-hand corner.

TRACING PROCEDURE. The film was arranged on the tracing desk in such a way that the pin holes at the top of the film were equidistant from the edge of the desk. The film was then covered with a sheet of tracing material. Having marked the position of the pin holes, the first observer traced the points, planes, and lines under review. The same procedure was carried out for all ten films and was repeated by the same observer one week later. The second observer also traced t,he ten films on two occasions. Thus, for each landma.rk there were four estimations on each of ten films; forty estimations in all.

READING OF RESULTS

Anatomic points. All the results were read by the same observer. With the aid of the T square, the tracing was aligned on the desk and the horizontal and vertical datum lines were drawn in. Again using the T square, the position of each point was projected horizontally and vertically onto the datum lines (Fig.

Volume 52 Number 9

Reproducibility of cephalometric landmarks 641

Fig. 3. The points projected onto the horizontal and vertical datum lines.

3). The coordinates of each point were then measured from the intersection of the datum lines, using a perspex scale calibrated to 0.5 mm.

De Coster and optic planes and ethmoidal triad. The technique for finding the discrepancies between two tracings is illustrated in Fig. 4. The tracings were superimposed for “best fit” by one observer, and the intersection of the datum lines on the first tracing was transferred to the top tracing by the second observer. This transferred point was then projected onto the horizontal and vertical datum lines and treated as for the anatomic points.

Angular variations-geometric planes. The procedure adopted for angular variations may be best explained by taking a specific line, such as S-N (Fig. 5).

6 42 Richardson

Fig. 4. Technique for finding the discrepancies between two trrxings of De Caster’s line.

Let A be the angle that S-N makes with the horizontal, S, and S, be the coordinates of S, and N, and N, be the coordinates of N.

In the right-angled triangle SNR,

tan A xz NR/SR

=Z (S, - N,)/(S, - N,j

Since S, S, and N, N, were already known, it was a simple matter to calcu- late the angle A for each tracing. These angular values were converted into radi- ans for statistical treatment in the same way as the coordinates of anatomic points.

Volume 5 2 Number 9 Reproducibility of cephalometric landmarks 643

Fig. 5. Calculation of the angle that S-N makes with the horizontal.

Angular variation-De Coder and optic planes and ethmoidal triad. The method of measuring these angular discrepancies is illustrated for De Coster’s line in Fig. 4.

In the right-angled triangle DEC, tan A = EC/DC

The distance EC was already known, and DC could be measured so that the angular discrepancy (A) for any two tracings could be calculated. These values were converted into radians, and the statistical analysis thereafter was similar to the angular values for geometric planes, except that it was not neces-

sary to c3lculatc the tlifftxwices hct.wwri tht! anglt3 fat‘ t-w‘0 1 t*wc*irigs, sitlw 111(k) had hccn found 1,~ the superimposition nlethod.

ST~\TISTIC~AI~ ANALYSIS. For t,ht horizontal and vertical coordinates clt’ (%(*I1 of’ thirteen points, there were availahlc ton cst,imatc~s 1)~ t>acli of tlic, two ob SCIT~W, A and B, on t.wo occasions, t., ;Illtl t,.

The differences between the &imatrs of the two ol~crvc~rs and l)c+wrtrn those of the same observer on scparatc occasions-( At L - Bt, ) , ( iZt? - Bt,‘), (At., - -4t,), and (Bt, - Bt,) -were calculated.

For Dc Caster’s line, the optic plnnc, and the cthmoidal triad, the horizontal and xrtical discrepancies bctweert ol~rvcrs and between times had already been measured by superirnposit,ion.

For the angulation of the six geometric planes, estimates had l~een made twice bp each observer on the ten films. The differences between these estimates--- (At, - Btl), (At, - Bt2), (AtI - At,), and (Bt, - B&)-were calculated.

The corresponding angular discrepancies for De Caster’s line, the optic plane, and the cthmoidal triad had already hcen found 1)~ superimposition.

