morphological study of the intra-articular space … › images › pdf_file ›...
TRANSCRIPT
1
Morphological Study of the Intra-articular Space between the Head of the
Condyle and the Articular Eminence on 67 European Dry Skulls.
Master Thesis for obtaining the academic grade
Master of Science in Dental Sciences (MSc)
Submitted by
Dr Alain Méthot
Department of Interdisciplinary Dentistry and Technology
At the University of Continuing Education / Danube-University Krems
Advisor: Univ.-Prof. MR Dr Rudolf Slavicek
Krems, September 2011
2
Introduction
The present study was done on 67 dried skulls from the Weissbach collection of
the Natural History Museum, Vienna. The objective of the present study was to
analyze the intra-articular space between the processus condylaris mandibulae
(condylar process) and the fossa mandibularis (articular fossa of the mandible) of
the temporal bone, and to correlate the intra-articular space with the supporting
teeth in occlusion.
A review of the literature on the intra-articular space showed some studies using
different technologies on living human subjects. Some studies are available in
French or English on the subject. In our revue of literature, no study has been
found on dry skulls.
In a study done by Hansson et al. (1977), they evaluated the thickness of the soft
tissue layers and articular disc of 48 right temporomandibular joints from Swedish
cadavers aged from 1 day to 93 years old without gross sign of arthrosis or
deviation in form. The specimens were examined histologically. The shrinkage of
these actual tissues seems to be less than 10% ( Hansson & Nordström). The
joint components were cut in 4 parts, lateral, latero-center, medio-center, and
medial. The total thickness of the soft tissue layers was measured in decalcified
sections. The middle and posterior parts of the articular disk were significally
thicker medio-centrally than laterally in the adults.
In a study done by Blaschke and Blaschke (1981) the condyle-temporal bone
spatial relationships were determined quantitatively in 50 asymptomatic TMJs (25
subjects) by making area measurements of the posterior and anterior portions of
the joint spaces on tomographic images. For both right and left sides, the
numerical expression of the joint relationship indicated that the condyle is
normally centered in the joint to a very high degree. Standard deviations around
the mean joint relationship values were large, however, which suggests that the
postero-anterior variation of condyle positions in asymptomatic TMJs is greater
than commonly thought. In addition, there was only mild correlation between
individual joint relationships on right and left sides.
A study by Christiansen et al. (1987) evaluated the condylar position and joint
space on 41 joints using computed tomography of the temporomandibular joint in
the axial plane with teeth in centric occlusion. Intra-articular joint spaces were
measured anterosuperiorly, superiorly, and posterosuperiorly (with the approach
of Pullinger and Hollender), and posteriorly by tracing a horizontal line from the
condylar surface to the anterior tympanic wall of the temporal bone. Those 4 joint
space measurements were done on 5 sagittal planes across the condyle.
3
The superior, the posterosuperior, and the posterior joint spaces in the normal
joint were greater than the anterosuperior joint space. When the disk was
anterior to the condyle, the anterosuperior joint interval widened. When the disk
was medial, the superior joint space was significantly wider than normal.
Huddleston et al. (1999) studied the intra-articular distance within the TMJ during
Free and Loaded Closing Movements width on 10 subjects with two cathode ray
tubes. The opening and closing movement traces of the kinematic center were
reconstructed, and the average difference between the traces (the intra-articular
distance) was calculated. The average intra-articular distance was significantly
smaller during loaded closing than during free closing, whereas no significant
differences were found in the intra-articular distances between the loaded
situations of low and high manual loading and contralateral chewing. The
average intra-articular distance and its standard deviation were from 0.25mm to
0.45mm.
A study by Kinniburgh et al. (2000) determinates the relationships and osseous
morphology between temporomandibular joints in adolescents with normal and
anterior disc positions using MRI. Condylar position was calculated according to
the method of Pullinger and Hollender. There was a significant difference in joint
space and curvature of the eminence-loading surface between male and female
adolescents with normal disc position.
A study by Major et al. (2002) analyzed the association between osseous
temporomandibular joint (TMJ) characteristics and TMJ internal derangement
(disc position and deformation) with magnetic resonance imaging (MRI) in 335
TMJs in 175 subjects between the ages of 7.27 and 20.0 year. The authors
identified associations between disc displacement and reduced superior joint
space, increased posterior joint space, increased anterior joint space, and
reduced articular eminence convexity. This study demonstrates that TMJ internal
derangement is associated with functional osseous adaptation within the joint.
In a study done by Elias et al. (2006), they took measurements for lateral and
anterior capsule-condyle distances in the closed and open-mouth positions,
accomplished in longitudinal (coronal) and transverse (axial) ultrasonographic
scans and MRI on 19 patients from 18 to 45 years old (average age: 27.4 years;
16 females and 3 males) The average values for the lateral capsule-condyle
distance in the closed-mouth position were 1.4 mm in longitudinal scans and 1.6
mm in transverse scans. In the open-mouth position, for both longitudinal and
transverse scans, the average value was 1.2 mm. The average values for the
anterior capsule-condyle distance in the closed- and open-mouth positions were
respectively 2.3 mm and 1.1 mm.
4
Hypothesis
Null hypothesis: The intra-articular space is not affected by the number of
posterior supporting teeth.
Definitions
Group of teeth: 3 groups of teeth have been created in relation with the number
of posterior occlusal contacts to support the occlusion:
4 teeth and less: means 4 posterior occlusal contacts or less.
5-7 teeth: means 5-7 posterior occlusal contacts
8 teeth and more: means 8 posterior occlusal contacts and more.
Virtual cut: Cuts made in the putties by the 3D software in 6 areas; 3 in protrusion
and 3 in mediotrusion at the lateral third, the center and the medial third.
Measurement: in each putty, 5 measurements were made at 10, 11, 12, 13, 14,
o‟clock for the right and left sides, 10 and 11 o‟clock being the posterior and
postero-superior intra-articular spaces and 13 and 14 o‟clock being the antero-
superior and anterior intra-articular spaces on both sides.
Intra-articular space: in our study, the term intra-articular space defines the space
between the processus condylaris and the fossa mandibularis. As our study was
done on dried skulls, this space includes also the space formerly occupied by the
articular disk and the cartilageous tissue covering the head of the condyle and
the eminentia on a living subject.
Putty: a mass of vinyl polysiloxane which was obtained by injection in the intra-
articular space.
This study has been done with 2 softwares; the first one named Catia and the
second one named Delcam.
Catia: This software treats 2D and 3D images in the same project.
Delcam : This software was used to make the cuts in the 3D putties. The X, Y
and Z axis measurements in both software (Catia & Delcam) do not correspond
to the X, Y and Z axis usually used in dentistry or orthopedics.
5
2-D long axis of the putties: As the previous long axis as been drawn on a 2D
image, we had to locate it in the third dimension.
3-D long axis of the putties: For doing so, we drew a line at the base of the
putties (base line) and selected the highest point in the concavity made by the
imprint of the condyles in the putties (most concave part of the imprint done by
the condyle). Having done several tests to locate the long axis in the third
dimension, the most appropriate location of the long axis in the third dimension
was to select a point which would give us the best measurements possible, i.e. to
have the long axis located in 3-D, in the geometrical center of the condylar
process. The result of our preliminary analysis brought us to choose a point
located at 60% from the base line or, if you prefer, at 40% from the highest point
in the concavity made by the condyle imprint in the putties.
Methodology
The reference plane chosen is the Frankfurt horizontal plane
Our study intended to analyse the thickness of the intra-articular space in the
lateral, the middle and the medial thirds of the intra-articular space.
The sample of skulls having served in our study comes from the Natural
History Museum in Vienna (Figure 1).
Figure 1
6
Thousands of skulls are stored in the anthropologic department. The skull
selection was done from the Weissbach collection (Figure 2). We had to find
skulls presenting dental arches articulating in a fairly good occlusion; it was
difficult to find very stable cases.
Figure 2
We had to select skulls with a solid and stable articulation. Once skulls
presenting a stable articulation were found we looked at the TMJ space to
see if there was enough space to inject an impression material in the intra
articular-space. The selected skulls were put on a table with the mandible in
occlusion (Figure 3).
7
Figure 3
A team of 4 persons was needed to take the “impression” of the intra-articular
space and the occlusal bite registration;
The impression material allowed us to work on 10 skulls at the time. Both
regions were injected with vinyl polysiloxane hydrophilic impression material.
(IMPRINT from 3M Company)
Sequence followed for impression of the intra-articular spaces and the bite
registration:
Step 1:
• Each group of ten skulls was placed upside down on a table with the
mandible besides
• Mineral oil was placed on the head of the condyles and in the fossae
mandibularis
• 3 members of the team (named 1 to 3) were needed to hold the skulls and
the mandible in each of their hands
• The fourth member of the team injected the silicone in the fossae
mandibularis of the first skull
• Then the same person took the skull and the mandibule in his hands to
articulate the mandibule in a proper relationship with the maxilla via the
occluding teeth, and put a firm pressure on the occluding teeth only and
gave back the skull to the member 1 of the holding team. The person
number 1 was stabilizing the bite during the hardening of the material
• Then, the fourth member injected the silicone in the second skull with the
member 2 of the holding team.
8
• This procedure was repeated for the following skulls. After the injection of
the material on the third skull, the impression material having hardened on
the first skull, the first skull was placed on a table (Figure 4) and a fourth
skull was taken by the member no 1 of the holding team and presented to
the fourth member of the team for injection of the impression material in
the intra-articular space (Figures 5 & 6). This procedure was repeated until
the impression material was injected in10 skulls.
Figure 4
Figure 5
9
Figure 6
Step 2:
• When the material has hardened in the first group of 10 skulls, a bite
registration was taken leaving in place the impression material in the intra-
articular spaces previously injected (Figure 7).
• The bite registration material (IMPRINT 3M ) was placed on the occlusal
surfaces of the maxillary teeth.
• The fourth member of the team, after having injected the impression.
material applied the same amount of pressure on the teeth as he applied
for the impression of the intra-articular space.
• Then he gave back the skull to the member no 1 for stabilization during
the hardening of the impression material.
10
Figure 7
Step 3:
We took out the intra-articular putty of each skull and we wrote on each
putty the skull number and the letter L for the left side and the letter R for
the right side (Figure 8 & 9). We left the occlusal registration bite in place
(Figure 10).
11
Figure 8
Bite registration and the first set of putties in place.
Figure 9
12
Figure 10
Step 4:
A second impression of the fossae mandibularis was taken by keeping the
bite registration in place on the teeth and using the same protocol as in step
1.
A picture of the occlusal bite registration and the first set of putties on both
right and left sides of each skull were taken on a trans-illuminating box to see
the occlusal contacts and the thickness of the putties (Figure 11).
13
Figure 11: Pictures of the bite registration and of the first set of putties
Step 5:
Each skull was placed on a metallic stand and was hold in place by ear
rods which were inserted in the auditory meatus. A third rod helped to
stabilize the skull and was placed at the lower margin of the orbit Figure
12).
14
Figure 12
The skull was then oriented perpendicularly to the floor to correspond to
the Frankfurt plane.
Photographs were then taken to see the putties in place in the fossae
mandibularis (Figure 13).
15
Figure 13
Our study having to be done in Canada, the second set of putties were
sent to Canada.
Our first intention was to physically cut the putties and to measure the
slices obtained with an electronic micrometer (caliper).
16
As our protocol was to analyze the thickness of the putties at the lateral,
central and medial part of the protrusive trajectory and of the mediotrusive
trajectory, we would have needed two separate sets of putties to use this
method.
As we had only one set of putties in Canada, it would not have been easily
feasible to do three cuts on the same putty on the protrusive trajectory and
then to do three cuts of this same putty on the mediotrusive trajectory
(Figure 14).
Figure 14
We analyzed the option of scanning the putties with a 3-D scanner and we
found the following advantages:
Due to the accuracy of the 3-D scanner, the results should be better than
trying to measure the thickness with a caliper, since the use of a caliper
could have easily compress the impression material
On 3-D software, it would be possible to draw lines (or vectors) more
easily than on the putties themselves, because it is possible to enlarge the
image on the software. So, the planes for the virtual cuts would be chosen
with greater accuracy
Last but not least, the putties could be kept intact and returned to Vienna
for further studies, if needed.
17
So, for the above mentioned advantages, it was decided to scan
electronically the second set of the intra-articular putties and to use
2 software to produce the results.
It has to be understood that certain variance in the putty especially on the
surface of the fossae mandibularis will give certain variance in the
thickness of the putties in the present study (Figure 15).
Figure 15
A photograph of each skull with the second putty in place was taken with
the identification of the skull on the left side of the picture (Figure 16).
18
Figure 16
The second set of putties shown on the picture was brought to Canada to
be scanned with a high precision scanner (Figure 17)
Called NextEngine 3D Scanner HD and the degree of precision is around
0.127 mm. See Appendix 1
Figure 17
19
Step 6:
As our study was done in Canada and that the skulls stayed in Vienna, we
had to superpose the 3D image of the putties on a 2D photograph of the
skulls (which were taken by a member of the team when he was at the
Natural History Museum, in Vienna. The superposition of the 3D image
over the 2D image was achieved by a well trained operator used to use
the Catia software.
Each left and right 3D putties were scanned with NextEngine 3D Scanner
HD. After the 3D scanning, each putty was superposed on top of the
corresponding 2D picture of the fossa mandibularis of the temporal bone
of the dried skull. Great care has been taken to correlate the scanned
image of the 3D putties in the best orientation possible over the 2D
images. Our goal was to position the putties in the same spatial orientation
in the fossae mandibularis on the 2D picture as well as it would be on the
skull.
In the present example the putty on the right side of the dried skull 470
was selected to show how the measurements were done (Figure 18).
20
Figure 18
21
In our study we had to cope with the X, Y, Z, axis given by the Delcam
software, which orientation is given below:
X axis: vertical axis
Y axis: horizontal axis
Z axis: transversal axis
If we place the dried skull with the Frankfurt plane parallel to the floor we
will get a view like the underneath picture (Figure 19).
Figure 19
22
Figure 20
Figure 21
23
6 different sections were made along the 3D long axis of the imprint of the
mandibular condyle (the long axis going from the lateral pole to the medial
pole of each condyle.)
It has to be considered that the three axis (X, Y, Z) used in dentistry and
orthopedics are not the same three axis (X, Y, Z) in use in the Catia and
Delcam software Figure 20 & 21).
The center of the skull was determined by the intersection of the Y axis
line and the Z axis line passing at the posterior nasal spine of the palatine
bone (Figure 22).
Figure 22
24
Figure 23
Once the 3-D scanned image was properly positioned on top of the 2-D
photograph of the fossae mandibularis, a line joining the lateral and the
medial poles of the putty was drawn (Figure 23 & 24). This line represents
the long axis of the imprint left in the putty by the condyle.
