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F r equ en cy o f B o l ton too th size d isc r epan c ies amon g
or thodon t ic pa t i en ts
J o h n E . F r e e m a n D D S a A . J . M a s k e r o n i D D S b a n d L e w i s L o r to n D D S M S D c
Fort George G. Meade Md.
The purpose of this study was to determine th e percentage of orthodontic patients who present
with an interarch tooth-size discrepancy l ikely to affect treatment planning or results. The Bolton
tooth-size discrepancies of 157 patients accepted for treatment in an orthodontic residency program
were eva luated for the frequency and the ma gnitude o f deviation from Bolton s mean.
Discrepancies outside of 2 SD were considered as potential ly significant with regard to treatment
planning and treatment results. Although the m ean of the sam ple was nearly identical to that of
Bolton s, the range and standard deviation varied considerably with a large percentage of the
orthodontic patients having discrepancies outside of Bolton s 2 SD. W ith such a high frequency of
significant discrepancies it would seem prudent to routinely perform a tooth-size analysis and
incorporate the findings into orthodontic treatment planning. (Am J Orthod D entofac Orthop
1996;110:24-7.)
On e of the goals in comprehensive ortho-
dontic treatment is to obtain an optimal final oc-
clusion, overbite, and overjet. There are many fac-
tors that will influence the attainability of this goal,
one o f which is the relationship of the total mesio-
distal width of the maxillary teeth to that of the
mandibular teeth. A significant variation in this
relationship should be compensated for in the
treatment planning by considering esthetic bond-
ing, prosthetic recontouring, stripping of enamel,
extraction, leaving spaces, or changing the desired
anterior overjet or overbite. The alternative to not
doing any of these may result in compromising the
occlusion in the buccal segments, an undesirable
result.
There has long been an understanding that a
certain maxilla ry-to-mandibular tooth size relation-
ship was important for proper occlusal relation-
ships. Over the years many investigators have at-
tempted to quantify this relationship. In 1923 Gil-
patric calculated that the total mesiodistal tooth
diameters in the maxillary arch exceeded that in
the mandibular arch by 8 to 12 ram. a Ballard, in
1944, evaluated 500 sets of models of orthodontic
patients and found that 90% possessed mesiodistal
From the U.S. Army Orthodontic Residency Program Fort Meade Md.
The views expressed in this article are those of the authors and do not
reflect the official policy of the Department of Defense or other Depart-
ments of the United States Government.
aLieutenant Commander Dental Corps Unit ed States Navy; Senior
Resident.
bCommander Denta l Corps United States Navy; Clinical Instructor.
CConsultant Statistics and Research Design.
Repri nt requests to: Dr. John E. Freeman Denta l Department U.S.
Naval Hospital Grea t Lakes IL 60088.
8/1/58926
4
crown discrepancies of at least 0.25 mm between
one or more pairs of teeth from opposite sides of
the arch, whereas 80% revealed discrepancies of at
least 0.5 mm. 2 In 1949, Neff developed the ante-
rior coefficient, '3 a method to compare the widths
of the anterior teeth in opposing arches. Neff
concluded, tha t everything else being normal an
orthodontic or nonorthodontic normal will settle to
the degree of overbite indicated by the anterior
coefficient. '3 Ballard reported in 1956 that, in a
study of 400 orthodontic cases, over 50% revealed
an excess of at least 2 mm of mesiodistal tooth
width in the mandibular anterior segment when
compared to the maxillary anterior teeth.4
Bolton's introduction of his analysis in 1958
included comparisons of total mesiodistal widths of
dental arches up to the distal surfaces of the first
molars, as well as segments of the arches. 5 Bolton
evaluated 55 cases with excel lent occlusions; 44
had been treated orthodontically without extrac-
tions and 11 were untreated. The following ratios
were established by Bolton:
Sum mandibular 12
Overall ratio = × 100
Sum maxillary 12
Sum mandibular 6
Anterio r ratio = x 100
Sum maxillary 6
The overal l rat io was calculated from the greatest
mesiodistal measurements of the tee th in each arch
from first molar to first molar. The anter ior rat io
was calculated from the greatest mesiodistal mea-
surements of the six anterior teeth in each arch.