Thus, there wcrc four sets of ten discrepancies for the horizontal and vrrtical coordinates of sixteen points or lines, and four sets of ten angular discrrpancies for each of nine planes or lines. In each case t,he mean of the ten discrepancies was calcula.ted. Each mean diffcrencc was first. tested against a throretical cs- pectation of zero (on the null hypothesis) using the “t” test, where t = mean/ standard error with 9 degrees of frciedom. Those means which differed sig- nificantly from zero (I’ < 0.05) a.rc marked 1,~ asterisks in Tahl~ T, II. TII, IV, VII. and YIII.

Table I. Table of ranking for horizontal co-ordinates of points and lines

Point or line Rank i Point or line

A.N.S. -0.23 1 0.59 1 Sella 0 7 0.48 1 Porion -0.25 2 1.03 4 Optic Pl. 0.05 2 3.83 1.7 P.N.S. 0.35 3 1 .li 6 De Coster --0.18 3 0.55 2 Nasion 0.43 4 0.69 2 Porion -0.23 4 1.46 70 Sella -0.48 5 0.89 3 Nasion 0.28 .5 0.79 6 Clinoidale 0.53 6 1.11 5 Clinoidale 0.55 6 1.24 x E.R.P. 0.63 7 1.82 8 Gonion -0.68” i 0.76 4 De Coder 0.65 8 3.04 10 Menton -0.75' x 0.60 3 Menton -0.65 8 4.81 1% E.R.P. -0.X0” 9 0.78 5 F. Tr. 1.08 10 7.73 15 -k.N.H. -0.83 1 0 1.30 9 Gonion 1.08” IO 1.18 7 P.N.S. -0,x8* 11 O.CJ4 7 Optic PI. -1.45 12 3.99 11 Orbitale 1.15 12 2.16 II Orbitale 1.98 13 2.79 9 E. Tr. -1.78 13 7.24 15 Opisthion 2.95 14 5.47 14 Opisthion -2.63 14 x.45 16 Bolton -3.33 15 8.77 16 11.0. 3.80" 15 2.72 12 R.O. 4.05* 16 4.85 13 Bolton -12.28++ 16 5.81 14

‘Denotes significance.

Volume 52 Number 9 Reproducibility of cephahmetric landmaSrks 645

Table II. Table of ranking for horizontal coordinates of points and lines

At, - At, Bt, - Bt,

Standard Standard Mean deviation Mean deviation

Point or line (mm.) Rank (mm.) Ra& Point or line (mm.) Rank (mm.) Ranlc

Sella -0.03 1 0.63 4 Clinoidale 0.10 1 0.64 2 Nasion 0.05 2 0.45 1 E.R.P. -0.15 2 0.27 1 Clinoidale 0.08 3 0.55 2 Porion -0.20 3 1.23 8 De Coster 0.28 4 1.34 8 Menton 0.23 4 1.71 10 Porion -0.28 4 1.88 10 Nasion 0.30 5 1.04 7 E. Tr. 0.43 6 3.43 13 A.N.S. -0.33 6 0.87 5 Menton 0.33 7 0.59 3 P.N.S. -0.48 7 0.85 4 A.N.S. 0.60 8 1.20 6 De Coster 0.48 7 1.71 10 Gonion 0.65" 9 0.66 5 Sella -0.53 9 0.81 3 P.N.S. 0.75 10 1.30 7 E. Tr. -0.78 10 4.56 13 E.R.P. 1.28 11 1.85 9 Gonion 1.10” 11 0.95 6 Optic Pl. 1.43 12 2.02 11 Orbitale 1.25" 12 1.61 9 Orbitale 1.58 13 2.53 12 Opisthion -2.48 13 5.10 14 R.O. -2.60 14 4.33 14 Optic Pl. 2.78 14 4.18 12 Opisthion 3.10 15 7.50 16 R.O. -2.85 15 5.13 15 Bolton 5.65* 16 5.53 15 Bolton -3.30 16 6.25 16

*Denotes significance.