Then, to obtain a 3-D long axis of the condyle, we had to figure out how it
should be positioned three-dimensionally in the virtual putty. After many
trials, it was concluded that this 3-D long axis should be placed vertically
(X axis) at a distance of 40% from the most concave part of the putty
(Figure 25 & 26).
25
Figure 24
Figure 25
26
Figure 26
1- 3 virtual cuts following the protrusion trajectory of the condyle were
analyzed in 3 areas: the lateral, the center and the median part of
imprint of the condyle (Figure 27).
2- 3 virtual cuts were made at 90 degrees from the long axis of the 3-D
long axis of the condyle and the intersection point of X axis and the
protrusion trajectory to determine the mediotrusion trajectory (Figure
28).
For each of the 6 virtual cuts 5 measurement were taken at 10:00,
11:00, 12:00, 1:00 and 2:00 o‟clock. 12.00 o‟clock representing the X
(vertical) axis (perpendicular to the Frankfurt plane).
27
Figure 27
Figure 28
The purpose of reproducing the 3D spatial position of the putties in the
dried skulls is to reproduce the real position of the putties to be able to
28
compare with other studies and to better understand the intra articular
space in relation to supporting teeth in occlusion.
By using this methodology, the resulting analysis should be closer to
reality. The results should reflect the spaces in a real spatial position.
In some studies, cuts were made with no relation between the physical
putties (radiographs) and the skulls. In those studies the 12:00 cut was in
the middle of the head of the condyle.
In our study, the cuts were relatively well angulated through the putties.
The results gave a good lecture of the intra-articular spaces at those
areas.
Results
The mean values, standard deviations, minimum and maximums for the three
groups of supporting teeth on the left and right side are shown in the following six
tables:
Table 1 Results for Right Sides of skulls with 4 teeth or less.
4 teeth or less - Right Side - Mediotrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 37 2.829 0.918 0.574 4.973
11h 37 2.499 1.120 0.441 5.996
12h 37 2.853 1.133 0.466 4.809
13h 37 3.209 1.305 0.283 5.483
14h 37 2.838 1.345 0.000 6.284
4 teeth or less - Right Side - Mediotrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 37 2.635 0.838 1.175 4.276
11h 37 3.129 1.157 0.777 5.316
12h 37 2.929 1.296 0.779 5.862
29
13h 37 2.747 1.257 0.324 5.514
14h 37 2.658 1.348 0.531 6.543
4 teeth or less - Right Side - Mediotrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 37 2.979 1.144 0.946 7.112
11h 37 2.356 0.953 0.809 4.516
12h 37 2.859 1.007 0.473 4.766
13h 37 3.335 1.283 0.000 5.697
14h 37 2.837 1.133 0.204 5.757
4 teeth or less - Right Side - Protrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 37 2.877 0.899 0.574 4.528
11h 37 2.582 1.158 0.441 6.422
12h 37 2.853 1.133 0.466 4.804
13h 37 3.305 1.302 0.000 5.584
14h 37 2.750 1.149 0.000 5.082
4 teeth or less - Right Side - Protrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 37 2.608 0.938 1.175 5.383
11h 37 3.063 1.105 0.574 5.386
12h 37 2.930 1.294 0.782 5.861
13h 37 2.961 1.271 0.519 5.856
14h 37 2.711 1.326 0.000 5.510
4 teeth or less - Right Side - Protrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 37 2.812 1.038 0.946 6.226
11h 37 2.323 0.975 0.613 4.972
30
12h 37 2.858 1.008 0.474 4.769
13h 37 3.292 1.224 0.000 5.618
14h 37 2.855 1.201 0.000 5.757
Table 2 Results for Left Sides of skulls with 4 teeth or less.
4 teeth or less - Left Side - Mediotrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 37 2.669 0.948 1.035 4.380
11h 37 2.206 0.888 0.320 3.951
12h 37 2.870 1.280 0.457 5.312
13h 37 3.448 1.479 0.801 6.634
14h 37 2.913 1.348 0.183 6.640
4 teeth or less - Left Side - Mediotrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 37 2.554 0.910 0.677 4.241
11h 37 2.882 1.132 0.931 5.096
12h 37 3.059 1.205 0.433 6.031
13h 37 2.999 1.350 0.655 6.807
14h 37 2.673 1.342 0.000 5.720
4 teeth or less - Left Side - Mediotrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 37 3.337 1.503 1.065 7.263
11h 37 2.521 0.923 1.065 4.144
12h 37 3.167 1.322 0.973 6.227
13h 37 3.697 1.600 1.086 7.584
14h 37 3.056 1.332 0.486 6.721
31
4 teeth or less - Left Side - Protrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 37 2.727 0.992 1.215 4.554
11h 37 2.350 1.001 0.301 4.314
12h 37 2.870 1.279 0.457 5.311
13h 37 3.628 1.505 0.901 7.044
14h 37 3.047 1.419 0.308 6.927
4 teeth or less - Left Side - Protrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 37 2.479 0.996 0.464 4.333
11h 37 2.714 1.125 0.632 5.341
12h 37 3.057 1.205 0.430 6.019
13h 37 3.320 1.408 0.747 7.105
14h 37 2.931 1.408 0.166 6.060
4 teeth or less - Left Side - Protrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 37 3.002 1.311 1.006 6.573
11h 37 2.467 0.946 0.959 4.262
12h 37 3.168 1.322 0.973 6.226
13h 37 3.620 1.490 0.977 7.051
14h 37 3.085 1.404 0.534 6.671
32
Table 3 Results for Right Sides of skulls with 5, 6 or 7 teeth.
5,6 or 7 teeth - Right Side - Mediotrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 25 2.695 0.872 0.996 4.959
11h 25 2.460 0.863 0.804 4.770
12h 25 2.732 1.091 1.082 5.335
13h 25 2.622 1.557 0.000 5.733
14h 25 1.913 1.301 0.000 5.447
5,6 or 7 teeth - Right Side - Mediotrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 25 2.784 0.997 0.601 4.289
11h 25 2.869 1.049 0.578 5.515
12h 25 2.587 1.092 0.988 4.900
13h 25 2.156 1.559 0.000 6.068
14h 25 2.060 1.333 0.000 5.953
5,6 or 7 teeth - Right Side - Mediotrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 25 2.752 1.027 1.257 5.590
11h 25 2.188 0.752 0.276 3.891
12h 25 2.767 1.231 1.021 6.202
13h 25 2.898 1.630 0.212 5.698
14h 25 2.295 1.496 0.024 5.221
5,6 or 7 teeth - Right Side - Protrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 25 2.945 1.035 0.839 5.118
11h 25 2.579 0.831 0.931 4.629
33
12h 25 2.732 1.090 1.089 5.335
13h 25 2.737 1.496 0.539 5.733
14h 25 2.044 1.358 0.141 5.447
5,6 or 7 teeth - Right Side - Protrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 25 2.848 0.976 0.507 4.627
11h 25 2.899 1.051 0.364 4.940
12h 25 2.587 1.091 0.990 4.899
13h 25 2.297 1.586 0.000 6.068
14h 25 1.977 1.424 0.000 5.953
5,6 or 7 teeth - Right Side - Protrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 25 2.619 0.876 0.967 4.555
11h 25 2.220 0.768 0.080 3.864
12h 25 2.769 1.231 1.023 6.202
13h 25 2.766 1.598 0.000 5.698
14h 25 2.205 1.492 0.000 5.221
34
Table 4 Results for Left Sides of skulls with 5, 6 or 7 teeth.
5,6 or 7 teeth - Left Side - Mediotrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 25 2.319 0.868 0.000 4.212
11h 25 2.344 0.743 0.811 4.072
12h 25 2.687 0.841 1.137 4.832
13h 25 3.089 1.796 0.439 7.306
14h 25 2.324 1.324 0.420 5.642
5,6 or 7 teeth - Left Side - Mediotrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 25 2.356 1.081 0.000 4.189
11h 25 2.526 0.973 0.611 4.254
12h 25 2.637 1.048 1.167 4.820
13h 25 2.443 1.468 0.509 6.043
14h 25 2.240 1.396 0.273 5.940
5,6 or 7 teeth - Left Side - Mediotrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 25 2.453 0.899 0.688 5.370
11h 25 2.007 0.571 0.818 3.447
12h 25 2.745 0.985 0.881 5.731
13h 25 3.355 1.831 0.000 7.901
14h 25 2.647 1.564 0.233 6.419
5,6 or 7 teeth - Left Side - Protrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 25 2.445 0.868 0.000 3.878
11h 25 2.479 0.859 0.904 4.906
35
12h 25 2.687 0.842 1.139 4.832
13h 25 3.195 1.762 0.631 7.606
14h 25 2.420 1.377 0.531 6.091
5,6 or 7 teeth - Left Side - Protrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 25 2.409 1.330 0.143 4.922
11h 25 2.471 0.976 0.522 4.178
12h 25 2.591 1.087 1.163 4.820
13h 25 2.641 1.588 0.572 7.146
14h 25 2.277 1.472 0.364 6.144
5,6 or 7 teeth - Left Side - Protrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 25 2.536 0.941 1.199 5.229
11h 25 2.031 0.625 0.979 3.991
12h 25 2.745 0.985 0.883 5.734
13h 25 3.238 1.754 0.000 7.451
14h 25 2.654 1.563 0.000 6.265
36
Table 5 Results for Right Sides of skulls with 8 teeth or more.
8 teeth or more - Right Side - Mediotrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 5 2.856 0.790 1.610 3.646
11h 5 2.355 0.652 1.808 3.414
12h 5 2.567 0.973 1.800 4.120
13h 5 2.063 0.917 0.554 2.791
14h 5 1.373 0.544 0.569 1.868
8 teeth or more - Right Side - Mediotrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 5 3.763 1.205 2.002 5.302
11h 5 3.462 1.016 2.072 4.761
12h 5 2.955 1.337 1.576 5.018
13h 5 1.634 0.723 0.445 2.260
14h 5 1.086 0.651 0.000 1.732
8 teeth or more - Right Side - Mediotrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 5 2.956 0.709 1.837 3.512
11h 5 2.315 0.454 1.735 2.976
12h 5 2.515 0.884 1.728 3.974
13h 5 2.508 1.321 0.846 4.532
14h 5 1.811 0.525 1.163 2.345
8 teeth or more - Right Side - Protrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 5 3.472 0.866 2.092 4.405
11h 5 2.589 0.923 1.906 4.094
37
12h 5 2.567 0.972 1.800 4.119
13h 5 2.274 0.938 0.736 3.199
14h 5 1.469 0.510 0.755 2.016
8 teeth or more - Right Side - Protrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 5 3.652 0.964 2.250 4.813
11h 5 3.581 1.019 2.075 4.797
12h 5 2.954 1.335 1.578 5.014
13h 5 1.782 0.756 0.511 2.427
14h 5 1.167 0.680 0.000 1.758
8 teeth or more - Right Side - Protrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 5 2.793 0.620 2.158 3.631
11h 5 2.292 0.487 1.759 3.080
12h 5 2.514 0.885 1.728 3.974
13h 5 2.476 1.245 0.999 4.436
14h 5 1.885 0.530 1.265 2.483
38
Table 6 Results for Left Sides of skulls with 8 teeth or more.
8 teeth or more - Left Side - Mediotrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 5 3.328 1.072 1.996 4.893
11h 5 3.446 1.007 2.435 5.142
12h 5 3.472 0.578 2.973 4.283
13h 5 2.703 0.648 1.752 3.344
14h 5 2.301 1.024 1.158 3.637
8 teeth or more - Left Side - Mediotrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 5 3.079 0.660 2.528 4.171
11h 5 3.710 0.710 2.703 4.410
12h 5 2.947 1.520 1.411 5.302
13h 5 1.941 0.830 0.986 3.234
14h 5 1.953 0.666 1.403 3.090
8 teeth or more - Left Side - Mediotrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 5 2.964 1.281 1.632 4.932
11h 5 2.523 0.359 2.132 2.969
12h 5 3.661 0.891 2.611 4.863
13h 5 3.764 0.813 2.545 4.693
14h 5 3.041 1.095 1.802 4.440
8 teeth or more - Left Side - Protrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 5 3.693 0.855 2.755 5.073
11h 5 3.707 0.908 2.681 5.150
39
12h 5 3.473 0.577 2.973 4.282
13h 5 2.962 0.654 1.897 3.654
14h 5 2.460 1.027 1.280 3.788
8 teeth or more - Left Side - Protrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 5 2.788 0.731 2.036 3.843
11h 5 3.736 1.243 2.472 5.403
12h 5 2.947 1.520 1.411 5.304
13h 5 2.142 0.784 1.181 3.314
14h 5 2.051 0.715 1.546 3.286
8 teeth or more - Left Side - Protrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 5 2.907 1.317 1.252 4.830
11h 5 2.586 0.410 2.146 3.197
12h 5 3.663 0.892 2.612 4.867
13h 5 3.696 0.766 2.588 4.491
14h 5 3.099 0.968 2.104 4.289
40
The following figures are a graphic representation of the mean values for each
group of supporting teeth:
Figure 29 Illustration of distances (mm) for Right Side of skulls with 4 teeth or
less- Protrusion.
41
Figure 30 Illustration of distances (mm) for Right Side of skulls with 4 teeth or
less- Mediotrusion.
42
Figure 31 Illustration of distances (mm) for Left Side of skulls with 4 teeth or
less- Protrusion.
43
Figure 32 Illustration of distances (mm) for Left Side of skulls with 4 teeth or
less- Mediotrusion.
44
Figure 33 Illustration of distances (mm) for Right Side of skulls with 5, 6 or 7
teeth - Protrusion.
45
Figure 34 Illustration of distances (mm) for Right Side of skulls with 5, 6 or 7
teeth - Mediotrusion.
46
Figure 35 Illustration of distances (mm) for Left Side of skulls with 5, 6 or 7 teeth
- Protrusion.
47
Figure 36 Illustration of distances (mm) for Left Side of skulls with 5, 6 or 7 teeth
- Mediotrusion.
48
Figure 37 Illustration of distances (mm) for Right Side of skulls with 8 teeth or
more - Protrusion.
49
Figure 38 Illustration of distances (mm) for Right Side of skulls with 8 teeth or
more - Mediotrusion.
50
Figure 39 Illustration of distances (mm) for Left Side of skulls with 8 teeth or
more - Protrusion.
51
Figure 40 Illustration of distances (mm) for Left Side of skulls with 8 teeth or
more - Mediotrusion.
52
The mean values, standard deviations, minimum and maximum for the three
groups of supporting teeth for each side are shown in the following two tables:
Table 7 Results for Right Sides using all skulls.
