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Estimation of Stature from Foot and Shoe Length:

Applications in Forensic Science

Brenda M. A. Rohren , M.A.1

Nebraska Wesleyan University

Department of Forensic Science, 5000 Saint Paul Avenue, Lincoln, Nebraska 68504-27941

RUNNING HEAD: Estimation of Stature from Foot and Shoe Length

Estimation of Stature from Foot and Shoe Length 2

ABSTRACT: Because time is a critical factor in crime scene investigation, rapid identification

of suspects is important. Stature is one describing characteristic that is used. In the mid-1800s,

Topinard developed a mathematical formula for estimating a person’s height from a foot print

(foot length:stature ratio) and determined this ratio to be 15%. Because Topinard’s formula was

developed over 150 years ago, is this a still valid and reliable formula to estimate stature in the

early 21 century? What is a comparable ratio for computing stature estimations based on shoest

length? Which stature estimation is of better predictive value in forensic sciences? An

experiment was conducted with 40 subjects. The foot length:stature ratio was determined to be

14.73% and the shoe length:stature ratio was 16.63%. The resulting correlation coefficients

indicated that although both foot and shoe lengths have positive correlations in stature

estimation, foot length is a better predictor of stature.

KEYWORDS: forensic sciences, stature, height estimation, foot length, footprints, shoe length,

shoeprints, humans, suspect identification


Estimation of Stature from Foot and Shoe Length:

Applications in Forensic Science

Time is a critical factor when a crime has been committed and the investigation begins.

The crime scene investigator needs to make rapid and accurate assessments in the field such as

identifying possible suspects, especially when the crime is a violent one such as homicide.

When processing a crime scene, many variables are usually not known about the suspect.

There may be few (if any) witnesses and the perpetrator seldom leaves behind specific

identifying information (e.g., driver’s license). Information about the perpetrator’s identity is

therefore deduced from the evidence left at the scene. A person’s height (i.e., stature) is one

identifying characteristic that is often used (1).

Many different parts of the body can be used to estimate stature. In forensic anthropology,

a common method of estimating stature of victims is to measure the long bone length and

extrapolating the data (1). Measurements of other body parts such as lower leg length, arm span,

and hand span can also be used (2-5) However, the aforementioned measurements are generally

not available about the perpetrator based on evidence left at the scene. Therefore, evidence that

is more readily available is needed to estimate stature.

Evidence that a suspect leaves at a crime scene is likely to include foot or shoe prints.

Because foot length has a biological correlation with stature, the latter can be estimated from foot

or shoe prints (2, 4-17). This evidence may provide the best (or only) opportunity to predict that

aspect of a suspect’s physical description (12). It can also be used to corroborate height estimates

obtained from witnesses (13).

When a foot or shoe print is found at the crime scene, it is photographed and a cast of the

print is made (18, 19). The photographs and cast are then used to provide information about the

person’s identity. Class and individual characteristics of a shoe print can be analyzed to provide


clues related to the suspect’s identity. However, this information is generally not readily

available at the scene. Therefore, it is more helpful for crime scene investigator to rely on

mathematical formulas to quickly estimate the suspect’s height based on the available foot and

shoe print measurements.

Hypothesis 1

In the mid-1800s, Topinard developed a simple mathematical formula for estimating a

person’s height from a foot print (16). This is referred to as the stature-foot length index (or foot

length:stature ratio) and is calculated as follows: Foot Length / Stature = 15% (11, 14, 16).

Research has shown that there are many factors which influence changes in the size and

morphology of the foot such as: sex, weight, pregnancy, nutrition, age, genetics, disease,

regional and ethnic variations due to heredity, and various environmental conditions such as

climate (9-10, 14, 20-23). (See also the Comments section on Table 1.) Because Topinard’s

formula was developed over 150 years ago, is this a still valid and reliable formula to estimate

stature? If not, what would be a more accurate formula? The research (or alternate) hypothesis

1 0(H ) and the null hypothesis (H ) are:

1H Foot Length / Stature � 15%

0H Foot Length / Stature ' 15%

Hypothesis 2

A review of the literature reveals multiple references to the ratio of foot length to stature.