Table III. Table of ranking for vertical coordinates of points and lines

At1 - Bt, At, - Bt,

Standard Standard Mean deviation Mean deviation

Point or line (mm.) Rank (mm.) Rank Point or line (mm.) Rank (mm.) Rank

Menton 0 1 0.70 2 De Coster -0.03 1 0.92 7 A.N.S. -0.03 2 0.75 4 Opisthion -0.15 2 0.65 3 Porion -0.08 3 1.46 8 A.N.S. 0.18 3 0.44 2 Clinoidale -0.13 4 1.23 6 Menton -0.18 3 0.73 5 Opisthion -0.18 5 3.13 13 Clinoidale 0.18 3 0.98 8 Sella -0.28 6 0.70 3 Sella 0.38 6 0.72 4 Orbitale 0.38 7 1.14 5 P.N.S. 0.43" 7 0.35 1 De Coster -0.40 8 2.87 12 Optic Pl. 0.65 8 2.74 12 P.N.S. 0.53" 9 0.52 1 Porion 0.73 9 1.61 9 Nasion -0.55 10 1.38 7 Gonion 0.78* 10 0.77 6 E. Tr. 0.73 11 5.72 16 R.O. 0.88 11 2.65 11 Gonion -0.78 12 1.51 9 Orbitale -1.28 12 4.20 14 E.R.P. -2.30* 13 2.44 10 Nasion -1.301 13 1.79 10 Bolton -2.68' 14 3.49 -3.93” 14 3.44 13 Optic PI. -3.65" 15 2.76 -4.60" 15 5.50 16 R.O. -4.63* 16 3.13 6.23* 16 5.41 15

*Denotes significance.

Table IV. Table of ranking for vertical coordinates of points cud 1iwr.s

At, - At, ! m, - T3fz --___

Mean Sfandard / / / / Standard dckti0~~, i

Point or line (mm.) Rank (mm.) j Rank I Point or lint 3ICYM al~i’iation j

(mm.) Rank (mm.) Ilank

P.N.S. 0 1 0.58 3 A.N.S. -0.03 1 0.56 2 Selia Nasioll Menton De Coster A.N.S. Clinoidale Gonion Porion R.O. Opisthion Optic PI. Orbitale E.R.P. Bolton E. Tr.

0 1 0.63 4 0.08 3 0.87 6 0.70 4 0.43 1 0.20 5 l.iY IO

-0.23 6 0.55 2 0.28 7 I .43 R

-0.38 8 0.87 5 0.40 9 1.15 7

-0.45 10 1.88 11 -0.50 11 2.5-l 12 -0.95 12 1.44 9

1.80 13 2.98 13 1.85 14 3.16 14 1.95 15 3.65 15

-2.55 16 3.91 16

Clinoidale Menton P.N.H. Orbitalc E.R.P. Porion Ik Coder Opisthion E. Tr. Hella Nasion Bolton Gonion Optic PI. R.O.

*Denotes significance.

Table V. Order of merit for horizontal differences

By m,eans By standard deviations By 95% con.fidence limits

~ ~ Point score Point 1 ~

9570 limits

Score Point (mm.) 1 Porion 13 Sella 11 Nasion 1.04 2 Nasion 3 Sella 4 Clinoidale 5 De Coder 6 A.N.S. 7 Menton 8 E.R.P. 9 P.N.S.

10 Gonion 11 E. Tr. 12 Optic PI. 13 Orbitale 14 Opisthion 15 R.O. 16 Bolton

16 Nasion 16 Clinoidale 16 A.N.S. 22 Gonion 25 E.R.P. 27 P.N.S. 29 Menton 31 De Coder 37 Porion 39 Orbitale 40 Optic Pl. 50 R.O. 56 E. Tr. 60 Opisthion 63 Bolton

I6 li 2~ 1 c> c> Yi 23 24 28 30 32 41 47 54 56 60 61

Sella 1.12 Clinoidale I..45 Porion 1.61 P.N.S. 1.68 A.N.8. 1.78 Gonion 1.92 E.R.P. 2.59 De Coster 2.81 Orbitale 3.9i Menton 4.09 Optic PI. 5.76 LO. 6.51 FL Tr. 6.96 Opisthion 8.66 Bolton 36.42

Volwtne 5 2 Xumber 9

Reproducibility of cephalonzetric landmarks 647

The reproducibility of the landmarks was then compared by ranking them, first, according to the mean and, second, according to the standard deviation of the differences between observers for a given time and between times of tracing for a given observer. In each case, the arithmetic value of the mean was taken, irrespective of sign. The points, planes, and lines appeared in the order shown in Tables I, II, III, IV, VII, and VIII.