Right Side - Mediotrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 67 2.775 0.958 0.601 5.302
11h 67 3.057 1.106 0.578 5.515
12h 67 2.803 1.219 0.779 5.862
13h 67 2.443 1.382 0.000 6.068
14h 67 2.318 1.367 0.000 6.543
Right Side - Mediotrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 67 2.781 0.882 0.574 4.973
11h 67 2.474 0.991 0.441 5.996
12h 67 2.786 1.095 0.466 5.335
13h 67 2.904 1.413 0.000 5.733
14h 67 2.383 1.377 0.000 6.284
Right Side - Mediotrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 67 2.893 1.068 0.946 7.112
11h 67 2.290 0.848 0.276 4.516
12h 67 2.799 1.077 0.473 6.202
13h 67 3.110 1.429 0.000 5.698
14h 67 2.558 1.282 0.024 5.757
Right Side - Protrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 67 2.776 0.979 0.507 5.383
53
11h 67 3.041 1.077 0.364 5.386
12h 67 2.804 1.218 0.782 5.861
13h 67 2.625 1.410 0.000 6.068
14h 67 2.322 1.398 0.000 5.953
Right Side - Protrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 67 2.947 0.948 0.574 5.118
11h 67 2.581 1.017 0.441 6.422
12h 67 2.786 1.094 0.466 5.335
13h 67 3.016 1.382 0.000 5.733
14h 67 2.391 1.260 0.000 5.447
Right Side - Protrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 67 2.739 0.948 0.946 6.226
11h 67 2.282 0.866 0.080 4.972
12h 67 2.799 1.078 0.474 6.202
13h 67 3.035 1.389 0.000 5.698
14h 67 2.540 1.320 0.000 5.757
54
Table 8 Results for Left Sides using all skulls.
Left Side - Mediotrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 67 2.519 0.968 0.000 4.241
11h 67 2.811 1.081 0.611 5.096
12h 67 2.893 1.171 0.433 6.031
13h 67 2.713 1.392 0.509 6.807
14h 67 2.458 1.334 0.000 5.940
Left Side - Mediotrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 67 2.588 0.952 0.000 4.893
11h 67 2.350 0.892 0.320 5.142
12h 67 2.847 1.100 0.457 5.312
13h 67 3.258 1.564 0.439 7.306
14h 67 2.647 1.334 0.183 6.640
Left Side - Mediotrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 67 2.979 1.342 0.688 7.263
11h 67 2.329 0.809 0.818 4.144
12h 67 3.047 1.194 0.881 6.227
13h 67 3.575 1.639 0.000 7.901
14h 67 2.902 1.403 0.233 6.721
Left Side - Protrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 67 2.476 1.107 0.143 4.922
11h 67 2.699 1.110 0.522 5.403
55
12h 67 2.875 1.188 0.430 6.019
13h 67 2.979 1.482 0.572 7.146
14h 67 2.621 1.423 0.166 6.144
Left Side - Protrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 67 2.694 0.977 0.000 5.073
11h 67 2.499 0.994 0.301 5.150
12h 67 2.847 1.100 0.457 5.311
13h 67 3.417 1.565 0.631 7.606
14h 67 2.769 1.396 0.308 6.927
Left Side - Protrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 67 2.821 1.189 1.006 6.573
11h 67 2.313 0.830 0.959 4.262
12h 67 3.047 1.194 0.883 6.226
13h 67 3.483 1.549 0.000 7.451
14h 67 2.925 1.437 0.000 6.671
56
The following figures illustrate the mean values for the three groups of supporting
teeth for each side:
Figure 41 Illustration of mean distances (mm) for Right Side - Protrusion.
57
Figure 42 Illustration of mean distances (mm) for Right Side - Mediotrusion.
58
Figure 43 Illustration of mean distances (mm) for Left Side - Protrusion.
59
Figure 44 Illustration of mean distances (mm) for Left Side - Mediotrusion.
60
The following table shows the mean values and the p-values between the
different groups of supporting teeth, for the lateral virtual cuts:
Table 9 Tests between number of teeth groups by Mediotrusion or protrusion
and Right or Left for Lateral results only.
Lateral
Mediotrusion Protrusion
Section = 10h Right Left Right Left
4 teeth or less 2.63 (b) 2.55 (a) 2.61 (a) 2.48 (a)
5, 6 or 7 teeth 2.78 (b) 2.36 (a) 2.85 (a) 2.41 (a)
8 teeth or more 3.76 (a) 3.08 (a) 3.65 (a) 2.79 (a)
p-value 0.0447 0.30 0.07 0.79
Mediotrusion Protrusion
Section = 11h Right Left Right Left
4 teeth or less 3.13 (a) 2.88 (a) 3.06 (a) 2.71 (a)
5, 6 or 7 teeth 2.87 (a) 2.53 (a) 2.90 (a) 2.47 (a)
8 teeth or more 3.46 (a) 3.71 (a) 3.58 (a) 3.74 (a)
p-value 0.47 0.07 0.43 0.06
Mediotrusion Protrusion
Section = 12h Right Left Right Left
4 teeth or less 2.93 (a) 3.06 (a) 2.93 (a) 3.06 (a)
5, 6 or 7 teeth 2.59 (a) 2.64 (a) 2.59 (a) 2.59 (a)
8 teeth or more 2.96 (a) 2.95 (a) 2.95 (a) 2.95 (a)
p-value 0.54 0.38 0.54 0.32
61
Mediotrusion Protrusion
Section = 13h Right Left Right Left
4 teeth or less 2.75 (a) 3.00 (a) 2.96 (a) 3.32 (a)
5, 6 or 7 teeth 2.16 (a) 2.44 (a) 2.30 (a) 2.64 (a)
8 teeth or more 1.63 (a) 1.94 (a) 1.78 (a) 2.14 (a)
p-value 0.10 0.13 0.07 0.09
Mediotrusion Protrusion
Section = 14h Right Left Right Left
4 teeth or less 2.66 (a) 2.67 (a) 2.71 (a) 2.93 (a)
5, 6 or 7 teeth 2.06 (ab) 2.24 (a) 1.98 (ab) 2.28 (a)
8 teeth or more 1.09 (b) 1.95 (a) 1.17 (b) 2.05 (a)
p-value 0.0242 0.31 0.0179 0.13
62
The following table shows the mean values and the p-values between the
different groups of supporting teeth, for the central virtual cuts:
Table 10 Tests between number of teeth groups by Mediotrusion or protrusion
and Right or Left for Center results only.
Center
Mediotrusion Protrusion
Section = 10h Right Left Right Left
4 teeth or less 2.83 (a) 2.67 (a) 2.88 (a) 2.73 (b)
5, 6 or 7 teeth 2.69 (a) 2.32 (a) 2.95 (a) 2.45 (b)
8 teeth or more 2.86 (a) 3.33 (a) 3.47 (a) 3.69 (a)
p-value 0.83 0.07 0.43 0.0294
Mediotrusion Protrusion
Section = 11h Right Left Right Left
4 teeth or less 2.50 (a) 2.21 (b) 2.58 (a) 2.35 (b)
5, 6 or 7 teeth 2.46 (a) 2.34 (b) 2.58 (a) 2.48 (b)
8 teeth or more 2.36 (a) 3.45 (a) 2.59 (a) 3.71 (a)
p-value 0.95 0.0120 0.99 0.0141
Mediotrusion Protrusion
Section = 12h Right Left Right Left
4 teeth or less 2.83 (a) 2.87 (a) 2.85 (a) 2.87 (a)
5, 6 or 7 teeth 2.73 (a) 2.69 (a) 2.73 (a) 2.69 (b)
8 teeth or more 2.57 (a) 3.47 (a) 2.57 (a) 3.47 (a)
p-value 0.82 0.35 0.82 0.34
63
Mediotrusion Protrusion
Section = 13h Right Left Right Left
4 teeth or less 3.21 (a) 3.45 (a) 3.30 (a) 3.63 (a)
5, 6 or 7 teeth 2.62 (a) 3.09 (a) 2.74 (a) 3.19 (a)
8 teeth or more 2.06 (a) 2.70 (a) 2.27 (a) 2.96 (a)
p-value 0.11 0.49 0.13 0.46
Mediotrusion Protrusion
Section = 14h Right Left Right Left
4 teeth or less 2.84 (a) 2.91 (a) 2.75 (a) 3.05 (a)
5, 6 or 7 teeth 1.91 (ab) 2.32 (a) 2.04 (ab) 2.42 (a)
8 teeth or more 1.37 (b) 2.30 (a) 1.47 (b) 2.46 (a)
p-value 0.0064 0.20 0.0202 0.20
64
The following table shows the mean values and the p-values between the
different groups of supporting teeth, for the medial virtual cuts:
Table 11 Tests between number of teeth groups by Mediotrusion or Protrusion
and Right or Left for Median results only.
Median
Mediotrusion Protrusion
Section = 10h Right Left Right Left
4 teeth or less 2,98 (a) 3,34 (a) 2,81 (a) 3,00 (a)
5, 6 or 7 teeth 2,75 (a) 2,45 (b) 2,62 (a) 2,54 (a)
8 teeth or more 2,96 (a) 2,96 (ab) 2,79 (a) 2,91 (a)
p-value 0.71 0.0368 0.73 0.32
Mediotrusion Protrusion
Section = 11h Right Left Right Left
4 teeth or less 2,36 (a) 2,52 (a) 2,32 (a) 2,47 (a)
5, 6 or 7 teeth 2,19 (a) 2,01 (b) 2,22 (a) 2,03 (a)
8 teeth or more 2,32 (a) 2,52 (a) 2,29 (a) 2,59 (a)
p-value 0.75 0.0397 0.90 0.09
Mediotrusion Protrusion
Section = 12h Right Left Right Left
4 teeth or less 2,85 (a) 3,17 (a) 2,86 (a) 3,17 (a)
5, 6 or 7 teeth 2,77 (a) 2,75 (a) 2,77 (a) 2,75 (a)
8 teeth or more 2,52 (a) 3,66 (a) 2,51 (a) 3,66 (a)
p-value 0.79 0.19 0.79 0.19
65
Mediotrusion Protrusion
Section = 13h Right Left Right Left
4 teeth or less 3,34 (a) 3,70 (a) 3,29 (a) 3,62 (a)
5, 6 or 7 teeth 2,90 (a) 3,36 (a) 2,77 (a) 3,24 (a)
8 teeth or more 2,51 (a) 3,76 (a) 2,48 (a) 3,70 (a)
p-value 0.31 0.70 0.22 0.61
Mediotrusion Protrusion
Section = 14h Right Left Right Left
4 teeth or less 2,84 (a) 3,06 (a) 2,86 (a) 3,09 (a)
5, 6 or 7 teeth 2,30 (a) 2,65 (a) 2,21 (a) 2,65 (a)
8 teeth or more 1,81 (a) 3,04 (a) 1,89 (a) 3,10 (a)
p-value 0.10 0.52 0.08 0.50
66
When we analyze the individual measurements of a single group of virtual cuts
(ex.: cuts on the protrusive vector, in the lateral third, for the right side), we found
very few results which present significative values between the groups of
supporting teeth. The only values that are significative are:
On the lateral cuts, there are significative differences on the
o 10 o‟clock cuts, mediotrusive vector, right side, between the group
< 4 teeth, the group 5-7 teeth and the group > 8 supporting teeth
(p-value: 0.0447), the mean value for the group > 8 supporting
contacts being larger than the two other groups
o 14 o‟clock cuts, protrusive vector, right side, between the group < 4
teeth and the group > 8 supporting teeth (p-value: 0.0179), the
mean value for the group < 4 supporting teeth being larger than the
group > 8 supporting teeth
o 14 o‟clock cuts, mediotrusive vector, right side, between the group
< 4 teeth and the group > 8 supporting teeth (p-value: 0.0242), the
mean value for the group < 4 supporting teeth being larger than the
group > 8 supporting teeth
On the central cuts, there are significative differences on the
o 10 o‟clock cuts, protrusive vector, left side, between the group < 4
teeth, the group 5-7 teeth and the group > 8 supporting teeth (p-
value: 0.0294), the mean value for the group > 8 supporting
contacts being larger than the two other groups
o 11 o‟clock cuts, protrusive vector, left side, between the group < 4
teeth, the group 5-7 teeth and the group > 8 supporting teeth (p-
value: 0.0141), the mean value for the group > 8 supporting
contacts being larger than the two other groups
o 11 o‟clock cuts, mediotrusive vector, left side, between the group <
4 teeth, the group 5-7 teeth and the group > 8 supporting teeth (p-
value: 0.0120), the mean value for the group > 8 supporting
contacts being larger than the two other groups
o 14 o‟clock cuts, protrusive vector, right side, between the group <
4 teeth and the group > 8 supporting teeth (p-value: 0.0202), the
67
mean value for the group < 4 supporting teeth being larger than the
group > 8 supporting teeth
o 14 o‟clock cuts, mediotrusive vector, right side, between the group
< 4 teeth and the group > 8 supporting teeth (p-value: 0.0064), the
mean value for the group < 4 supporting teeth being larger than the
group > 8 supporting teeth
On the medial cuts, there are significative differences on the
o 11 o‟clock cuts, mediotrusive vector, left side,
Between the group < 4 supporting teeth and the group 5-7
teeth (p-value: 0.0397).
between the group 5-7 teeth and the group > 8 supporting
teeth (p-value: 0.0397).
o the mean value for the group < 4 supporting teeth being equal to
the group > 8 supporting teeth. Both groups present larger values
than the group 5-7 supporting teeth.
It is important to note that as the number of measurements is relatively low (67)
when we analyze an individual series of cuts (ex.: cuts on the protrusive vector,
in the lateral third, for the right side). So, it is more difficult to find statistical
significative differences because the power of the test is lowered. Thus, this was
rather normal to find less significative differences between individual cuts.
68
The following table shows the mean values and the p-values for the three virtual
cuts together (lateral, center and medial) on the protrusive vector and the
mediotrusive vectors:
Table 12 Tests between number of teeth groups by Mediotrusion or Protrusion
and Right or Left.