However, only one reference could be found regarding a similar ratio formula for the calculation

of shoe length and stature (8). Therefore, an additional question is posed: What is the shoe

2 0length:stature ratio? The research (alternate) hypothesis (H ) and the null hypothesis (H ) are:

2H Shoe Length / Stature � 17%

0H Shoe Length / Stature ' 17%


Comparison of Foot and Shoe Length as Best Estimation of Stature

As indicated previously, a significant amount of research has been conducted on the

relationship between foot length and stature. Some of this research has also focused on the

correlation between shoe length and stature. Although the correlation coefficients have been

provided for each, a literature review indicated comparatively few specific comparisons of the

two as to which is a better predictor of stature (3, 14,15, 17). Therefore, this element was added

to the current study and the results will be reviewed in the Discussion section.

Method

For this experiment, 40 individuals were randomly selected and asked to participate in the

study. As indicated in Table 1, slightly more than half of the subjects were women and the

remainder were men (21 women and 19 men). Because foot length does not typically stabilize

until adulthood (9), only individuals who were 18 years of age or older were invited to

participate. The Ethics section of this report reviews how subjects were identified and selected.

Although it was desired that a diverse group of subjects be involved in the study, 90% of

the individuals were Caucasian and only 10% were of other racial groups (primarily Hispanic).

More diversity was displayed regarding ages of the subjects: the age range was between 18 and

67 (the mean was 36 and the median was 32).

Each subject was first asked to provide age, race/ethnicity, shoe size and to state at what

age his/her foot stabilized to this shoe size. Then the measurement of height (in inches) was

obtained using a standard tape measure. All of this information was recorded on the Data

Collection Form (Appendix A).

In order to obtain the foot and shoe length measurements, the Data Collection Form was

then placed on the floor. The subject was first asked to place a foot (typically the right foot) on


the paper and an outline of the shoe was traced. Then the person was asked to remove his or her

shoe and sock. The bare foot was then traced on the opposite side of the paper. (Refer to the

Ethics section for accommodations made for some subjects.)

Measurements were then taken from the outlines of the foot and shoe as traced onto the

Data Collection Form. Foot length was determined to be the distance between the extreme point

of the longest toe (Acropodion) and the extreme point of the heel (Pternion) when the foot was

fully stretched (9, 14). Shoe length was determined to be the distance between the heel of the

shoe and the extreme point of the shoe (i.e., the most anterior and posterior points of the shoe).

All measurements for height, foot length, and shoe length were obtained in inches. Prior to

statistical computation, the measurements were converted to centimeters (1 inch = 2.54

centimeters).

Ethics

The majority of the subjects (about 75%) were co-workers of the investigator. They were

approached individually and the purpose and nature of the experiment were explained. The

agency director was informed about the study and he approved the involvement of the

investigator’s co-workers.

The remainder of the subjects were students at a local community college who were

enrolled in classes taught by the investigator. Prior to recruiting student volunteers, the

chairperson of the department was contacted. The purpose and nature of the experiment were

explained to him and approval was given for students to participate in the study.

Regarding informed consent, individuals were asked to participate in a study that involved

obtaining measurements of foot length, shoe length, and height. None of the individuals who

were asked to participate in the study were coerced in any way or provided a reward for their

involvement. It should be noted that several students asked if they could receive extra credit for


participating and were told that they would not. Their participation was voluntary and data was

collected before or after class sessions.

Due to the nature of the project (an informal course assignment), it seemed important to

respect the boundaries of the volunteer participants. Therefore, as the foot length data was being

collected (i.e., foot prints were traced on the paper), some individuals were allowed to trace their

own bare foot while the investigator observed. In several cases, the subject was allowed to keep

the sock on the foot as the measurement was taken due to the individual’s concern about the

appearance of his/her foot (e.g., warts). If this had been a more formal experiment, the

investigator (or other approved staff) would have taken all of the measurements and ensured

more consistent collection of data. In addition, socks would have been removed from the

measured foot of all subjects.

Statistics

Once the measurements of stature, foot length, shoe length and other information were

obtained, this data was entered into an Excel worksheet (Table 1). A statistical analysis was

performed on all measurements (except stated shoe size) in order to determine the following:

minimum, maximum, mean, median, mode, and standard deviation (to include +/- 2).

After Table 1 was constructed, scatter diagrams were then drawn on separate Excel

worksheets showing the relationship between foot length/stature (Table 2) and shoe

length/stature (Table 3). A best fit line was calculated for each diagram. (The slopes of these

lines are representative of the average foot or shoe length for each subject expressed as a

percentage of their height.) Correlations between stature and foot or shoe measurements were

established statistically using the Pearson correlation coefficient (r).