No very definite pa.ttern was apparent in these tables and, in order to clarify the picture, the horizontal and vertical coordinates of the points and lines were treated separately, and each point or line was given a score according to its

Table VI. Order of merit for vertical diff’erences

By means

SCOrC

By standard deviations By 95% GOnjidenCe limits

95% limits

Point Score Point (mm.)

1 Menton 2 A.N.S. 3 Clinoidale 4 P.N.S. 5 De Coster 6 Sella 7 Opisthion 8 Porion 9 Orbitale

10 N&on 11 Gonion 12 E.R.P. 13 Optic PI. 14 R.O. 15 E. Tr. 16 Bolton

11 Menton 12 A.N.S. 15 P.N.S. 21 Sella 22 Porion 24 Gonion 27 Clinoidale 28 Nasion 37 De Coster 38 Opisthion 44 E.R.P. 47 Orbitale 50 Optic Pl. 53 R.O. 53 E. Tr. 57 Bolton

9 Menton 0.49 10 A.N.S. 0.61 11 Porion 0.66 16 P.N.S. 0.89 27 Clinoidale 1.30 27 Sella 1.10 31 Gonion 1.90 33 Opisthion 2.40 37 De Coster 2.46 39 Nasion 2.57 41 Orbitale 4.24 45 E.R,.P. 6.39 47 Optic Pl. 7.48 50 R.O. 7.88 59 Bolton 8.51 62 E. Tr. 10.09

Table VII. Table of ranking for angular diferences of planes and lines

At, - Bt, At, - Bt,

Plane or line 1 (rZZs) I,n~~~!ZZ~~RanJc plTZeor ~(rEiZsjlZank!~iiiiiZi~ Rank

Mandibular -0.0012 1 0.0170 2 De Coster -0.0008 1 0.0000 1 His -0.0012 1 0.0270 5 Bolton 0.0018 2 0.0480 7 S-N 0.0048 3 0.0170 2 Optic PI. -0.0022 3 0.0370 6 Bolton -0.0077 4 0.0390 7 Frankfort -0.0032 4 0.0500 9 Frankfort 0.0086 5 0.0170 2 His 0.0041 5 0.0100 2 Maxillary -0.0107” 6 0.0140 1 Maxillary -0.0051 6 0.0140 4 De Coster -0.0291 7 0.1170 9 Mandibular 0.0107’ 7 0.0100 2 Optic Pl. 0.0479’ 8 0.0370 6 S-N 0.0234’ 8 0.0280 5 E. Tr. -0.0483 9 0.1110 8 E. Tr. 0.0317 9 0.0490 8

*Denotes significance.

Table VIII. Table of ranking for crtr(~uhr tlifSercncc.s of p/fi)le.S mtri /itlc s --

At, - At, I<(, - Bt,

Standnrd I ’ stn~/~.dawl~ Plane or ALean tle~intion ; Pla~nc or ,lf i,ff’ll dcriatihn /

line (radians) Rank (radians) Xank / line (rndinrls) Bank (radians)’ Rnnk

S-N -0.0005 1 0.0140 3 Maxillary 0.0017 1. 0.0140 1 His -0.0005 1 0.0220 3 His 0.004x 2 0.0200 4 Bolton -0.0010 3 0.0360 9 nc caster -0.005T 3 0.0140 I Mandibular 0.0036 4 0.0100 1 Nandibular -0.0058 -C 0.0140 1 Maxillary -0.0043 5 0.0 100 1. 1”rankfort 0.0072 5 0.0410 6 De caster -0.0046 6 0.0170 4 Holton (I.OOX3 6 Il.11440 X FL Tr. -0.0168 7 0.0320 7 1,:. Tr. 0.0099 7 0.0410 6 Frankfort 0.0190 8 0.0350 8 S-N 0.01x0 8 0.0300 3 Optic Pl. -0.0245* 9 0.0250 6 optic Pl. 0.0723” 9 0.0780 !I

‘Denotes significance.