The results of Bolton's study are summarized in
Tables I and II. From Bolton's results it can be
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American Journal of Orthodontics and Dentofacial Orthopedics Freeman, Maskeroni, and Lort on 5
Volume 110,No. 1
Table I S t a ti s ti c a l c o m p a r i s o n B o l t o n s t u d y v e r s u s F o r t M e a d e s t u d y . O v e r a l l 1 2 r a t io
Bolton Fort Meade
Samp le size 55 157
Mea n 91.3 91.4
Median No t available 91.3
Range 87.5-94.8 82.8-99.4
Standa rd deviation 1.91 2.57
Standard error of mean 0.26 0.21
Coefficient of variation 2.09% 2.81%
a b l e I I, S t a ti s ti c a l c o m p a r i s o n B o l t o n s tu d y v e r s u s F o r t M e a d e s tu d y . A n t e r i o r 6 r a t io
Bolton
Fort Meade
Sample size 55 157
Mean 77.2 77.8
Median Not available 77.9
Ra nge 74.5-80.4 68.4-87.9
Stand ard deviation 1.65 3.07
Standard error of mean 0.22 0.25
Coefficient of variation 2.14% 3.95%
s e e n t h a t t h e r e i s a re l a t iv e l y s m a l l r a n g e i n w h i c h
t o o t h s i ze r a ti o s s h o u l d f a ll t o b e a b l e t o a c h i e v e
o p t i m a l o c c l u s a l r e l a t io n s h i p s , s t i r r e r e v a l u a t e d
B o l t o n ' s s t u d y a n d a r r i v e d a t s i m i la r r e s u lt s . 6
C r o s b y a n d A l e x a n d e r f o u n d a l a r g e n u m b e r o f
o r t h o d o n t i c p a t i e n t s p r e s e n t e d w i t h a s i g n i f i c a n t
B o l t o n t o o t h - s i z e d i s c r e p a n c y . 7
T h e p u r p o s e o f th i s s tu d y w a s t o e v a lu a t e t h e
p e r c e n t a g e o f p a t i e n ts w h o p r e s e n t e d w i t h a s ig n if -
i c a n t t o o th - s i z e d i s c r e p a n c y a t t h e U . S . A r m y
O r t h o d o n t i c R e s i d e n c y P r o g r a m a t F o r t G e o r g e G .
M e a d e , M d . A s i g n if i c a n t d i s c r e p a n c y w a s d e f i n e d
a s o n e w h o s e v a l u e w a s o u t s i d e o f 2 S D f r o m
B o l t o n ' s m e a n , 7' 8 a s a p p r o x i m a t e l y 9 5 % o f B o l t o n ' s
c a s e s w e r e w i t h in t h is r a n g e . F o r th e o v e r a l l 1 2
r a ti o , a s i g n if i c a n t d i s c r e p a n c y i s t h e r e f o r e d e f i n e d
a s a r a t i o b e l o w 8 7 . 5 o r a b o v e 9 5 . 1 , w i t h r a t i o s
i n - b e t w e e n f a ll in g w i th i n 2 S D o f B o l t o n ' s m e a n .
L i k e w i s e , a n y r a t i o b e l o w 7 3 . 9 o r a b o v e 8 0 . 5 is
c o n s i d e r e d t o b e a s ig n i f ic a n t d i s c r e p a n c y f o r t h e
a n t e r i o r 6 r a t i o .