As most research on stature estimations based on foot or shoe length provides separate

statistics for females and males, these separate calculations are also provided in Tables 2 and 3


for the following: minimum, maximum, mean, median, mode, and standard deviation (to include

+/- 2). The respective research (alternate) hypotheses and null hypotheses were indicated on each

table.

Results

Hypothesis 1

As indicated in Tables 1 and 2, the mean foot length:stature ratio of the 40 subjects was

014.73%. Therefore, the null hypothesis (H Foot Length / Stature ' 15%) is rejected and the

1research (alternate) hypothesis is accepted (H Foot Length / Stature � 15%).

Hypothesis 2

As indicated in Tables 1 and 3, the mean shoe length:stature ratio of the 40 subjects was

016.63%. Therefore, the null hypothesis (H Foot Length / Stature ' 17%) is rejected and the

1research (alternate) hypothesis is accepted (H Foot Length / Stature � 17%).


In the study of 40 subjects, the correlation coefficient (r) for estimation of stature using foot

length was 0.8402 and the correlation coefficient (r) for estimate of stature using shoe length was

0.8135. These indicate that both measurements are positively correlated with estimation of

stature. However, as the foot length:stature correlation coefficient has a value closer to +1, this

indicates that a measurement of foot length provide a more accurate estimation of stature than

does shoe length. (A perfect positive linear correlation is indicated by a value of +1).

Discussion

Hypothesis 1

At the beginning of this report, the question was posed: “Because Topinard’s formula was

developed over 150 years ago, is this a still valid and reliable formula to estimate stature?” It

was upon this question that the first research hypothesis was based. Because the null hypothesis


(Topinard’s formula) was rejected, what are the implications of this result for forensic science

application? Should the formula be revised to more accurately reflect the current world

population (i.e., early 21 century vs. mid 19 century)? How do the results of this studyst th

compare to previous research on the topic?

As indicated in Tables 1 and 2, the current experiment of 40 subjects resulted in a mean

foot length:stature ratio of 14.73%. A similar 2002 study conducted by Burke (22 subjects)

indicated a foot length:stature ratio of 15.2% (8). (The mean of the ratios obtained from these

two small studies is 14.97%.) A cross-cultural archival study by Fessler et al. in 2005 of 31

previous experiments conducted with about 12,000 subjects between 1935 and 2001 indicated a

foot length:stature ratio of 14.99% (9). (This information was extrapolated by the author using

information provided in Table 1 of Fessler et al.’s article “Sexual Dimorphism in Foot Length

Proportionate to Stature.”)

In summary, even though the null hypothesis for this experiment was rejected, comparison

with other studies indicates that the foot length:stature ratio of 15% is still a valid measure and

appropriate to use in the field of forensic science today.

Use of a Range Versus an Absolute. Researchers emphasize that stature is not a fixed trait

as this characteristic changes over the course of a lifetime (1). Therefore, it is important that

when providing an estimate of stature of a living person, the measurement is provided as a range.

This is especially true when extrapolating estimates of stature from body measurements such as

foot length which can be also influenced by morphological changes due to pregnancy, culture,

environment, nutrition, disease, etc. (10, 14). (See also the Comments section in Table 1.)

Another factor in support of using range estimates is that errors often occur regarding

stature measurements. For example, American men tend to exaggerate their height on their


driver’s licenses by as much as 1 or 2 inches (1). This observation became apparent during the

collection of data for this study. Prior to measuring her stature, one subject was asked to provide

information about her height. She hesitated, then asked if she should provide the measurement

she tells to others (5" 5"), or if she should provide her actual height (5' 4").

As indicated in Tables 1 and 2, the current experiment of 40 subjects indicated a foot

length:stature ratio range of 13.27% to 16.03%. Calculation of the standard deviation indicates

that at +/- 2 standard deviations, there is a 95% confidence that accurate estimations of foot

length:stature ratios would be between 13.47% and 15.98%.

The 2002 Burke study provided a foot length:stature ratio range of 13.90% to 16.70% (8).

The 2005 Fessler et al. study provided a foot length:stature ratio range of 14.50% to 16.11% (9).