Mediotrusion Protrusion
Section = 10h Right Left Right Left
4 teeth or less 2.81 (a) 2.85 (ab) 2.77 (a) 2.74 (a)
5, 6 or 7 teeth 2.74 (a) 2.38 (b) 2.80 (a) 2.46 (a)
8 teeth or more 3.19 (a) 3.12 (a) 3.31 (a) 3.12 (a)
p-value 0.26 0.0046 0.12 0.0578
Mediotrusion Protrusion
Section = 11h Right Left Right Left
4 teeth or less 2.66 (a) 2.54 (b) 2.66 (a) 2.51 (b)
5, 6 or 7 teeth 2.51 (a) 2.29 (b) 2.57 (a) 2.33 (b)
8 teeth or more 2.71 (a) 3.23 (a) 2.82 (a) 3.34 (a)
p-value 0.56 0.0018 0.65 0.0012
Mediotrusion Protrusion
Section = 12h Right Left Right Left
4 teeth or less 2.88 (a) 3.03 (ab) 2.88 (a) 3.03 (ab)
5, 6 or 7 teeth 2.70 (a) 2.69 (b) 2.70 (a) 2.67 (b)
8 teeth or more 2.68 (a) 3.36 (a) 2.68 (a) 3.36 (a)
p-value 0.50 0.0441 0.50 0.0367
69
Mediotrusion Protrusion
Section = 13h Right Left Right Left
4 teeth or less 3.10 (a) 3.38 (a) 3.19 (a) 3.52 (a)
5, 6 or 7 teeth 2.56 (ab) 2.96 (a) 2.60 (ab) 3.02 (a)
8 teeth or more 2.07 (b) 2.80 (a) 2.18 (b) 2.93 (a)
p-value 0.0040 0.13 0.0021 0.0614
Mediotrusion Protrusion
Section = 14h Right Left Right Left
4 teeth or less 2.78 (a) 2.88 (a) 2.77 (a) 3.02 (a)
5, 6 or 7 teeth 2.09 (b) 2.40 (a) 2.08 (b) 2.45 (a)
8 teeth or more 1.42 (c) 2.43 (a) 1.51 (b) 2.54 (a)
p-value <0.0001 0.05 <0.0001 0.0204
When we group the lateral, central and medial virtual cuts and we analyze the
values for the protrusive and mediotrusive vectors for the right and left sides, we
found significative differences for the cuts, at:
10 o‟clock, mediotrusive vector, left side, between the group 5-7
supporting contacts and the group > 8 (p-value: 0.0046), the mean value
for the group > 8 supporting contacts being larger than the group 5-7
supporting teeth
11 o‟clock cuts,
o protrusive vector, left side, between the group < 4 teeth, the group
5-7 teeth and the group > 8 supporting teeth (p-value: 0.0012), the
70
mean value for the group > 8 supporting contacts being larger than
the two other groups
o mediotrusive vector, left side, between the group < 4 teeth, the
group 5-7 teeth and the group > 8 supporting teeth (p-value:
0.0018), the mean value for the group > 8 supporting contacts
being larger than the two other groups
12 o‟clock cuts,
o Protrusive vector, left side, between the group 5-7 supporting
contacts and the group > 8 (p-value: 0.0367), the mean value for
the group > 8 supporting contacts being larger than the group 5-7
supporting teeth
o Mediotrusive vector, left side, between the group 5-7 supporting
contacts and the group > 8 (p-value: 0.0441), the mean value for
the group > 8 supporting contacts being larger than the group 5-7
supporting teeth
13 o‟clock cuts,
o Protrusive vector, right side, between the group 5-7 supporting
contacts and the group > 8 (p-value: 0.0021), the mean value for
the group < 4 supporting contacts being larger than the group > 8
supporting teeth
o Mediotrusive vector, right side, between the group 5-7 supporting
contacts and the group > 8 (p-value: 0.0040), the mean value for
the group < 4 supporting teeth being larger than the group > 8
supporting teeth
14 o‟clock cuts,
o Protrusive vector, right side, between the group < 4 teeth, the group
5-7 teeth and the group > 8 supporting teeth (p-value: < 0.0001),
the mean value for the group < 4 supporting teeth being larger than
the two other groups
o Mediotrusive vector, right side, between the group < 4 teeth, the
group 5-7 teeth and the group > 8 supporting teeth (p-value: <
0.0001), the mean value for the group < 4 supporting teeth being
larger than the group 5-7 supporting teeth which mean value is also
larger than the group > 8 supporting teeth
71
The following table shows the mean values and the p-values for:
for the lateral cuts (right and left, on the protrusive and mediotrusive
vectors)
for the center cuts (right and left, on the protrusive and mediotrusive
vectors)
for the medial cuts (right and left, on the protrusive and mediotrusive
vectors)
Table 13 Test results between number of teeth groups for Section at 10h.
Section = 10h Lateral**** Center***** Median******
4 teeth or less 2.57 (b) 2.78 (b) 3.03 (a)
5, 6 or 7 teeth 2.60 (b) 2.60 (b) 2.59 (b)
8 teeth or more 3.32 (a) 3.34 (a) 2.91 (a)
p-value 0.0064 0.0054 0.0107
Section = 11h Lateral**** Center***** Median******
4 teeth or less 2.95 (b) 2.41 (b) 2.42 (a)
5, 6 or 7 teeth 2.69 (b) 2.47 (b) 2.11 (b)
8 teeth or more 3.62 (a) 3.02 (a) 2.43 (a)
p-value 0.0017 0.0285 0.0141
Section = 12h Lateral**** Center***** Median******
4 teeth or less 2.99 (a) 2.86 (a) 3.01 (a)
5, 6 or 7 teeth 2.60 (b) 2.71 (a) 2.76 (a)
8 teeth or more 2.95 (a) 3.02 (a) 3.09 (a)
p-value 0.0354 0.39 0.18
Section = 13h Lateral**** Center***** Median******
4 teeth or less 3.01 (a) 3.40 (a) 3.49 (a)
5, 6 or 7 teeth 2.38 (b) 2.91 (ab) 3.06 (a)
72
8 teeth or more 1.87 (b) 2.50 (b) 3.11 (a)
p-value <0.0001 0.005 0.0832
Section = 14h Lateral**** Center***** Median******
4 teeth or less 2.74 (a) 2.89 (a) 2.96 (a)
5, 6 or 7 teeth 2.14 (b) 2.17 (b) 2.45 (b)
8 teeth or more 1.56 (c) 1.90 (b) 2.46 (b)
p-value <0.0001 <0.0001 0.0101
If we group both sides (right and left) plus the protrusive and mediotrusive
vectors and that we analyze the values on the lateral, center and medial vectors,
we find more significative differences:
For the lateral cuts:
o 10 o‟clock, between the group < 4 teeth, the group 5-7 teeth and
the group > 8 supporting teeth (p-value: 0.0064), the mean value
for the group > 8 supporting contacts being larger than the two
other groups
o 11 o‟clock, between the group < 4 teeth, the group 5-7 teeth and
the group > 8 supporting teeth (p-value: 0.0017), the mean value
for the group > 8 supporting contacts being larger than the two
other groups
o 12 o‟clock, between the group 5-7 teeth and the group >8
supporting contacts (p-value: 0.0354), the mean value for the group
< 4 supporting teeth being almost equal to the group > 8 supporting
teeth. Both groups present larger values than the group 5-7
supporting teeth.
o 13 o‟clock, between the group < 4 contacts and the groups 5-7
contacts and > 8, (p-value: < 0.0001), the mean value for the group
< 4 supporting teeth being larger than the two other groups
o 14 o‟clock, between the 3 groups (p-value: < 0.0001), the mean
value for the group < 4 supporting teeth being larger than the group
5-7 teeth which mean value is also larger then the group > 8
supporting teeth
73
For the central cuts;
o 10 o‟clock, between the group < 4 teeth, the group 5-7 teeth and
the group > 8 supporting teeth (p-value: 0.0054), the mean value
for the group > 8 supporting contacts being larger than the two
other groups
o 11 o‟clock, between the group < 4 teeth, the group 5-7 teeth and
the group > 8 supporting teeth (p-value: 0.0285), the mean value
for the group > 8 supporting contacts being larger than the two
other groups
o 13 o‟clock, between the group < 4 teeth and the group > 8
supporting teeth (p-value: 0.005), the mean value for the group < 4
supporting teeth being larger than the group > 8 supporting teeth
o 14 o‟clock, between the group < 4 teeth, the group 5-7 teeth and
the group > 8 supporting teeth (p-value: < 0.0001), the mean value
for the group < 4 supporting teeth being larger than the group > 8
supporting teeth
For the medial cuts:
o 10 o‟clock, between the groups < 4 supporting teeth, > 8 supporting
teeth and the group 5-7 supporting teeth (p-value: 0.0107), the
mean values of the groups < 4 supporting teeth and > 8 supporting
teeth being almost equal but larger than the group 5-7 teeth
o 11 o‟clock, between the groups < 4 supporting teeth, > 8 supporting
teeth and the group 5-7 supporting teeth (p-value: 0.0107), the
mean values of the groups < 4 supporting teeth and > 8 supporting
teeth being almost equal but larger than the group 5-7 teeth
o 14 o‟clock, the group < 4 supporting teeth and the group 5-7
supporting teeth, > 8 supporting teeth (p-value: 0.0101), the mean
value of the the group < 4 supporting teeth being larger than the
two other groups.
74
The following table shows the results, for all the skulls, of the lateral, central,
medial virtual cuts on the protrusive and mediotrusive vectors.
Table 14 Test results between number of teeth groups for Section at 10, 11, 12,
13, 14 o‟clock.
Section = 10h Right** Left***
4 teeth or less 2.79 (b) 2.79 (a)
5, 6 or 7 teeth 2.77 (b) 2.42 (b)
8 teeth or more 3.25 (a) 3.13 (a)
p-value 0.0382 0.0004
Section = 11h Right** Left***
4 teeth or less 2.66 (a) 2.52 (b)
5, 6 or 7 teeth 2.54 (a) 2.31 (b)
8 teeth or more 2.77 (a) 3.28 (a)
p-value 0.39 <0.0001
Section = 12h Right** Left***
4 teeth or less 2.88 (a) 3.03 (ab)
5, 6 or 7 teeth 2.70 (a) 2.68 (b)
8 teeth or more 2.68 (a) 3.36 (a)
p-value 0.25 0.0015
Section = 13h Right** Left***
4 teeth or less 3.14 (a) 3.45 (a)
5, 6 or 7 teeth 2.58 (b) 2.99 (ab)
8 teeth or more 2.12 (b) 2.87 (b)
p-value <0.0001 0.0079
Section = 14h Right** Left***
4 teeth or less 2.77 (a) 2.95 (a)
5, 6 or 7 teeth 2.08 (b) 2.43 (b)
75
8 teeth or more 1.47 (c) 2.48 (b)
p-value <0.0001 0.001
If we group all the cuts together (lateral, central, medial on the protrusive and
mediotrusive vectors) and that we analyse the data per side and by group of
teeth, we find the following significative values:
Right side:
10 o‟clock, between the group < 4 teeth, the group 5-7 teeth and the group
> 8 supporting teeth (p-value: 0.0382), the mean value for the group > 8
supporting teeth being larger than the two other groups
13 o‟clock, between the group < 4 teeth, the group 5-7 teeth and the group
> 8 supporting teeth (p-value: < 0.0001), the mean value of the the group
< 4 supporting teeth being larger than the two other groups.
14 o‟clock, between the group < 4 teeth, the group 5-7 teeth and the group
> 8 supporting teeth (p-value: < 0.0001), the mean value for the group < 4
supporting teeth being larger than the group 5-7 teeth which mean value
is also larger then the group > 8 supporting teeth
Left side:
10 o‟clock, between the group 5-7 teeth and the group > 8 supporting
teeth (p-value: 0.0004), the mean value for the group < 4 supporting teeth
being almost equal to the group > 8 supporting teeth. Both groups present
larger values than the group 5-7 supporting teeth.
11 o‟clock, between the group < 4 teeth, the group 5-7 teeth and the
group > 8 supporting teeth (p-value: < 0.0001), the mean value for the
group > 8 supporting contacts being larger than the two other groups
12 o‟clock, between the group 5-7 teeth and the group > 8 supporting
teeth (p-value: 0.0015), the mean value for the group > 8 supporting teeth
being larger than the group 5-7 supporting teeth
13 o‟clock, between the group < 4 teeth and the group > 8 supporting
teeth (p-value: 0.0079), the mean value for the group < 4 supporting teeth
being larger than the group > 8 supporting teeth
76
14 o‟clock, between the group < 4 teeth, the group 5-7 teeth and the group
> 8 supporting teeth (p-value: 0.001), the mean value of the the group < 4
supporting teeth being larger than the two other groups.
The following table shows the results, for all the skulls, both sides, of the lateral,
central, medial virtual cuts on the protrusive and mediotrusive vectors.
Table 15 Test results between number of teeth groups for Section at 10, 11, 12,
13, 14 o‟clock.
Section = 10h All*
4 teeth or less 2.79 (b)
5, 6 or 7 teeth 2.60 (b)
8 teeth or more 3.19 (a)
p-value 0.0001
Section = 11h All*
4 teeth or less 2.59 (b)
5, 6 or 7 teeth 2.42 (b)
8 teeth or more 3.03 (a)
p-value <0.0001
Section = 12h All*
4 teeth or less 2.96 (ab)
5, 6 or 7 teeth 2.69 (b)
8 teeth or more 3.02 (a)
p-value 0.0039
Section = 13h All*
4 teeth or less 3.30 (a)
5, 6 or 7 teeth 2.79 (b)
8 teeth or more 2.50 (b)
77
p-value <0.0001
Section = 14h All*
4 teeth or less 2.86 (a)
5, 6 or 7 teeth 2.25 (b)
8 teeth or more 1.97 (b)
p-value <0.0001
If we group all the right and left cuts together (lateral, central, medial on the
protrusive and mediotrusive vectors), and that we analyze the data by group of
supporting teeth, we find the following significative values:
10 o‟clock, between the group < 4 teeth, the group 5-7 teeth and the group
> 8 supporting teeth (p-value: 0.0001), the mean value for the group > 8
supporting teeth being larger than the two other groups
11 o‟clock, between the group < 4 teeth, the group 5-7 teeth and the group
> 8 supporting teeth (p-value: < 0.0001), the mean value for the group > 8
supporting teeth being larger than the two other groups
12 o‟clock, between the group 5-7 teeth and the group > 8 supporting
teeth (p-value: 0.0039), the mean value for the group > 8 supporting teeth
being larger than the group 5-7 supporting teeth
13 o‟clock, between the group < 4 teeth, the group 5-7 teeth and the group
> 8 supporting teeth (p-value: < 0.0001), the mean value of the group < 4
supporting teeth being larger than the two other groups.
14 o‟clock, between the group < 4 teeth, the group 5-7 teeth and the group
> 8 supporting teeth (p-value: < 0.001), the mean value of the group < 4
supporting teeth being larger than the two other groups.
78
Comparison with other studies
In a study from Kazumi Ikeda and Akira Kawamura show the following results
with Pullinger measurement protocol (Figure 45).
Figure 45
It is mentioned in that study that there are no quantitative standards for the
optimal position of the mandibular condyle in the glenoid fossa. Recently
developed limited cone-beam computed tomography (LCBCT) allows
measurement of this position with high accuracy. Methods: LCBCT was used to
assess 24 joints in 22 symptom-free subjects (10 male, 12 female; mean age, 18
years) who had no disc displacement as verified by magnetic resonance imaging.