M A T E R I A L S A N D M E T H O D S
T h e d a t a f o r t h is s t u d y w e r e o b t a i n e d f r o m r e c o r d s
t a k e n a t t h e F t . M e a d e R e s i d e n c y P r o g r a m , w h e r e a
B o l t on t oo t h - s i z e a na l ys i s i s pe r f o r m e d r ou t i ne l y on a l l
p a t i e n t s a c c e p t e d i n t o th e p r o g r a m . O n l y re c o r d s o f
t h o s e p a t i e n t s w i t h p e r m a n e n t d e n t i t i o n s w e r e c o n s i d -
e r e d f o r e v a l u a ti o n t o e l i m i n a t e e r r o r s t h a t m a y b e
i n c o r p o r a t e d f r o m t h e p r e d i c t i o n o f si z es o f u n e r u p t e d
t e e t h . Thos e w i t h a ny s i gn i f i c a n t a t t r i t i on o r t hos e m i s s -
i n g a n y p e r m a n e n t t e e t h o t h e r t h a n s e c o n d o r t h ir d
m o l a r s w e r e n o t c o n s i d e r e d . A t o t a l o f 4 5 9 r e c o r d s w e r e
e v a l u a t e d a t r a n d o m , a n d 1 5 7 m e t t h e e s t a b li s h e d c r i t e ri a
a n d w e r e u s e d f o r t h i s s t u d y .
T h e 1 5 7 r e c o r d s a l l c o n t a i n e d a B o l t o n t o o t h - s i z e
a n a ly s is p r e v i o u sl y c o m p l e t e d b y a F o r t M e a d e r e s id e n t .
T h e a n a l y se s h a d b e e n c o m p l e t e d b y 2 4 d i ff e r e n t r e si -
d e n t s . T h e s a m p l e c o n s i s t e d o f 8 9 f e m a l e a n d 6 8 m a l e
pa t i e n t s . The r e w e r e 115 w h i t e pa t i e n t s , 27 b l a c k pa -
t i e n ts , a n d 15 pa t i e n t s o f o t he r e t hn i c o r i g i n s .
T h e B o l t o n t o o t h - s i z e a n a l y s i s p e r f o r m e d a t F o r t
M e a d e c o n s is t s o f t w o p a r t s a s d e s c r i b e d i n B o l t o n ' s
pub l i c a t i on . 5 Th e f i rs t pa r t i s t he i nd i v i dua l m e s i od i s t a l
m e a s u r e m e n t s o f a l l t e e t h f r om t he f i r s t m o l a r s m e s i a l l y .
T o o t h - s i z e m e a s u r e m e n t s w e r e t y p i c a ll y t a k e n w i th
s h a r p - p o i n t e d B o l e y g au g e s , m e a s u r i n g t h e w i d e s t m e -
s i o d is t al d i m e n s i o n o f e a c h t o o t h a s d e s c r i b e d b y B o l t o n .
T h e s e c o n d p a r t i s th e c a l c u l at i o n o f a r c h l e n g t h c o m -
p a r i s o n s a n d d e t e r m i n a t i o n o f to o t h - s i z e d i sc r e p a n c y
a c c o r d i n g t o t h e m e t h o d o u t l i n e d b y B o R o n ? T h i s d i s -
c r e p a n c y i n c l u d e s a c o m p a r i s o n o f t h e o v e r a l l a rc h e s ( u p
t h r o u g h f ir st m o l a r s ) a n d a l so a c o m p a r i s o n o f t h e
a n t e r i o r s e g m e n t s .
T h e d a t a c o l l e c t e d f r o m t h e r e c o r d s w e r e e v a l u a t e d
t o d e t e r m i n e t h e p e r c e n t a g e o f p a t i e n t s w h o h a d t o o t h -
s i z e d i s c r e pa nc i e s w h i c h w e r e w i t h i n one , w i t h i n t w o , o r
g r e a t e r t h a n t w o s t a n d a r d d e v i a t io n s f r o m B o l t o n ' s
m e a n . A m e a n , m e d i a n , r a n g e , s t a n d a r d d e v i a t i o n , s t a n -
d a r d e r r o r o f t h e m e a n , a n d c o e f f ic i e n t o f v a r i a t io n w e r e
c a l c u l a t e d f o r b o t h t h e o v e r a ll 1 2 r a t io a n d a n t e r i o r
6 r a t i o . The no r m a l i t y o f t he va r i a b l e s w a s i nve s t i ga t e d
by c a l c u l a t i ng t he s ke w ne s s a nd ku r t o s i s o f t he va r i a b l e s .