The foot length:stature ratio range provided by Topinard in the mid-1800s was 14.90% to

18.10% (7). (No information was available about the 95% confidence ranges for these studies)

In summary, even though Topinard’s foot length:stature ratio of 15% appears to still be a

valid estimation of stature, it would seem that the range used in the mid-1800s is no longer

relevant and needs to be revised. It is therefore recommended that a range such as provided by

Fessler et al. (14.50% to 16.11%) be adapted for current use in forensic science applications.

Hypothesis 2

As discussed in the first section of this report, a literature review revealed only one study

which indicated a shoe length:stature ratio (8). Therefore, the question was posed: “What is the

shoe length:stature ratio?”

As indicated in Tables 1 and 3, the current experiment of 40 subjects resulted in a shoe

length:stature ratio of 16.63%. Burke’s 2002 study indicated a ratio of 17.50% (8). The

comprehensive cross-cultural archival study by Fessler et al. in 2005 did not indicate a shoe


length:stature ratio (9). The mean shoe length:stature ratio of the first two studies was 17.07%.

Therefore, even though the null hypothesis of a shoe length:stature ratio of 17% was rejected, it

would appear that it may indeed be a valuable formula to estimate stature. However, because

conclusions cannot be based solely on two small and informal experiments, more research is

clearly needed in this area.

Use of a Range Versus an Absolute. The current study of 40 subjects indicated a shoe

length:stature ratio range of 14.29% to 18.12%. (See Tables 1 and 3). Calculation of the

standard deviation indicates that at +/- 2 standard deviations, there is a 95% confidence that

accurate estimations of shoe length:stature ratios would be between 14.88% and 18.38%.

No information could be obtained regarding the Tucker and Fessler et al. studies (8, 9).

Therefore, more research is needed to provide valid and reliable shoe length:stature ratio ranges.


The results of the study of 40 subjects indicated a higher positive correlation between foot

length and stature than for shoe length and stature. This is consistent with the findings of other

researchers (3, 14, 15, 17). Therefore, it is recommended that preference be given to foot length

measurements in estimating stature whenever possible.

Acknowledgments

The author would like to thank several people for their support and encouragement:

Charlyn Shickell, Ph.D. (Community Mental Health Center) and Dave Lamb, B.A. (Southeast

Community College) who are supervisors of the author; and Butch Rohren (the author’s

husband). All have been very patient and understanding with the need to have a flexible

schedule. The author would also like to acknowledge Larry Barksdale (forensic science

instructor at Nebraska Wesleyan University) for providing the opportunity and motivation to

conduct an experiment using statistical calculations (which she has been avoiding doing for over

20 years).


References

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APPENDIX A

Foot and Shoe Length Data Collection Form

Measurement # : ____ Age: ____ Race/Ethnicity: ___________________ Height: ______ Shoe Size: _____ since age ___

footprint ______ length in cm

shoeprint ______ length in cm

Note. This appendix is representative of the form that was used to collect information about foot

length, shoe length, and other relevant information. The data collection form was printed on

legal size paper (the shoeprint was on the reverse side of the sheet).

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4.2

9 1

6.7

0 31

M

48

C

au

casi

an

1

85.

42

27

.94

31

.43

11

17

1

5.0

7 1

6.9

5

32

M

30

C.a

ucas

ian

190

.50

27.4

6 31

.43

11

17

1

4.4

2

16

.50

33

M

4

3

Cau

casi

an

194

.95

28.7

7 31

.59

12

18

1

4.7

6 1

6.2

1 34

M

5

4

Cau

casi

an

175

.26

26.6

7

31.7

5

10

4

0

15

.22

18

.12

35

M

31

C

auca

sian

18

0.3

4

26.6

7 32

.39

10.5

1

5

14.7

9 1

7.9

6

36

M

4

2

Cau

casi

an

172

.72

25

.08

27

.62

9 18

1

4.5

2 1

5.9

9

37

M

21

B

lack

18

2.88

28

.73

31 .7

5 1

2.5

19

1

5.7

1 1

7.3

6 38

M

5

9

Cau

casi

an

189

.23

29.2

1 31

.27

11

18

1

5.4

4

16.5

3

39

M

58

C

auca

sian

18

5.4

2

27.9

4 31

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11

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25

1

5.0

7

16

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4

0

M

42

C

auca

sian

19

3.6

8 28

.58

34

.45

1

4

18

14

.75

1

7.7

9

min

18

15

2.40

21

.91

24

.77

11

13.