Table IX. Order of merit for angular diferences

By means By standard

deriations By 95% confidewe limits --___-

Plane Score Plane Score Plane

His 9 Mandibular 6 Maxillary 0.012 0” 42’ Holton 15 Maxillary 7 S-N 0.017 0” 59’ Mandibular 16 S-N 15 Mandibular 0.01s 1” 1’ De caster 17 ne caster 15 His 0.020 1” 11’ Maxillary 18 His 16 Bolton 0.040 2” 16’ S-N 20 Frankfort 25 Frankfort 0.044 2O 30’ Frankfort 22 Optic Pl. 27 De Costw 0.113 6” 27’ Optic Pl. 29 E. Tr. 29 E. Tr. 0.127 7” 18’ IS. Tr. 32 Rolton 31 Optic El. 0.128 7” 21’

position in the tables of ranking. When these scores were added together, the points and lines emerged in an “order of merit. ” Angular differences in planes and lines were treated similarly. Finally, the 95 per cent confidence limits for horizontal, vertical, and angular differences in points, planes, and lines were calculated. The largest of the four possible upper limits so obtained was selected in each case, irrespective of sign, and points, planes, and lines were ranked according to these values (Tables V, VI, and IX).

DISCUSSION

As Bjiirkl has pointed out, the errors in measuring the distance between two points whose positions have been clearly marked are very small. Neverthe- less, Richardson, Adams, and McCartney? have shown that the discrepancies in measuring an apparently simple entity, such as the width of a tooth, may be

Volume 5 2 Number 9

Reproducibility of cephalometric landmarks 64 9

surprisingly large. These authors found that while one observer could reproduce his measurements with an acceptable degree of accuracy, the discrepancies between measurements made by different observers were more serious. Although there is no direct evidence that a similar pattern of variability would emerge from measurements made on tracings with a perspex scale, it seems reasonable to suppose that the picture would not be very much different. For this reason, in the present investigation all measurement of results was carried out by the same observer, and it had to be assumed that he did not vary in his measuring technique or that he did so consistently throughout. All measurements were checked only to ensure that the observer had not misread the scale. The first set of measurements was used for the calculations. Fine-grain plastic tracing material and very hard pencils with sharp points were employed in order to keep the precision of tracing at the highest possible level.

Of a total of 164 mean differences, thirty-three differed significantly from zero at the 5 per cent level. Twenty-three of these were differences between tracings made by separate observers.

These findings may require some explanation. Large ‘It” values, or signifi- cant variations, may a.rise either because the mean difference is large or because the standard error of the mean is small. As the magnitude of the standard error is influenced by the size of the standard deviation, a point which is poorly reproducible, and hence has a large standard deviation, may show a nonsignifi- cant ‘ ’ t ” value if the estimates of the two observers, or of the same observer on separate occasions, happen to fall together in such a way as to give a small mean. Similarly, a point which ca.n be reproduced accurately will have a small standard error, but it may happen that the mean is relatively large and a significant ‘ ‘ t ’ ’ value occurs.

Most of the differences in the present study were of relatively small mag- nitude. One has to look more than halfway down the mean differences shown in Tables I, II, III, and IV to encounter a mean difference greater than 1 mm.

In comparing the reproducibility of points, lines, and planes, the ranking by means should be considered with that for the dispersion of the differences (the standard deviation). For horizontal differences (Table V), the first ten points ranked by means are the same as the first ten ranked by standard devia- tions. These are the better points. Again, for vertical differences (Table VI), the first ten points ranked by means correspond with the first ten ranked by standard deviations, with the exception of orbitale.