Their joints had optimum function with the starting and end points of all functional
jaw movements coincident with maximum intercuspation.
Linear measurements of anterior space (AS), superior space (SS), and posterior
space (PS) were made to determine the position of the condyle for each joint.
Results: The mean AS, SS, and PS values were 1.3 mm (SD 6 0.2 mm), 2.5 mm
(SD 6 0.5 mm), and 2.1 mm (SD 6 0.3 mm), respectively (Figure 46). No
significant sex difference was noted in joint space distances. The results showed
less variability of condylar position in the fossa than previously reported in normal
subjects. Conclusions: These data from optimal joints might serve as norms for
the clinical assessment of condylar position obtained by LCBCT.
79
Figure 46
Ikeda Méthot (8 teeth and more)
10:00 = 2.10 mm 3.19 mm
12:00 = 2.50 mm 3.02mm
14:00 = 1.30 mm 1.97mm
We put the mean values of measurements of a few studies in a tabloid and the
results are quite similar. The results in red are the only ones that were made on
dried skulls.
Table 16
Studies 10 :00 12 :00 14 :00
Crhistiansen , Thompson 2.48 mm 2.26 mm 1.78 mm
Christiansen, Chan __ 2,25 mm 1.80 mm
Major 3.09 mm 2.65 mm 2.22 mm
80
Kinniburgh 3.62 mm 2.95 mm 1.92 mm
Ikeda 2.10 mm 2.50 mm 1.30 mm
Methot 3.19 mm 3.02 mm 1.97 mm
Discussion
We didn‟t found any study measuring the intra articular space on dried skulls.
We had many constraints doing this study;
First we didn‟t work directly on the skulls.
Second we scanned the imprint of the intra articular spaces; even if we worked
with high precision software and scanner the biggest error factor was in
positioning the 3D putties over the 2D pictures. In the repeatability test the
degree of repeatability gave certain credibility in the technique.
REPEATABILITY TEST
The repeatability test was performed by repeating three times on the same skulls
in order to evaluate the variability associated to the measure taking. The
statistical analyses associated to the repeatability test consist in presentation of
descriptive statistics allowing the evaluation of the measure taking variability.
The descriptive statistics presented are:
- Mean (in mm); In the repeatability study, this statistic is mainly used to calculate the coefficient of variation,
- Standard deviation (St. Dev.) (in mm); This statistic give a first estimate associated to the measure variability,
- Coefficient of variation (St. Dev. Divided by the Mean, does not have a unity of measure and is generally presented in %); This statistic is the most important to study the repeatability. Even though no statistical test associated to the coefficient of variation and no universally accepted value to indicate acceptable repeatability are available, in the present study, a coefficient of variation smaller than 5% or 10% will be considered as values to aim for.
81
- Minimum and maximum values (in mm); In addition to the direct information given by these statistics, they also allow an estimation of the variability by defining the range between the smallest and largest values of the three repetitions.
Tables 17 to 20 present the statistics for each measure. The statistics are
obtained for each skull, with three repetitions of the same measure. These tables
show that the vast majority of the measures present a coefficient of variation
smaller than 10% and almost all measures present a coefficient of variation
smaller than 20%. These results show that there is a non negligible variability
associated to the measure taking but this variability did not prevent the detection
of significant differences between the numbers of teeth groups. The measure
variability may however have reduced the number of significant differences
found, with a less variable measure, a larger number of significant differences
would probably have been found between the numbers of teeth groups.
Table 17 Descriptive statistics for the repeatability study for Mediotrusion on the
Right Side.
Right Side - Mediotrusion - Lateral - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 3.14 0.04 1.3% 3.10 3.18
11h 3 3.41 0.27 8.0% 3.24 3.72
12h 3 3.50 0.48 13.7% 3.15 4.05
13h 3 2.97 0.31 10.3% 2.68 3.29
14h 3 3.10 0.02 0.6% 3.08 3.12
Right Side - Mediotrusion - Lateral - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 1.94 0.46 23.7% 1.66 2.47
11h 3 1.21 0.05 4.1% 1.16 1.25
12h 3 2.09 0.19 9.3% 1.87 2.22
13h 3 2.36 0.12 5.0% 2.27 2.49
14h 3 2.57 0.12 4.5% 2.44 2.64
Right Side - Mediotrusion - Center - Skull #468
82
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 3.07 0.28 9.2% 2.74 3.28
11h 3 3.42 0.21 6.2% 3.23 3.65
12h 3 4.27 0.10 2.2% 4.19 4.37
13h 3 2.91 0.14 4.8% 2.81 3.07
14h 3 2.31 0.18 7.9% 2.10 2.43
Right Side - Mediotrusion - Center - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.71 0.42 15.5% 2.39 3.19
11h 3 1.31 0.19 14.3% 1.20 1.53
12h 3 2.37 0.18 7.7% 2.21 2.57
13h 3 2.22 0.06 2.7% 2.15 2.26
14h 3 1.92 0.04 1.9% 1.89 1.96
Right Side - Mediotrusion - Median - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.88 0.15 5.2% 2.77 3.06
11h 3 3.70 0.18 4.9% 3.52 3.88
12h 3 4.35 0.19 4.3% 4.14 4.47
13h 3 2.94 0.16 5.5% 2.83 3.13
14h 3 2.01 0.22 11.0% 1.85 2.26
Right Side - Mediotrusion - Median - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.46 0.47 19.2% 2.06 2.98
11h 3 1.24 0.05 3.8% 1.20 1.29
12h 3 2.09 0.24 11.4% 1.93 2.36
13h 3 2.20 0.13 5.9% 2.11 2.35
14h 3 1.98 0.07 3.4% 1.91 2.05
83
Table 18 Descriptive statistics for the repeatability study for Protrusion on the
Right Side.
Right Side - Protrusion - Lateral - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 3.26 0.07 2.1% 3.20 3.34
11h 3 3.61 0.30 8.4% 3.41 3.96
12h 3 3.50 0.48 13.7% 3.15 4.05
13h 3 2.96 0.23 7.8% 2.76 3.21
14h 3 3.32 0.03 0.9% 3.29 3.35
Right Side - Protrusion - Lateral - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.40 0.51 21.3% 2.05 2.98
11h 3 1.30 0.08 6.2% 1.21 1.35
12h 3 2.09 0.20 9.4% 1.87 2.22
13h 3 1.95 0.14 7.1% 1.83 2.10
14h 3 2.35 0.10 4.0% 2.25 2.44
Right Side - Protrusion - Center - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.96 0.14 4.6% 2.81 3.06
11h 3 3.54 0.24 6.7% 3.35 3.80
12h 3 4.26 0.09 2.2% 4.19 4.37
13h 3 2.88 0.17 5.9% 2.72 3.06
14h 3 2.71 0.22 8.1% 2.49 2.93
Right Side - Protrusion - Center - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.92 0.51 17.6% 2.51 3.49
84
11h 3 1.31 0.14 10.8% 1.21 1.48
12h 3 2.37 0.18 7.7% 2.21 2.57
13h 3 2.20 0.04 1.6% 2.18 2.25
14h 3 2.19 0.07 3.0% 2.11 2.24
Right Side - Protrusion - Median - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.98 0.20 6.7% 2.83 3.21
11h 3 3.74 0.16 4.3% 3.59 3.91
12h 3 4.36 0.19 4.4% 4.14 4.47
13h 3 3.07 0.25 8.0% 2.91 3.35
14h 3 1.92 0.13 6.7% 1.79 2.04
Right Side - Protrusion - Median - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.03 0.31 15.5% 1.74 2.36
11h 3 1.19 0.03 2.3% 1.17 1.22
12h 3 2.08 0.24 11.4% 1.93 2.36
13h 3 2.50 0.16 6.2% 2.38 2.68
14h 3 1.90 0.04 1.9% 1.87 1.94
85
Table 19 Descriptive statistics for the repeatability study for Mediotrusion on the
Left Side.
Left Side - Mediotrusion - Lateral - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.80 0.24 8.4% 2.53 2.96
11h 3 3.35 0.52 15.6% 2.83 3.88
12h 3 3.33 0.41 12.3% 2.89 3.70
13h 3 3.36 0.38 11.2% 3.00 3.75
14h 3 3.06 0.06 1.9% 3.00 3.12
Left Side - Mediotrusion - Lateral - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.85 0.14 4.7% 2.73 3.00
11h 3 2.85 0.30 10.4% 2.57 3.16
12h 3 3.56 0.22 6.2% 3.38 3.80
13h 3 2.83 0.10 3.5% 2.73 2.93
14h 3 2.65 0.20 7.4% 2.48 2.86
Left Side - Mediotrusion - Center - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.79 0.20 7.2% 2.60 3.00
11h 3 3.23 0.44 13.7% 2.75 3.62
12h 3 4.65 0.35 7.6% 4.45 5.06
13h 3 4.02 0.71 17.7% 3.47 4.83
14h 3 3.15 0.16 4.9% 3.02 3.32
Left Side - Mediotrusion - Center - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 4.13 0.11 2.7% 4.00 4.22
11h 3 4.37 0.38 8.7% 3.97 4.72
86
12h 3 4.59 0.15 3.3% 4.43 4.73
13h 3 3.48 0.07 2.0% 3.42 3.55
14h 3 2.57 0.12 4.6% 2.45 2.69
Left Side - Mediotrusion - Median - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.30 0.09 4.1% 2.19 2.35
11h 3 2.82 0.21 7.6% 2.63 3.05
12h 3 5.02 0.86 17.0% 4.04 5.55
13h 3 4.49 0.62 13.8% 4.02 5.19
14h 3 3.39 0.16 4.6% 3.21 3.49
Left Side - Mediotrusion - Median - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.89 0.23 8.0% 2.69 3.14
11h 3 3.35 0.11 3.3% 3.24 3.46
12h 3 5.31 0.03 0.5% 5.30 5.34
13h 3 4.21 0.07 1.7% 4.17 4.30
14h 3 2.49 0.06 2.4% 2.44 2.55
87
Table 20 Descriptive statistics for the repeatability study for Protrusion on the
Left Side.
Left Side - Protrusion - Lateral - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.87 0.22 7.7% 2.65 3.09
11h 3 3.01 0.58 19.1% 2.38 3.52
12h 3 3.33 0.41 12.3% 2.89 3.70
13h 3 3.65 0.43 11.8% 3.24 4.10
14h 3 3.26 0.08 2.5% 3.19 3.35
Left Side - Protrusion - Lateral - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.32 0.07 3.2% 2.24 2.39
11h 3 2.42 0.23 9.4% 2.23 2.67
12h 3 3.55 0.22 6.1% 3.38 3.80
13h 3 3.43 0.10 3.0% 3.33 3.54
14h 3 2.83 0.11 3.9% 2.75 2.96
Left Side - Protrusion - Center - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 3.12 0.10 3.3% 3.03 3.23
11h 3 3.41 0.47 13.8% 2.86 3.70
12h 3 4.65 0.35 7.6% 4.45 5.06
13h 3 4.10 0.70 17.1% 3.60 4.90
14h 3 3.21 0.14 4.3% 3.12 3.37
Left Side - Protrusion - Center - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 3.89 0.31 7.9% 3.65 4.24
11h 3 4.15 0.12 3.0% 4.03 4.27
88
12h 3 4.59 0.15 3.3% 4.42 4.73
13h 3 4.14 0.04 0.9% 4.11 4.19
14h 3 2.42 0.00 0.2% 2.41 2.42
Left Side - Protrusion - Median - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.28 0.11 4.7% 2.16 2.35
11h 3 2.88 0.28 9.6% 2.58 3.11
12h 3 5.02 0.86 17.0% 4.04 5.55
13h 3 4.65 0.58 12.5% 4.25 5.32
14h 3 3.49 0.23 6.5% 3.24 3.68
Left Side - Protrusion - Median - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 3.18 0.36 11.3% 2.88 3.58
11h 3 3.63 0.07 1.8% 3.59 3.71
12h 3 5.31 0.03 0.5% 5.30 5.34
13h 3 4.41 0.12 2.8% 4.29 4.54
14h 3 2.64 0.02 0.8% 2.62 2.66
These tables show that the vast majority of the measures present a coefficient of
variation smaller than 10% and almost all measures present a coefficient of
variation smaller than 20%.
It have to be noted that in some studies like a study done by Hansson et al. on
Thickness of Soft Tissue Layer and Articular Disk in the Temporomandibular
Joint, the shrinkage of tissues on cadavers seems to be around 10%.
As it can be seen by the analysis of the data in the section “Results”, the more
we group the data, the more we find significative values.
Furthermore, the more we group the data, the p-values are greatly decreased.
To have significative values for individual groups of cuts (ex.: right side, lateral
cuts on the protrusive vector) we would have needed a larger number of skulls.
89
If we look at all the data, we can observe that there are significative differences
(p-values < 0.05) between the groups of supporting teeth, particularly between
the groups < 4 supporting teeth and the group > 8 supporting teeth.
Interestingly, the group > 8 supporting teeth presents more significative
differences on the cuts done at 10 o‟clock and 11 o‟clock and the mean values
are larger than the group < 4 supporting teeth. This suggests that the postero-
superior intra-articular space is larger for the group > 8 supporting teeth than for
the group < 4 supporting teeth. Also, the group of > 8 supporting teeth does not
show significative differences at 13 and 14 o‟clock and the mean values are
smaller than for the group < 4 supporting teeth which means that the antero-
superior intra-articular space is smaller for the group > 8 supporting teeth.
Also, the group < 4 supporting teeth presents more significative differences (p-
values < 0.05) on the cuts done at 13 o‟clock and 14 o‟clock, with mean values
larger than the group > 8 supporting teeth. This suggests that the antero-superior
intra-articular space is larger for the group < 4 supporting teeth than for the group
> 8 supporting teeth. Also, the group of < 4 supporting teeth does not show
significative differences at 10 and 11 o‟clock and the mean values are smaller
than for the group > 8 supporting teeth which means that the postero-superior
intra-articular space is smaller for the group < 4 supporting teeth.
To summarize, the intra-articular space seems to be larger postero-
superiorly and smaller antero-superiorly for the group > 8 supporting teeth.
Conversely, the intra-articular space seems to be smaller postero-
superiorly and larger antero-superiorly for the group < 4 supporting teeth.
It appears that the group > 8supporting teeth has the condyle positioned
more “anteriorly” in the so-called “glenoid fossae” than the group < 4
supporting teeth.
Conversely, the group < 4 supporting teeth has the condyle positioned
more postero-superiorly in the “glenoid fossae” than the group > 8
supporting teeth.
90
Figure 47 Right side; 4 teeth and less
Figure 48 Right side; 8 teeth and more
91
Figure 49 Left side; 4 teeth and less
Figure 50 Left side; 8 teeth and more
92
Conclusion
The null hypothesis is rejected.