I n a d d i t i o n , a P e a r s o n ' s c o r r e l a t i o n b e t w e e n t h e v a r i -
a b l e s w a s p e r f o r m e d .
R E S U L T S
T h e m e a n o v e r a ll 1 2 r a ti o f o r t h e o r t h o d o n t i c
p a t i e n t s w a s f o u n d t o b e 9 1 . 4 ( T a b l e I ) , w i t h a
s t a n d a r d d e v i a t i o n o f 2 .5 7 . T h e v a l u e s r a n g e d f r o m
8/17/2019 Freeman 1996
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2 6 Fr ee m an M as ke ro ni an d L or to n American Journal of Orthodontics and Dentofacial Orthopedics
July 996
FORT ME DE ORTHODONTICC SES
No, of
C a s e s
50
4
20 I ~ ~ l
19
< 87 .5 87 .5-89 .3 89 .4-91 .2 91 .3 91 .4-9 3 .2 93 .3-95 .1 > 95.1
OVERALL "12" RATIO
91.3 = Bo l ton s mean .
89.4-91.2 a nd 91.4-93.2 are wi th in 1 stan dar d deviation.
87.5 .89.3 and 93.3-95.1 a re outs ide 1 s tanda rd dev iat ion , bu t w i th in 2
standard deviat ions.
< 87.5 an d > 95.1 are outs ide 2 s tand ard dev iat ions .
F i g .
1 . F o rt M e a d e o r t h o d o n t i c c a s e s . O v e r a ll " 1 2 " r a ti o : 9 1 . 3 = B o l t o n ' s m e a n . 8 9 . 4 t o 9 1 . 2 a n d
9 1 . 4 t o 9 3 , 2 a r e w i t h i n 1 S D . 8 7 . 5 t o 8 9 . 3 a n d 9 3 . 3 to 9 5 . 1 a r e o u t s i d e 1 S D , b u t w i th 2 S D . < 8 7 . 5
a n d > 9 5 . 1 a r e o u t s i d e 2 S D .
No. of
C a s e s
FORT ME DE ORTHODONTICC SES
< 73.9
73.9-75.4 75.5-77.1
7 ; ~ . 2 7 7 . 3 7 8 . 8 7 8 . 9 8 0 .5
ANTERIOR "6" R ATIO
80.5
7 z 2 = B o l t o n s m e a n .
75.5-7Z 1 an d 7Z3-78.8 are w i th in I s tan dard dev ia t ion .
73.9.75.4 an d 78.9-80.5 are outs ide I s tanda rd dev iat ion , bu t w i th in 2
standard deviat ions.
< 73.9 and > 80.5 r e o u t s i d e 2 standard deviat ions.
F i g . 2 . F o r t M e a d e o r t h o d o n t i c c a s e s . A n t e r io r " 6 " r a ti o : 7 7 . 2 = B o l t o n ' s m e a n . 7 5 . 5 to 7 7 .1 a n d
7 7 . 3 t o 7 8 . 8 a r e w i t h i n 1 S D . 7 3 . 9 t o 7 5 . 4 a n d 7 8 . 9 t o 8 0 . 5 a r e o u t s i d e 1 S D , b u t w i th i n 2 S D . < 7 3 . 9
a n d > 8 0 . 5 a r e o u t s i d e 2 S D . a n d > 9 5 . 1 a r e o u t s i d e 2 S D .