27

1

4.29

m

ax

67

19

4.95

29

. 21

34.4

5

40

16

.03

1

8.1

2

me

an

3

6

174

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25.6

8 29

. 01

18

14.7

3 16

.63

m

ed

ian

32

17

5.26

28

.50

28.5

0 16

.5

14.

65

16

.86

mo

de

19

16

5.10

23

. 81

27

.94

14

1

4.2

0

16

.92

st

de

v 13

.67

10.0

7 1.

97

2

.54

5.4

8

0.6

3

0.8

7

+2

std

ev

63

.06

19

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34

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28.5

8 1

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tde

v

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foo

tle

ng

th is

lo

ng

er t

han

sho

e le

ngth

; sh

e w

ore

3"

heel

s

shoe

siz

e w

as

6.5

at

age

18, t

he

n f

oo

t g

rew

dur

ing

pre

gn

an

cy

shoe

siz

e w

as

10

.5 a

t ag

e 1

6,t

he

nfo

otg

rew

late

rin

life

shoe

siz

e w

as 9

at

age

2O

,th

en

foo

tgre

wla

teri

n li

fe

No

tes

: 1.

M

ea

sure

me

nts

for

he

igh

t, f

oo

t le

ngth

, an

d sh

oe le

ngth

ar

e in

cen

timet

ers

(cm

) 2

. S

tatis

tical

cal

cula

tions

are

no

t pr

ovid

ed f

or

shoe

siz

e as

th

e w

om

en

's s

hoe

size

s w

ere

no

t co

nver

ted

to a

co

mm

on

st

anda

rd (

i.e.,

me

n's

sho

e si

zes)

.

~ 6; t""I

M -

tI1

en .... 13' a .....

o ::s o .....,

r/)

~.

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o :3 "Tj

o o .... ~ 0

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::

r' o <Ii L' g os.

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rrel

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n B

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Sta

ture

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d F

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t L

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(n =

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y

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ture

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rre

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tatu

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26

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orr

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n S

tatu

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nd

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177.

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25

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Fe

ma

les

Ma

les

All

----fi2i-------1~f.29-------13

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190

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27

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19

4.95

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ax

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n

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med

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5 H

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ng

th I

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ture

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172.

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14

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88

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st

de

v 0

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0.51

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rrel

atio

n B

etw

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Sta

ture

an

d S

ho

e L

eng

th

(n =

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x y

S

ho

e

(Fe

ma

les

and

Mal

es)

S

tatu

re

Le

ng

th

% C

orr

ela

tio

n

16

5.1

0

24.7

7 1

5.0

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1

66

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28

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77

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165

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=

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0

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65

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2

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0.00

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84

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31

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16.9

2 S

tatu

re (

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t) i

n C

en

tim

ete

rs1

77

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31

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6 1

82

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31

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85

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31

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17. 2

1 18

0.3

4 31

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75

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30

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17.6

6 %

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rre

lati

on

Be

twe

en

Sta

ture

an

d S

ho

e L

en

gth

17

7.8

0

29.6

9 16

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18

5.4

2

31.4

3 16

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Fe

ma

les

Ma

les

All

----1-4~2-9-------15.99-------14~29----

19

0.5

0 31

.43

16.5

0 m

in

194.

95

31 .5

9 1

6.2

1 m

ax

17.5

0 18

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18.1

2

17

5.2

6

31 .

75

18.1

2 m

ea

n

16.1

6 1

7.1

4

16.6

3 •

H2

: S

ho

e L

en

gth

I S

tatu

re *

-1

7%

18

0.3

4 32

.39

17.9

6 m

ed

ian

15

.91

17.2

1 16

.86

Ho:

S

ho

e L

en

gth

I S

tatu

re =

17

%

172

.72

27.6

2 1

5.99

m

od

e

16.9

2 17

.91

16. 9

2 1

82

.88

31

.75

17.3

6 st

de

v 0.

83

0.60

0

. 87

189

.23

31 .2

7 16

. 53

+2

std

ev

17.8

2 18

.35

18.3

8 1

85

.42

31

.27

1 6.8

7 -2

std

ev

14.5

1 1

5.94

14

.88

193

.68

34.4

5 17

.79

00

estimation of stature from foot and shoe length: …neiai.org/neiai/uploads/kent...

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