The present study shows that there is a relationship between the number of
posterior teeth supporting the vertical dimension of occlusion and the intra-
articular space.
A further study including a larger number of skulls should be done to reinforce
this statement.
93
Appendix 1
Technical Specifications
94
Appendix 2
Report
Statistical analyses of thesis data.
Prepared for : Dr. Alain
Méthot
Claude Laberge
Experts-Conseils STATEX
August 3rd, 2011
95
TABLE OF CONTENTS
TABLE OF CONTENTS ................................................................................................................................... 95
INTRODUCTION .............................................................................................................................................. 96
DESCRIPTIVE RESULTS FOR ALL SKULLS ............................................................................................ 96
DESCRIPTIVE RESULTS BY NUMBER OF TEETH GROUPS .............................................................. 105
TESTS BETWEEN NUMBER OF TEETH GROUPS ................................................................................. 130
SUPPLEMENTARY TESTS BETWEEN NUMBER OF TEETH GROUPS ............................................ 133
REPEATABILITY TEST .................................................................................................................................. 80
96
INTRODUCTION
This report presents the statistical results for the data from Dr. Alain Méthot’s thesis.
DESCRIPTIVE RESULTS FOR ALL SKULLS
The statistical results presented for all skulls are:
1) A series of tables presenting Mean, standard deviation (St. Dev.), minimum and maximum in addition to the number of skulls used to calculate this statistics.;
2) Graphs of mean values to allow a more comprehensive visualisation of the results.
97
Table 1. Results for Right Sides using all skulls.
Right Side - Mediotrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 67 2.775 0.958 0.601 5.302
11h 67 3.057 1.106 0.578 5.515
12h 67 2.803 1.219 0.779 5.862
13h 67 2.443 1.382 0.000 6.068
14h 67 2.318 1.367 0.000 6.543
Right Side - Mediotrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 67 2.781 0.882 0.574 4.973
11h 67 2.474 0.991 0.441 5.996
12h 67 2.786 1.095 0.466 5.335
13h 67 2.904 1.413 0.000 5.733
14h 67 2.383 1.377 0.000 6.284
Right Side - Mediotrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 67 2.893 1.068 0.946 7.112
11h 67 2.290 0.848 0.276 4.516
12h 67 2.799 1.077 0.473 6.202
13h 67 3.110 1.429 0.000 5.698
14h 67 2.558 1.282 0.024 5.757
Right Side - Protrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 67 2.776 0.979 0.507 5.383
11h 67 3.041 1.077 0.364 5.386
98
12h 67 2.804 1.218 0.782 5.861
13h 67 2.625 1.410 0.000 6.068
14h 67 2.322 1.398 0.000 5.953
Right Side - Protrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 67 2.947 0.948 0.574 5.118
11h 67 2.581 1.017 0.441 6.422
12h 67 2.786 1.094 0.466 5.335
13h 67 3.016 1.382 0.000 5.733
14h 67 2.391 1.260 0.000 5.447
Right Side - Protrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 67 2.739 0.948 0.946 6.226
11h 67 2.282 0.866 0.080 4.972
12h 67 2.799 1.078 0.474 6.202
13h 67 3.035 1.389 0.000 5.698
14h 67 2.540 1.320 0.000 5.757
Table 2. Results for Left Sides using all skulls.
Left Side - Mediotrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 67 2.519 0.968 0.000 4.241
11h 67 2.811 1.081 0.611 5.096
12h 67 2.893 1.171 0.433 6.031
13h 67 2.713 1.392 0.509 6.807
14h 67 2.458 1.334 0.000 5.940
Left Side - Mediotrusion - Center
99
Section N Mean St. Dev. Minimum Maximum
10h 67 2.588 0.952 0.000 4.893
11h 67 2.350 0.892 0.320 5.142
12h 67 2.847 1.100 0.457 5.312
13h 67 3.258 1.564 0.439 7.306
14h 67 2.647 1.334 0.183 6.640
Left Side - Mediotrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 67 2.979 1.342 0.688 7.263
11h 67 2.329 0.809 0.818 4.144
12h 67 3.047 1.194 0.881 6.227
13h 67 3.575 1.639 0.000 7.901
14h 67 2.902 1.403 0.233 6.721
Left Side - Protrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 67 2.476 1.107 0.143 4.922
11h 67 2.699 1.110 0.522 5.403
12h 67 2.875 1.188 0.430 6.019
13h 67 2.979 1.482 0.572 7.146
14h 67 2.621 1.423 0.166 6.144
Left Side - Protrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 67 2.694 0.977 0.000 5.073
11h 67 2.499 0.994 0.301 5.150
12h 67 2.847 1.100 0.457 5.311
13h 67 3.417 1.565 0.631 7.606
14h 67 2.769 1.396 0.308 6.927
100
Left Side - Protrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 67 2.821 1.189 1.006 6.573
11h 67 2.313 0.830 0.959 4.262
12h 67 3.047 1.194 0.883 6.226
13h 67 3.483 1.549 0.000 7.451
14h 67 2.925 1.437 0.000 6.671
101
Figure 1. Illustration of mean distances (mm) for Right Side - Mediotrusion.
102
Figure 2. Illustration of mean distances (mm) for Right Side - Protrusion.
103
Figure 3. Illustration of mean distances (mm) for Left Side - Mediotrusion.
104
Figure 4. Illustration of mean distances (mm) for Left Side - Protrusion.
105
DESCRIPTIVE RESULTS BY NUMBER OF TEETH GROUPS
As for the preceding section for all skulls, the descriptive results by number of teeth groups are:
1) A series of tables presenting Mean, standard deviation (St. Dev.), minimum and maximum in addition to the number of skulls used to calculate this statistics.;
2) Graphs of mean values to allow a more comprehensive visualisation of the results.
Three number of teeth groups were defined as:
1) Skulls with 4 teeth or less; 2) Skulls with 5, 6 or 7 teeth; 3) Skulls with 8 teeth or more.
106
Table 3. Results for Left Sides of skulls with 4 teeth or less.
4 teeth or less - Left Side - Mediotrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 37 2.669 0.948 1.035 4.380
11h 37 2.206 0.888 0.320 3.951
12h 37 2.870 1.280 0.457 5.312
13h 37 3.448 1.479 0.801 6.634
14h 37 2.913 1.348 0.183 6.640
4 teeth or less - Left Side - Mediotrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 37 2.554 0.910 0.677 4.241
11h 37 2.882 1.132 0.931 5.096
12h 37 3.059 1.205 0.433 6.031
13h 37 2.999 1.350 0.655 6.807
14h 37 2.673 1.342 0.000 5.720
4 teeth or less - Left Side - Mediotrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 37 3.337 1.503 1.065 7.263
11h 37 2.521 0.923 1.065 4.144
12h 37 3.167 1.322 0.973 6.227
13h 37 3.697 1.600 1.086 7.584
14h 37 3.056 1.332 0.486 6.721
4 teeth or less - Left Side - Protrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 37 2.727 0.992 1.215 4.554
11h 37 2.350 1.001 0.301 4.314
107
12h 37 2.870 1.279 0.457 5.311
13h 37 3.628 1.505 0.901 7.044
14h 37 3.047 1.419 0.308 6.927
4 teeth or less - Left Side - Protrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 37 2.479 0.996 0.464 4.333
11h 37 2.714 1.125 0.632 5.341
12h 37 3.057 1.205 0.430 6.019
13h 37 3.320 1.408 0.747 7.105
14h 37 2.931 1.408 0.166 6.060
4 teeth or less - Left Side - Protrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 37 3.002 1.311 1.006 6.573
11h 37 2.467 0.946 0.959 4.262
12h 37 3.168 1.322 0.973 6.226
13h 37 3.620 1.490 0.977 7.051
14h 37 3.085 1.404 0.534 6.671
108
Table 4. Results for Right Sides of skulls with 4 teeth or less.
4 teeth or less - Right Side - Mediotrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 37 2.829 0.918 0.574 4.973
11h 37 2.499 1.120 0.441 5.996
12h 37 2.853 1.133 0.466 4.809
13h 37 3.209 1.305 0.283 5.483
14h 37 2.838 1.345 0.000 6.284
4 teeth or less - Right Side - Mediotrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 37 2.635 0.838 1.175 4.276
11h 37 3.129 1.157 0.777 5.316
12h 37 2.929 1.296 0.779 5.862
13h 37 2.747 1.257 0.324 5.514
14h 37 2.658 1.348 0.531 6.543
4 teeth or less - Right Side - Mediotrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 37 2.979 1.144 0.946 7.112
11h 37 2.356 0.953 0.809 4.516
12h 37 2.859 1.007 0.473 4.766
13h 37 3.335 1.283 0.000 5.697
14h 37 2.837 1.133 0.204 5.757
4 teeth or less - Right Side - Protrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 37 2.877 0.899 0.574 4.528
11h 37 2.582 1.158 0.441 6.422
109
12h 37 2.853 1.133 0.466 4.804
13h 37 3.305 1.302 0.000 5.584
14h 37 2.750 1.149 0.000 5.082
4 teeth or less - Right Side - Protrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 37 2.608 0.938 1.175 5.383
11h 37 3.063 1.105 0.574 5.386
12h 37 2.930 1.294 0.782 5.861
13h 37 2.961 1.271 0.519 5.856
14h 37 2.711 1.326 0.000 5.510
4 teeth or less - Right Side - Protrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 37 2.812 1.038 0.946 6.226
11h 37 2.323 0.975 0.613 4.972
12h 37 2.858 1.008 0.474 4.769
13h 37 3.292 1.224 0.000 5.618
14h 37 2.855 1.201 0.000 5.757
110
Table 5. Results for Left Sides of skulls with 5, 6 or 7 teeth.
5,6 or 7 teeth - Left Side - Mediotrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 25 2.319 0.868 0.000 4.212
11h 25 2.344 0.743 0.811 4.072
12h 25 2.687 0.841 1.137 4.832
13h 25 3.089 1.796 0.439 7.306
14h 25 2.324 1.324 0.420 5.642
5,6 or 7 teeth - Left Side - Mediotrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 25 2.356 1.081 0.000 4.189
11h 25 2.526 0.973 0.611 4.254
12h 25 2.637 1.048 1.167 4.820
13h 25 2.443 1.468 0.509 6.043
14h 25 2.240 1.396 0.273 5.940
5,6 or 7 teeth - Left Side - Mediotrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 25 2.453 0.899 0.688 5.370
11h 25 2.007 0.571 0.818 3.447
12h 25 2.745 0.985 0.881 5.731
13h 25 3.355 1.831 0.000 7.901
14h 25 2.647 1.564 0.233 6.419
5,6 or 7 teeth - Left Side - Protrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 25 2.445 0.868 0.000 3.878
11h 25 2.479 0.859 0.904 4.906
111
12h 25 2.687 0.842 1.139 4.832
13h 25 3.195 1.762 0.631 7.606
14h 25 2.420 1.377 0.531 6.091
5,6 or 7 teeth - Left Side - Protrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 25 2.409 1.330 0.143 4.922
11h 25 2.471 0.976 0.522 4.178
12h 25 2.591 1.087 1.163 4.820
13h 25 2.641 1.588 0.572 7.146
14h 25 2.277 1.472 0.364 6.144
5,6 or 7 teeth - Left Side - Protrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 25 2.536 0.941 1.199 5.229
11h 25 2.031 0.625 0.979 3.991
12h 25 2.745 0.985 0.883 5.734
13h 25 3.238 1.754 0.000 7.451
14h 25 2.654 1.563 0.000 6.265
112
Table 6. Results for Right Sides of skulls with 5, 6 or 7 teeth.
5,6 or 7 teeth - Right Side - Mediotrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 25 2.695 0.872 0.996 4.959
11h 25 2.460 0.863 0.804 4.770
12h 25 2.732 1.091 1.082 5.335
13h 25 2.622 1.557 0.000 5.733
14h 25 1.913 1.301 0.000 5.447
5,6 or 7 teeth - Right Side - Mediotrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 25 2.784 0.997 0.601 4.289
11h 25 2.869 1.049 0.578 5.515
12h 25 2.587 1.092 0.988 4.900
13h 25 2.156 1.559 0.000 6.068
14h 25 2.060 1.333 0.000 5.953
5,6 or 7 teeth - Right Side - Mediotrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 25 2.752 1.027 1.257 5.590
11h 25 2.188 0.752 0.276 3.891
12h 25 2.767 1.231 1.021 6.202
13h 25 2.898 1.630 0.212 5.698
14h 25 2.295 1.496 0.024 5.221
5,6 or 7 teeth - Right Side - Protrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 25 2.945 1.035 0.839 5.118
11h 25 2.579 0.831 0.931 4.629
113
12h 25 2.732 1.090 1.089 5.335
13h 25 2.737 1.496 0.539 5.733
14h 25 2.044 1.358 0.141 5.447
5,6 or 7 teeth - Right Side - Protrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 25 2.848 0.976 0.507 4.627
11h 25 2.899 1.051 0.364 4.940
12h 25 2.587 1.091 0.990 4.899
13h 25 2.297 1.586 0.000 6.068
14h 25 1.977 1.424 0.000 5.953
5,6 or 7 teeth - Right Side - Protrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 25 2.619 0.876 0.967 4.555
11h 25 2.220 0.768 0.080 3.864
12h 25 2.769 1.231 1.023 6.202
13h 25 2.766 1.598 0.000 5.698
14h 25 2.205 1.492 0.000 5.221
Table 7. Results for Left Sides of skulls with 8 teeth or more.
8 teeth or more - Left Side - Mediotrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 5 3.328 1.072 1.996 4.893
11h 5 3.446 1.007 2.435 5.142
12h 5 3.472 0.578 2.973 4.283
13h 5 2.703 0.648 1.752 3.344
14h 5 2.301 1.024 1.158 3.637
8 teeth or more - Left Side - Mediotrusion - Lateral
114
Section N Mean St. Dev. Minimum Maximum
10h 5 3.079 0.660 2.528 4.171
11h 5 3.710 0.710 2.703 4.410
12h 5 2.947 1.520 1.411 5.302
13h 5 1.941 0.830 0.986 3.234
14h 5 1.953 0.666 1.403 3.090
8 teeth or more - Left Side - Mediotrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 5 2.964 1.281 1.632 4.932
11h 5 2.523 0.359 2.132 2.969
12h 5 3.661 0.891 2.611 4.863
13h 5 3.764 0.813 2.545 4.693
14h 5 3.041 1.095 1.802 4.440
8 teeth or more - Left Side - Protrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 5 3.693 0.855 2.755 5.073
11h 5 3.707 0.908 2.681 5.150
12h 5 3.473 0.577 2.973 4.282
13h 5 2.962 0.654 1.897 3.654
14h 5 2.460 1.027 1.280 3.788
8 teeth or more - Left Side - Protrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 5 2.788 0.731 2.036 3.843
11h 5 3.736 1.243 2.472 5.403
12h 5 2.947 1.520 1.411 5.304
13h 5 2.142 0.784 1.181 3.314
14h 5 2.051 0.715 1.546 3.286
115
8 teeth or more - Left Side - Protrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 5 2.907 1.317 1.252 4.830
11h 5 2.586 0.410 2.146 3.197
12h 5 3.663 0.892 2.612 4.867
13h 5 3.696 0.766 2.588 4.491
14h 5 3.099 0.968 2.104 4.289
116
Table 8. Results for Right Sides of skulls with 8 teeth or more.