a l o w o f 82 . 8 t o a h i g h o f 9 9 .4 , a n d t h e m e d i a n w a s
9 1 .3 . T h e s t a n d a r d e r r o r o f t h e m e a n w a s 0 . 21 a n d
t h e c o e f f i c i e n t o f v a r i a t i o n w a s 2 . 8 1 % . O f t h e 1 5 7
c a s es , 2 1 ( 1 3 . 4 % ) h a d o v e r a l l 1 2 r a t i o s o u t s i d e o f
2 S D f r o m B o l t o n ' s m e a n ( F i g . 1 ) .
T h e m e a n a n t er i o r 6 r a ti o f o r t h e o r t h o d o n t i c
p a t i e n t s w a s f o u n d t o b e 7 7 . 8 ( T a b l e I I ) , w i t h a
s t a n d a r d d e v i a t io n o f 3 .0 7 . T h e v a l u e s r a n g e d f r o m
6 8 .4 t o 87 . 9, a n d t h e m e d i a n w a s 7 7 .9 . T h e s t a n d a r d
e r r o r o f t h e m e a n w a s 0 . 25 a n d t h e c o e f f ic i e n t o f
v a r i a t i o n w a s 3 .9 5 % . F o r t y - e i g h t ( 3 0 . 6 % ) c a s e s h a d
a n t e r i o r 6 r a t i o s t h a t fe l l o u t s i d e o f 2 S D f r o m
B o l t o n ' s m e a n v a l u e ( s e e F i g . 2 ) .
T h e c o r r e l a t i o n s w e r e h i g h a n d s t a ti s ti c a ll y s ig -
n i f i c a n t b u t t h e r e i s t h e i n d i c a t i o n t h a t t h e o v e r a l l
1 2 r a t io a n d a n t e r i o r 6 r a t io w o u l d n o t p r e d i c t
t h e o t h e r c o n s i s t e n t l y . B o t h g r a p h i n g t h e d a t a a n d
m e a s u r i n g t h e s k e w n e s s a n d k u r t o s i s i n d i c a t e d t h a t
t h e d a t a s e t s w e r e n o t n o r m a l l y d i s t ri b u t e d a n d
t h u s t h e u s e o f 2 S D u n i t s t o in d i c a t e th e n o r m a l
r a n g e is n o t a p p r o p r i a t e .
D I S U S S I O N
A l t h o u g h t h e m e a n s o f t h e o r t h o d o n t i c p a t i e n t s
i n th i s s tu d y a n d t h o s e o f t h e B o l t o n s t u d y a r e
n e a r l y id e n t i c a l , t h e r a n g e s a n d s t a n d a r d d e v i a t i o n s
o f t h e o r t h o d o n t i c p a t i e n t s a r e s i g n if i ca n t ly la r g e r .
S i m i l a r f i n d in g s w e r e f o u n d b y C r o s b y a n d A l e x -
a n d e r i n e v a l u a t i n g o r t h o d o n t i c p a t i e n t s i n a c iv il -
i a n p r a c t i c e ? I f t h o s e c a s e s w i t h r a t i o s g r e a t e r t h a n
8/17/2019 Freeman 1996
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American Journal of Orthodontics and Dentofacial Orthopedics Freeman M askeroni and Lorton 7
Volume 110, No 1
2 S D a w a y f r o m B o l t o n ' s m e a n s t r ul y r e p r e s e n t a
s i g n i f i c a n t d i s c r e p a n c y , t h e n a l a r g e p e r c e n t a g e o f
o r t h o d o n t i c p a t i e n t s p r e s e n t w i t h r e l a t i v e t o o t h
s i z e s t h a t c o u l d p o t e n t i a l l y c a u s e p r o b l e m s i n a t -
t a i n i n g a n o p t i m a l o c c l u s a l r e l a t i o n s h i p . W h i l e
1 3 . 5% o f t h e o r t h o d o n t i c c a s e s p r e s e n t e d w i t h a
s i g n i f ic a n t d i s c r e p a n c y o f t h e o v e r a l l 1 2 r a t i o ,
3 0 . 6 % p r e s e n t e d w i t h a s i g n if i ca n t a n t e r i o r 6
d i s c r e p a n c y . T h e o v e r a l l d i s c r e p a n c y w a s e q u a l l y
l i ke l y t o b e a n e x c e s s in t h e m a x i l l a o r t h e m a n -
d i b le , w h e r e a s t h e a n t e r i o r d i s c r e p a n c y w a s n e a r l y
t w i c e a s li k e ly t o b e a m a n d i b u l a r e x c e s s ( 1 9 .7 % )
t h a n a m a x i l l a r y e x c e s s ( 1 0 . 8 % ) .