It was interesting to compare the order of merit for vertical differences with that for horizontal differences for a given point. Where a curved anatomic out- line is involved (for example, in the case of menton), it is possible to err appre- ciably anteroposteriorly around the circumference of the symphysis without greatly altering the vertical position of menton. These expectations are borne out in Tables V and VI. Menton ranks high in order of reproducibility vertically but not horizontally. The same holds good for opisthion. Nasion, on the other hand, is more reproducible horizontally than vertically. Furthermore, it was not surprising to find that A.N.S. and P.N.S. were much more reproducible vertically than horizontally. The radiographic image of the bone in these regions

tends t,o f’adc out when followed horizontall\-, but. the gener*aI Iinch ot’ the llits;lI floor gives a useful indication ol’ t,lrr vci?icai situa.tiorrs oi’ thcsc lantlm~r’ks. Some points and lines showed approxirnatcly equal TaGntions ;rrrter.ol)ostcr,i(~~l~ and vertically (for example, sella, gonion, tlinoidale, and I )C (:ostc>r ‘s linv)

With regard to the angular variations, examination of ‘I’ahlo VI alight. lcad one to believe that the maxillary and mandibular planes anti sclla-nasion would show the smallest variations, sincca P.?;.S., A.N.S., h o.onion, nionton, scl la, and nasion showed sma,ll vertical discrepancies. To a large extent! t.hcsc impressions are borne out in Table IX.

The figures quoted -for De Caster’s line show the discrepancies that, one might expect to find in measuring changes by a method which involved supcr- imposing two tracings. These findings indicate that I)e (lo&r’s line is orlly

rnoderately good as far* as reproducibilit,y is concerned. Jf, however, two films are superimposed, 1)~ Coster’s line rnight show a dcfinitc gain in reproducibility, since it would be possible to register* the small detail of lxmr structure much more effectively than two tracings.

The values in the columns headed “%o/, confidttncte limits” (Tables V. VI, and IX) give an indication of the rnaximum rnean discrepancies in local- ing landmarks which would he encountered in rcpeatcd st,udies of r’oentg-eno- grams similar in quality to those used in this investigation. Thus, it is 95 pi cent certain that, in comparable studies, horizontal estimates of nasion would not differ by more than 1.04 mm., on an average (Table V) .

On the whole, the results of this inrestigation agree closely wit,h Bjiirk’s findings.l The notable exception is porion, which emerges more favorahly in t,hc present study. This may be a result of using the anatomic porion rat,her t,han the top of the ccphalostat earpost.

CONCI,USIONS

1. Some cephalometric landmarks can be located with greater accuracy than others. The relative reproducibility of some points, planes, and lines used in cephalometric analysis is shown in Tables V, VI, and IX.

‘2. Since some landmarks were found to be more reproducible vertically than horizontally, and vice versa, this factor must be taken into account in assessing the suitability of points, planes, or lines for a particular investigation.

3. The results of this investigation do not favor De Caster’s line or the optic plane, which might find preference on grounds other than reproducibility.

The author wishes to thank Professor E. A. Cheesman for his adviw on statistical pro- cedures.

REFERENCES

1. BjSrk, A. : The Face in Profile, Lund, 1947, Berlingska Boktryckeriet. 2. Broadbent, B. H. : The Face of the Normal Child, Angle Orthodontist 7: 1 X3, 1937. 3. De Coster, L.: A New Line of Reference for the Study of Lateral Facial Teleradiographs,

AK J. ORTHODONTICS 39: 304,1953. 4. Graber, T. M.: A Critical Review of Clinical Cephalometrie Radiography, A&z. J. ORTHO-

DONTICS 40: 1, 1954.

Volume 52 Number 9

Reproducibility of cephalometric landmarks 6 5 1

5. Moore, A. W.: In Salzmann, J. A. (editor) : Roentgenographic Cephalometrics, Phila- delphia, 1959, J. B. Lippineott Company, p. 51.

6. Moorrees, C. F. A.: Normal Variation and Its Bearing on the Use of Cephalometric Radiographs in Orthodontic Diagnosis, AM. J. ORTHODONTICS 39: 942,1953.

7. Richardson, M. E., Adams, C. P., and McCartney, T. P. G.: Analysis of Tooth Measuring Methods on Dental Casts, Tr. European Orthodont. Sot., pp. 285-301, 1963.

8. Sassouni, V.: Clinical Cephalometry, Philadelphia, 1959, Philadelphia Center for Research in Child Growth, p. 41.