8 teeth or more - Right Side - Mediotrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 5 2.856 0.790 1.610 3.646
11h 5 2.355 0.652 1.808 3.414
12h 5 2.567 0.973 1.800 4.120
13h 5 2.063 0.917 0.554 2.791
14h 5 1.373 0.544 0.569 1.868
8 teeth or more - Right Side - Mediotrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 5 3.763 1.205 2.002 5.302
11h 5 3.462 1.016 2.072 4.761
12h 5 2.955 1.337 1.576 5.018
13h 5 1.634 0.723 0.445 2.260
14h 5 1.086 0.651 0.000 1.732
8 teeth or more - Right Side - Mediotrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 5 2.956 0.709 1.837 3.512
11h 5 2.315 0.454 1.735 2.976
12h 5 2.515 0.884 1.728 3.974
13h 5 2.508 1.321 0.846 4.532
14h 5 1.811 0.525 1.163 2.345
8 teeth or more - Right Side - Protrusion - Center
Section N Mean St. Dev. Minimum Maximum
10h 5 3.472 0.866 2.092 4.405
11h 5 2.589 0.923 1.906 4.094
117
12h 5 2.567 0.972 1.800 4.119
13h 5 2.274 0.938 0.736 3.199
14h 5 1.469 0.510 0.755 2.016
8 teeth or more - Right Side - Protrusion - Lateral
Section N Mean St. Dev. Minimum Maximum
10h 5 3.652 0.964 2.250 4.813
11h 5 3.581 1.019 2.075 4.797
12h 5 2.954 1.335 1.578 5.014
13h 5 1.782 0.756 0.511 2.427
14h 5 1.167 0.680 0.000 1.758
8 teeth or more - Right Side - Protrusion - Median
Section N Mean St. Dev. Minimum Maximum
10h 5 2.793 0.620 2.158 3.631
11h 5 2.292 0.487 1.759 3.080
12h 5 2.514 0.885 1.728 3.974
13h 5 2.476 1.245 0.999 4.436
14h 5 1.885 0.530 1.265 2.483
118
Figure 5. Illustration of distances (mm) for Right Side of skulls with 4 teeth or less-
Mediotrusion.
119
Figure 6. Illustration of distances (mm) for Right Side of skulls with 4 teeth or less- Protrusion.
120
Figure 7. Illustration of distances (mm) for Left Side of skulls with 4 teeth or less- Mediotrusion.
121
Figure 8. Illustration of distances (mm) for Left Side of skulls with 4 teeth or less- Protrusion.
122
Figure 9. Illustration of distances (mm) for Right Side of skulls with 5,6 or 7 teeth -
Mediotrusion.
123
Figure 10. Illustration of distances (mm) for Right Side of skulls with 5,6 or 7 teeth - Protrusion.
124
Figure 11. Illustration of distances (mm) for Left Side of skulls with 5,6 or 7 teeth -
Mediotrusion.
125
Figure 12. Illustration of distances (mm) for Left Side of skulls with 5,6 or 7 teeth - Protrusion.
126
Figure 13. Illustration of distances (mm) for Right Side of skulls with 8 teeth or more -
Mediotrusion.
127
Figure 14. Illustration of distances (mm) for Right Side of skulls with 8 teeth or more -
Protrusion.
128
Figure 15. Illustration of distances (mm) for Left Side of skulls with 8 teeth or more -
Mediotrusion.
129
Figure 16. Illustration of distances (mm) for Left Side of skulls with 8 teeth or more - Protrusion.
130
TESTS BETWEEN NUMBER OF TEETH GROUPS
Tests for mean differences between number of teeth groups are performed by section (10h,
11h, 12h, 13h and 14h). The tests are also performed using different groupings of the studied
factors. Hence, tables with test results contain 6 columns :
*In column „All‟ : Means are compared using all results for Right and Left, Mediotrusion and protrusion, Lateral, Median and Center.
** In column „Right‟ : Means are compared for Right Side using all results for Mediotrusion and protrusion, Lateral, Median and Center.
*** In column „Left‟ : Means are compared for Left Side using all results for Mediotrusion and protrusion, Lateral, Median and Center.
**** In column „Lateral‟ Means are compared for „Lateral‟ using all results for Right and Left, Mediotrusion and protrusion.
***** In column „Center‟ Means are compared for 'Center' using all results for Right and Left, Mediotrusion and protrusion.
****** In column „Median‟ Means are compared for 'Median' using all results for Right and Left, Mediotrusion and protrusion.
The test used to compare means between number of teeth groups is the F-Test from an Analysis
of Variance (ANOVA). This analysis test if at least two of the means are significantly different; a
significant conclusion (at least two means are different) can be drawn if the p-value (last line in
the tables) is smaller than 0.05. When the ANOVA conclude to a significant difference, a Duncan
multiple comparison test is performed to determine which means are significantly different.
The conclusions of Duncan multiple comparison tests are presented with the help of letters
which group means that are not significantly different. Hence, two means associated to the
same letter are not significantly different. For example, in Table 9, column ‘All’ : Group of 8
teeth or more has a mean significantly higher than the other two groups, however, groups of 4
teeth or less and 5, 6 or 7 teeth do not present significantly different means, since these groups
are both associated to the letter (b). Similarly, in Table 11 and column ‘All’: Group of 8 teeth or
more has a mean significantly higher than group 5, 6 or 7 teeth, but groups 4 teeth or less and 5,
6 or 7 teeth are not significantly different, since they both have letter (b) in common; similarly,
groups 4 teeth or less and 8 teeth or more are not significantly different, since they both have
letter (a) in common.
131
Table 9. Test results between number of teeth groups for Section at 10h.
Section = 10h All* Right** Left*** Lateral**** Center***** Median******
4 teeth or less 2.79 (b) 2.79 (b) 2.79 (a) 2.57 (b) 2.78 (b) 3.03 (a)
5, 6 or 7 teeth 2.60 (b) 2.77 (b) 2.42 (b) 2.60 (b) 2.60 (b) 2.59 (b)
8 teeth or more 3.19 (a) 3.25 (a) 3.13 (a) 3.32 (a) 3.34 (a) 2.91 (a)
p-value 0.0001 0.0382 0.0004 0.0064 0.0054 0.0107
Table 10. Test results between number of teeth groups for Section at 11h.
Section = 11h All* Right** Left*** Lateral**** Center***** Median******
4 teeth or less 2.59 (b) 2.66 (a) 2.52 (b) 2.95 (b) 2.41 (b) 2.42 (a)
5, 6 or 7 teeth 2.42 (b) 2.54 (a) 2.31 (b) 2.69 (b) 2.47 (b) 2.11 (b)
8 teeth or more 3.03 (a) 2.77 (a) 3.28 (a) 3.62 (a) 3.02 (a) 2.43 (a)
p-value <0.0001 0.39 <0.0001 0.0017 0.0285 0.0141
Table 11. Test results between number of teeth groups for Section at 12h.
Section = 12h All* Right** Left*** Lateral**** Center***** Median******
4 teeth or less 2.96 (ab) 2.88 (a) 3.03 (ab) 2.99 (a) 2.86 (a) 3.01 (a)
5, 6 or 7 teeth 2.69 (b) 2.70 (a) 2.68 (b) 2.60 (b) 2.71 (a) 2.76 (a)
8 teeth or more 3.02 (a) 2.68 (a) 3.36 (a) 2.95 (a) 3.02 (a) 3.09 (a)
p-value 0.0039 0.25 0.0015 0.0354 0.39 0.18
Table 12. Test results between number of teeth groups for Section at 13h.
Section = 13h All* Right** Left*** Lateral**** Center***** Median******
4 teeth or less 3.30 (a) 3.14 (a) 3.45 (a) 3.01 (a) 3.40 (a) 3.49 (a)
5, 6 or 7 teeth 2.79 (b) 2.58 (b) 2.99 (ab) 2.38 (b) 2.91 (ab) 3.06 (a)
132
8 teeth or more 2.50 (b) 2.12 (b) 2.87 (b) 1.87 (b) 2.50 (b) 3.11 (a)
p-value <0.0001 <0.0001 0.0079 <0.0001 0.005 0.0832
Table 13. Test results between number of teeth groups for Section at 14h.
Section = 14h All* Right** Left*** Lateral**** Center***** Median******
4 teeth or less 2.86 (a) 2.77 (a) 2.95 (a) 2.74 (a) 2.89 (a) 2.96 (a)
5, 6 or 7 teeth 2.25 (b) 2.08 (b) 2.43 (b) 2.14 (b) 2.17 (b) 2.45 (b)
8 teeth or more 1.97 (b) 1.47 (c) 2.48 (b) 1.56 (c) 1.90 (b) 2.46 (b)
p-value <0.0001 <0.0001 0.001 <0.0001 <0.0001 0.0101
133
SUPPLEMENTARY TESTS BETWEEN NUMBER OF TEETH GROUPS
A supplementary series of tests between number of teeth groups is presented in this section.
These supplementary tests are also performed by section (10h, 11h, 12h, 13h and 14h).
However, the groupings by Side, Protrusion or Mediotrusion and by lateral, median or center
are different.
Table 14. Tests between number of teeth groups by Mediotrusion or Protrusion and Right or
Left.
Mediotrusion Protrusion
Section = 10h Right Left Right Left
4 teeth or less 2.81 (a) 2.85 (ab) 2.77 (a) 2.74 (a)
5, 6 or 7 teeth 2.74 (a) 2.38 (b) 2.80 (a) 2.46 (a)
8 teeth or more 3.19 (a) 3.12 (a) 3.31 (a) 3.12 (a)
p-value 0.26 0.0046 0.12 0.0578
Mediotrusion Protrusion
Section = 11h Right Left Right Left
4 teeth or less 2.66 (a) 2.54 (b) 2.66 (a) 2.51 (b)
5, 6 or 7 teeth 2.51 (a) 2.29 (b) 2.57 (a) 2.33 (b)
8 teeth or more 2.71 (a) 3.23 (a) 2.82 (a) 3.34 (a)
p-value 0.56 0.0018 0.65 0.0012
Mediotrusion Protrusion
Section = 12h Right Left Right Left
4 teeth or less 2.88 (a) 3.03 (ab) 2.88 (a) 3.03 (ab)
5, 6 or 7 teeth 2.70 (a) 2.69 (b) 2.70 (a) 2.67 (b)
134
8 teeth or more 2.68 (a) 3.36 (a) 2.68 (a) 3.36 (a)
p-value 0.50 0.0441 0.50 0.0367
Mediotrusion Protrusion
Section = 13h Right Left Right Left
4 teeth or less 3.10 (a) 3.38 (a) 3.19 (a) 3.52 (a)
5, 6 or 7 teeth 2.56 (ab) 2.96 (a) 2.60 (ab) 3.02 (a)
8 teeth or more 2.07 (b) 2.80 (a) 2.18 (b) 2.93 (a)
p-value 0.0040 0.13 0.0021 0.0614
Mediotrusion Protrusion
Section = 14h Right Left Right Left
4 teeth or less 2.78 (a) 2.88 (a) 2.77 (a) 3.02 (a)
5, 6 or 7 teeth 2.09 (b) 2.40 (a) 2.08 (b) 2.45 (a)
8 teeth or more 1.42 (c) 2.43 (a) 1.51 (b) 2.54 (a)
p-value <0.0001 0.05 <0.0001 0.0204
Table 15. Tests between number of teeth groups by Mediotrusion or Protrusion and Right or
Left for Median results only.
Median
Mediotrusion Protrusion
Section = 10h Right Left Right Left
4 teeth or less 2,98 (a) 3,34 (a) 2,81 (a) 3,00 (a)
5, 6 or 7 teeth 2,75 (a) 2,45 (b) 2,62 (a) 2,54 (a)
8 teeth or more 2,96 (a) 2,96 (ab) 2,79 (a) 2,91 (a)
p-value 0.71 0.0368 0.73 0.32
135
Mediotrusion Protrusion
Section = 11h Right Left Right Left
4 teeth or less 2,36 (a) 2,52 (a) 2,32 (a) 2,47 (a)
5, 6 or 7 teeth 2,19 (a) 2,01 (b) 2,22 (a) 2,03 (a)
8 teeth or more 2,32 (a) 2,52 (a) 2,29 (a) 2,59 (a)
p-value 0.75 0.0397 0.90 0.09
Mediotrusion Protrusion
Section = 12h Right Left Right Left
4 teeth or less 2,85 (a) 3,17 (a) 2,86 (a) 3,17 (a)
5, 6 or 7 teeth 2,77 (a) 2,75 (a) 2,77 (a) 2,75 (a)
8 teeth or more 2,52 (a) 3,66 (a) 2,51 (a) 3,66 (a)
p-value 0.79 0.19 0.79 0.19
Mediotrusion Protrusion
Section = 13h Right Left Right Left
4 teeth or less 3,34 (a) 3,70 (a) 3,29 (a) 3,62 (a)
5, 6 or 7 teeth 2,90 (a) 3,36 (a) 2,77 (a) 3,24 (a)
8 teeth or more 2,51 (a) 3,76 (a) 2,48 (a) 3,70 (a)
p-value 0.31 0.70 0.22 0.61
Mediotrusion Protrusion
Section = 14h Right Left Right Left
4 teeth or less 2,84 (a) 3,06 (a) 2,86 (a) 3,09 (a)
5, 6 or 7 teeth 2,30 (a) 2,65 (a) 2,21 (a) 2,65 (a)
136
8 teeth or more 1,81 (a) 3,04 (a) 1,89 (a) 3,10 (a)
p-value 0.10 0.52 0.08 0.50
137
Table 16. Tests between number of teeth groups by Mediotrusion or protrusion and Right or
Left for Lateral results only.