A p o s s ib l e s o u r c e o f e r r o r m a y b e i n t r o d u c e d b y
u s i ng t h e m e a s u r e m e n t s f o u n d b y 24 d i f f er e n t e x-
a m i n e r s . O f t h e 1 5 7 r e c o r d s u s e d i n t h is s t u d y t h e
m o s t f r o m a n y si n g l e e x a m i n e r w a s 1 5 , t h u s t h e
i m p a c t f r o m e r r o n e o u s d a t a f r o m a n y o n e p e r s o n
w o u l d b e m i n i m a l . I t w a s n o t f e a s i b l e to t e s t
i n d i v i d u a l e r r o r a s t h e e x a m i n e r s a r e n o w a t v a r i -
o u s l o c a t io n s a r o u n d t h e w o r l d . A n a l t e r n a t iv e
o p t i o n i n t h is s t u d y w o u l d h a v e b e e n f o r o n e p e r s o n
t o d o a l l o f t h e m e a s u r e m e n t s , t h e n i f t h e r e w a s a n y
c o n s i st e n t e r r o r, i t w o u l d h a v e b e e n d e m o n s t r a t e d
t h r o u g h o u t t h e d a t a .
O N L U S I O N S
Thes e f ind ings sugges t tha t a l a rge num ber o f pa -
t i e n t s p r e s e n t i n g f o r o r t h o d o n t i c t r e a t m e n t p o s s e s s a
Bol ton too th-s ize d i s c repancy tha t m ay in f luence t rea t -
m ent goa l s and re su l t s . Th i s s tudy found 30 . 6% of
or thod ont ic p a t i en t s to have a s ign i fi can t an te r io r too th-
s i z e d i s c r e p a n c y c o m p a r e d w i t h t h e 2 2 . 9 % f o u n d b y
C r o s b y a n d A l e x a n d e r . 7 P e r h a p s t h e d i f f e re n c e m a y b e
expla ined by the pa t i en t s e lec t ion p roces s in a m i l i t a ry
res idency program ve rsus a p r iva te p rac t i ce . Because o f
l im i ted re sources , pa t i en t s in m i l i t a ry o r thodont ic p ro-
gram s a re typ ica lly those wi th the m ore s eve re m a locc lu-
s ions , even though those re fused t rea tm ent cou ld ve ry
of ten de r ive bene f i t s i f they were to b e t rea ted . I t i s a l so
p o s s ib l e t h a t t h e p o p u l a t i o n o f p a t i e n t s m a y b e m o r e
d ive rse in th e m i l it a ry p rac t i ce wi th rega rd to race and
e thn ic background . Thus , i t would s eem log ica l tha t the
pe rce n tage o f pa t i en t s wi th s ign if icant d i s c repanc ies m ay
b e s o m e w h a t d e p e n d e n t o n t h e s e l e c ti o n p r o c e ss o r t h e
cha rac te r i s t i c s o f the popu la t ion f ro m which the pa t i en t s
a re d rawn.
As a re su l t o f our f indings , i t would s eem p rud en t fo r
cl inic ians to rout inely include a tooth-s ize analys is in
the i r in i t i a l case workup . Iden t i fy ing such a d i s c repancy
before f ina l too th a l ignm ent would p rove bene f ic ia l in
b o t h t r e a t m e n t p l a n n i n g a n d f i n a l e x p e c t a t i o n s o f b o t h
the c l in ic ian and the pa t i en t . Al though such an ana lys i s
m a y a p p e a r t o b e t i m e - c o n s u m i n g , t h e b e n e f i t s w o u l d
seem to ou twe igh th i s m inor inconvenience by a l lowing
m o re e f f i c ien t d iagnos is o f p ro b lem s , m ore spec if ic ity in
t rea tm ent p lann ing , and a h ighe r succes s ra te in ach iev-
ing opt im al occlusions, overb i te , and o verje t .
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