Lateral
Mediotrusion Protrusion
Section = 10h Right Left Right Left
4 teeth or less 2.63 (b) 2.55 (a) 2.61 (a) 2.48 (a)
5, 6 or 7 teeth 2.78 (b) 2.36 (a) 2.85 (a) 2.41 (a)
8 teeth or more 3.76 (a) 3.08 (a) 3.65 (a) 2.79 (a)
p-value 0.0447 0.30 0.07 0.79
Mediotrusion Protrusion
Section = 11h Right Left Right Left
4 teeth or less 3.13 (a) 2.88 (a) 3.06 (a) 2.71 (a)
5, 6 or 7 teeth 2.87 (a) 2.53 (a) 2.90 (a) 2.47 (a)
8 teeth or more 3.46 (a) 3.71 (a) 3.58 (a) 3.74 (a)
p-value 0.47 0.07 0.43 0.06
Mediotrusion Protrusion
Section = 12h Right Left Right Left
4 teeth or less 2.93 (a) 3.06 (a) 2.93 (a) 3.06 (a)
5, 6 or 7 teeth 2.59 (a) 2.64 (a) 2.59 (a) 2.59 (a)
8 teeth or more 2.96 (a) 2.95 (a) 2.95 (a) 2.95 (a)
p-value 0.54 0.38 0.54 0.32
Mediotrusion Protrusion
Section = 13h Right Left Right Left
4 teeth or less 2.75 (a) 3.00 (a) 2.96 (a) 3.32 (a)
138
5, 6 or 7 teeth 2.16 (a) 2.44 (a) 2.30 (a) 2.64 (a)
8 teeth or more 1.63 (a) 1.94 (a) 1.78 (a) 2.14 (a)
p-value 0.10 0.13 0.07 0.09
Mediotrusion Protrusion
Section = 14h Right Left Right Left
4 teeth or less 2.66 (a) 2.67 (a) 2.71 (a) 2.93 (a)
5, 6 or 7 teeth 2.06 (ab) 2.24 (a) 1.98 (ab) 2.28 (a)
8 teeth or more 1.09 (b) 1.95 (a) 1.17 (b) 2.05 (a)
p-value 0.0242 0.31 0.0179 0.13
139
Table 17. Tests between number of teeth groups by Mediotrusion or protrusion and Right or
Left for Center results only.
Center
Mediotrusion Protrusion
Section = 10h Right Left Right Left
4 teeth or less 2.83 (a) 2.67 (a) 2.88 (a) 2.73 (b)
5, 6 or 7 teeth 2.69 (a) 2.32 (a) 2.95 (a) 2.45 (b)
8 teeth or more 2.86 (a) 3.33 (a) 3.47 (a) 3.69 (a)
p-value 0.83 0.07 0.43 0.0294
Mediotrusion Protrusion
Section = 11h Right Left Right Left
4 teeth or less 2.50 (a) 2.21 (b) 2.58 (a) 2.35 (b)
5, 6 or 7 teeth 2.46 (a) 2.34 (b) 2.58 (a) 2.48 (b)
8 teeth or more 2.36 (a) 3.45 (a) 2.59 (a) 3.71 (a)
p-value 0.95 0.0120 0.99 0.0141
Mediotrusion Protrusion
Section = 12h Right Left Right Left
4 teeth or less 2.83 (a) 2.87 (a) 2.85 (a) 2.87 (a)
5, 6 or 7 teeth 2.73 (a) 2.69 (a) 2.73 (a) 2.69 (b)
8 teeth or more 2.57 (a) 3.47 (a) 2.57 (a) 3.47 (a)
p-value 0.82 0.35 0.82 0.34
Mediotrusion Protrusion
Section = 13h Right Left Right Left
4 teeth or less 3.21 (a) 3.45 (a) 3.30 (a) 3.63 (a)
140
5, 6 or 7 teeth 2.62 (a) 3.09 (a) 2.74 (a) 3.19 (a)
8 teeth or more 2.06 (a) 2.70 (a) 2.27 (a) 2.96 (a)
p-value 0.11 0.49 0.13 0.46
Mediotrusion Protrusion
Section = 14h Right Left Right Left
4 teeth or less 2.84 (a) 2.91 (a) 2.75 (a) 3.05 (a)
5, 6 or 7 teeth 1.91 (ab) 2.32 (a) 2.04 (ab) 2.42 (a)
8 teeth or more 1.37 (b) 2.30 (a) 1.47 (b) 2.46 (a)
p-value 0.0064 0.20 0.0202 0.20
It is important to note that the fact that the number of observation decreases when more
restricted groups are considered (for example: Right, protrusion, Lateral has less measures than
Right with other factors grouped) result in increasing difficulties to find statistically significant
differences (i.e. smaller power for the test). Consequently, it is normal to find a smaller number
of significant results in tables 15 through 17.
141
REPEATABILITY TEST
The repeatability test was performed by repeating three times on the same skulls in order to
evaluate the variability associated to the measure taking. The statistical analyses associated to
the repeatability test consist in presentation of descriptive statistics allowing the evaluation of
the measure taking variability.
The descriptive statistics presented are:
- Mean (in mm); In the repeatability study, this statistic is mainly used to calculate the coefficient of variation,
- Standard deviation (St. Dev.) (in mm); This statistic give a first estimate associated to the measure variability,
- Coefficient of variation (St. Dev. Divided by the Mean, does not have a unity of measure and is generally presented in %); This statistic is the most important to study the repeatability. Even though no statistical test associated to the coefficient of variation and no universally accepted value to indicate acceptable repeatability are available, in the present study, a coefficient of variation smaller than 5% or 10% will be considered as values to aim for.
- Minimum and maximum values (in mm); In addition to the direct information given by these statistics, they also allow an estimation of the variability by defining the range between the smallest and largest values of the three repetitions.
Tables 18 to 21 present the statistics for each measure. The statistics are obtained for each skull,
with three repetitions of the same measure. These tables show that the vast majority of the
measures present a coefficient of variation smaller than 10% and almost all measures present a
coefficient of variation smaller than 20%. These results show that there is a non negligible
variability associated to the measure taking but this variability did not prevent the detection of
significant differences between the number of teeth groups. The measure variability may
however have reduced the number of significant differences found, with a less variable
measure, a larger number of significant differences would probably have been found between
the number of teeth groups.
142
Table 18. Descriptive statistics for the repeatability study for Mediotrusion on the Right Side.
Right Side - Mediotrusion - Lateral - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 3.14 0.04 1.3% 3.10 3.18
11h 3 3.41 0.27 8.0% 3.24 3.72
12h 3 3.50 0.48 13.7% 3.15 4.05
13h 3 2.97 0.31 10.3% 2.68 3.29
14h 3 3.10 0.02 0.6% 3.08 3.12
Right Side - Mediotrusion - Lateral - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 1.94 0.46 23.7% 1.66 2.47
11h 3 1.21 0.05 4.1% 1.16 1.25
12h 3 2.09 0.19 9.3% 1.87 2.22
13h 3 2.36 0.12 5.0% 2.27 2.49
14h 3 2.57 0.12 4.5% 2.44 2.64
Right Side - Mediotrusion - Center - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 3.07 0.28 9.2% 2.74 3.28
11h 3 3.42 0.21 6.2% 3.23 3.65
12h 3 4.27 0.10 2.2% 4.19 4.37
13h 3 2.91 0.14 4.8% 2.81 3.07
14h 3 2.31 0.18 7.9% 2.10 2.43
Right Side - Mediotrusion - Center - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.71 0.42 15.5% 2.39 3.19
11h 3 1.31 0.19 14.3% 1.20 1.53
12h 3 2.37 0.18 7.7% 2.21 2.57
143
13h 3 2.22 0.06 2.7% 2.15 2.26
14h 3 1.92 0.04 1.9% 1.89 1.96
Right Side - Mediotrusion - Median - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.88 0.15 5.2% 2.77 3.06
11h 3 3.70 0.18 4.9% 3.52 3.88
12h 3 4.35 0.19 4.3% 4.14 4.47
13h 3 2.94 0.16 5.5% 2.83 3.13
14h 3 2.01 0.22 11.0% 1.85 2.26
Right Side - Mediotrusion - Median - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.46 0.47 19.2% 2.06 2.98
11h 3 1.24 0.05 3.8% 1.20 1.29
12h 3 2.09 0.24 11.4% 1.93 2.36
13h 3 2.20 0.13 5.9% 2.11 2.35
14h 3 1.98 0.07 3.4% 1.91 2.05
144
Table 19. Descriptive statistics for the repeatability study for Protrusion on the Right Side.
Right Side - Protrusion - Lateral - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 3.26 0.07 2.1% 3.20 3.34
11h 3 3.61 0.30 8.4% 3.41 3.96
12h 3 3.50 0.48 13.7% 3.15 4.05
13h 3 2.96 0.23 7.8% 2.76 3.21
14h 3 3.32 0.03 0.9% 3.29 3.35
Right Side - Protrusion - Lateral - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.40 0.51 21.3% 2.05 2.98
11h 3 1.30 0.08 6.2% 1.21 1.35
12h 3 2.09 0.20 9.4% 1.87 2.22
13h 3 1.95 0.14 7.1% 1.83 2.10
14h 3 2.35 0.10 4.0% 2.25 2.44
Right Side - Protrusion - Center - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.96 0.14 4.6% 2.81 3.06
11h 3 3.54 0.24 6.7% 3.35 3.80
12h 3 4.26 0.09 2.2% 4.19 4.37
13h 3 2.88 0.17 5.9% 2.72 3.06
14h 3 2.71 0.22 8.1% 2.49 2.93
Right Side - Protrusion - Center - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.92 0.51 17.6% 2.51 3.49
11h 3 1.31 0.14 10.8% 1.21 1.48
12h 3 2.37 0.18 7.7% 2.21 2.57
145
13h 3 2.20 0.04 1.6% 2.18 2.25
14h 3 2.19 0.07 3.0% 2.11 2.24
Right Side - Protrusion - Median - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.98 0.20 6.7% 2.83 3.21
11h 3 3.74 0.16 4.3% 3.59 3.91
12h 3 4.36 0.19 4.4% 4.14 4.47
13h 3 3.07 0.25 8.0% 2.91 3.35
14h 3 1.92 0.13 6.7% 1.79 2.04
Right Side - Protrusion - Median - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.03 0.31 15.5% 1.74 2.36
11h 3 1.19 0.03 2.3% 1.17 1.22
12h 3 2.08 0.24 11.4% 1.93 2.36
13h 3 2.50 0.16 6.2% 2.38 2.68
14h 3 1.90 0.04 1.9% 1.87 1.94
146
Table 20. Descriptive statistics for the repeatability study for Mediotrusion on the Left Side.
Left Side - Mediotrusion - Lateral - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.80 0.24 8.4% 2.53 2.96
11h 3 3.35 0.52 15.6% 2.83 3.88
12h 3 3.33 0.41 12.3% 2.89 3.70
13h 3 3.36 0.38 11.2% 3.00 3.75
14h 3 3.06 0.06 1.9% 3.00 3.12
Left Side - Mediotrusion - Lateral - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.85 0.14 4.7% 2.73 3.00
11h 3 2.85 0.30 10.4% 2.57 3.16
12h 3 3.56 0.22 6.2% 3.38 3.80
13h 3 2.83 0.10 3.5% 2.73 2.93
14h 3 2.65 0.20 7.4% 2.48 2.86
Left Side - Mediotrusion - Center - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.79 0.20 7.2% 2.60 3.00
11h 3 3.23 0.44 13.7% 2.75 3.62
12h 3 4.65 0.35 7.6% 4.45 5.06
13h 3 4.02 0.71 17.7% 3.47 4.83
14h 3 3.15 0.16 4.9% 3.02 3.32
Left Side - Mediotrusion - Center - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 4.13 0.11 2.7% 4.00 4.22
11h 3 4.37 0.38 8.7% 3.97 4.72
12h 3 4.59 0.15 3.3% 4.43 4.73
147
13h 3 3.48 0.07 2.0% 3.42 3.55
14h 3 2.57 0.12 4.6% 2.45 2.69
Left Side - Mediotrusion - Median - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.30 0.09 4.1% 2.19 2.35
11h 3 2.82 0.21 7.6% 2.63 3.05
12h 3 5.02 0.86 17.0% 4.04 5.55
13h 3 4.49 0.62 13.8% 4.02 5.19
14h 3 3.39 0.16 4.6% 3.21 3.49
Left Side - Mediotrusion - Median - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.89 0.23 8.0% 2.69 3.14
11h 3 3.35 0.11 3.3% 3.24 3.46
12h 3 5.31 0.03 0.5% 5.30 5.34
13h 3 4.21 0.07 1.7% 4.17 4.30
14h 3 2.49 0.06 2.4% 2.44 2.55
148
Table 21. Descriptive statistics for the repeatability study for Protrusion on the Left Side.
Left Side - Protrusion - Lateral - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.87 0.22 7.7% 2.65 3.09
11h 3 3.01 0.58 19.1% 2.38 3.52
12h 3 3.33 0.41 12.3% 2.89 3.70
13h 3 3.65 0.43 11.8% 3.24 4.10
14h 3 3.26 0.08 2.5% 3.19 3.35
Left Side - Protrusion - Lateral - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.32 0.07 3.2% 2.24 2.39
11h 3 2.42 0.23 9.4% 2.23 2.67
12h 3 3.55 0.22 6.1% 3.38 3.80
13h 3 3.43 0.10 3.0% 3.33 3.54
14h 3 2.83 0.11 3.9% 2.75 2.96
Left Side - Protrusion - Center - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 3.12 0.10 3.3% 3.03 3.23
11h 3 3.41 0.47 13.8% 2.86 3.70
12h 3 4.65 0.35 7.6% 4.45 5.06
13h 3 4.10 0.70 17.1% 3.60 4.90
14h 3 3.21 0.14 4.3% 3.12 3.37
Left Side - Protrusion - Center - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 3.89 0.31 7.9% 3.65 4.24
11h 3 4.15 0.12 3.0% 4.03 4.27
12h 3 4.59 0.15 3.3% 4.42 4.73
149
13h 3 4.14 0.04 0.9% 4.11 4.19
14h 3 2.42 0.00 0.2% 2.41 2.42
Left Side - Protrusion - Median - Skull #468
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 2.28 0.11 4.7% 2.16 2.35
11h 3 2.88 0.28 9.6% 2.58 3.11
12h 3 5.02 0.86 17.0% 4.04 5.55
13h 3 4.65 0.58 12.5% 4.25 5.32
14h 3 3.49 0.23 6.5% 3.24 3.68
Left Side - Protrusion - Median - Skull #554
Section N Mean St. Dev. Coeff. of var. Minimum Maximum
10h 3 3.18 0.36 11.3% 2.88 3.58
11h 3 3.63 0.07 1.8% 3.59 3.71
12h 3 5.31 0.03 0.5% 5.30 5.34
13h 3 4.41 0.12 2.8% 4.29 4.54
14h 3 2.64 0.02 0.8% 2.62 2.66
150
Appendix 3
Pictures of skulls with the putties in the fossae mandibularis
Pictures of the bite & putties on trans-illuminating box
Please see the 2 files on the CD-Rom enclosed