Popularization of the Modern Cesarean Section in the United States and its Effects on Female Pelvic Morphology

Popularization of the Modern Cesarean Section in the United States and its Effects on

Female Pelvic Morphology

by

Rose Leach, B.S.

A Thesis

In

Physical Anthropology

Submitted to the Graduate Faculty

of Texas Tech University in

Partial Fulfillment of

the Requirements for

the Degree of

Master of Arts

Approved

Arthur Durband, PhD

Chair of Committee

Robert Paine, PhD

Mark Sheridan

Dean of the Graduate School

May, 2015

Copyright 2015, Rose Leach

Texas Tech University, Rose Leach, May 2015

ii

Acknowledgements

I want to thank many wonderful people who have helped me get to this point in

my career. First off, I would like to thank Dr. Durband for being my committee chair and

being there at every step of the journey to this degree. I would also like to thank Dr. Paine

for being a part of my defense committee and providing helpful feedback. Lastly, I want

to thank Dr. James Surles for assistance with all of the statistical work.

Thank you to the staff and researchers at the Cleveland Museum of Natural

History and the Forensic Anthropology Center at University of Tennessee-Knoxville for

the generous use of their collections, help, and equipment that made all of this research

possible.

Of course, I could not have done any of this without the love and support of my

parents, friends, and my ever patient, loving Michael. Thank you for sticking by my side

and supporting me through every moment of these past few years, you all mean so much

to me.


iii

Table of Contents

Acknowledgements ........................................................................................................... ii

Abstract ...............................................................................................................................v

List of Tables .................................................................................................................... vi

List of Figures .................................................................................................................. vii

I. Introduction ....................................................................................................................1

II. Background ...................................................................................................................3

Basic Pelvic Morphology ...............................................................................................3

The Primate Pelvic Shape from an Evolutionary View .................................................4

Labor and Maternal/Fetal Mortality...............................................................................4

Cesarean Sections ..........................................................................................................5

Secular Skeletal Changes in the United States ..............................................................7

Research Goals...............................................................................................................9

III. Materials and Methods .............................................................................................11

Study Parameters .........................................................................................................11

Pre-Integration: Hamann-Todd Collection ..................................................................13

Post-Integration: William M. Bass Collection .............................................................14

Methodology ................................................................................................................14

Data Analysis ...............................................................................................................18

IV. Results .........................................................................................................................22

F-Test Results ..............................................................................................................22

T-Test Results ..............................................................................................................23


iv

Linear Discriminant Analysis ......................................................................................25

V. Discussion .....................................................................................................................28

MANOVA and its Significance ...................................................................................28

Linear Discriminant Analysis ......................................................................................28

Overall Changes in the Female Birth Canal ................................................................29

VI. Conclusion ..................................................................................................................32

Nutrition, Maternal Age, and Bipedalism ....................................................................32

Future Research ...........................................................................................................33

Bibliography .....................................................................................................................36

Appendices

A. Pre-Cesarean Sample Data ............................................................................................38

B. Post-Cesarean Sample Data ..........................................................................................44

C. F-Test Results ...............................................................................................................51

D. Normal Probability Plot of Residuals ...........................................................................54

E. Residuals Versus Fit Plots .............................................................................................62

F. Test and Confidence Intervals for Two Variances ........................................................70


v

Abstract

The shift in locomotion of our predecessors to obligate bipedalism caused

significant changes in our pelvic morphology. However, these morphological changes

had an adverse effect on the ability of women to successfully give birth without

complications, referring specifically to the issue of obstructed labor. AL 288-1 had a

platypelloid pelvis, making it extremely difficult for neonates to pass through the birth

canal due to an ovular inlet with a long transverse axis. Anatomically modern females

have a gynecoid pelvis, consisting of a rounded inlet with a larger subpubic angle. This

shape better facilitated natural birth, but obstructed labor was still a significant issue in

modern populations. The advent of the modern cesarean section throughout the United

States in 1882 revolutionized labor processes, allowing women who would not have

survived the natural birthing process to contribute to the morphology of future

generations. Research has acknowledged changes in female pelvic anatomy, but these

have yet to be detailed.

This research utilized two samples from the United States (pre and post

introduction) to determine if the popularization of the modern cesarean section has any

correlations with changes in female pelvic anatomy. The collected pelvic data was put

through statistical analyses to test for significant changes. Principal component analysis

and F-tests were used to explore shape variation and levels of diversity. The results detail

changes in female pelvic morphology following the introduction of the cesarean section.


vi

List of Tables

4.1 Results of F-Test .....................................................................................................21

4.2 T-test Results by Measurement ...............................................................................22

4.3 Linear Discriminant Analysis Results: Summary of Classifications ......................23

4.4 Linear Discriminant Analysis Results: Squared Distance ......................................23

4.5 Linear Discriminant Analysis Results: Linear Discriminate Function ...................24

4.6 MANOVA Results ..................................................................................................25

A.1 Pre-Cesarean Sample Data ......................................................................................34

B.1 Post-Cesarean Sample Data ....................................................................................39


vii

List of Figures

3.1 Example of Skeletal Pathology (Scoliosis) .............................................................11

3.2 Example of Skeletal Pathology (Sacralized Lumbar and Fusion of Vertebra) .......12

3.3 Superior View of Pelvis ..........................................................................................15

3.4 Inferior View of Pelvis............................................................................................15

3.5 Medial View of Pelvis ............................................................................................16

3.6 Medial View of Pelvis, Continued ..........................................................................16


1

Chapter I

Introduction

During the labor process in anatomically modern humans, the morphology of the

pelvis facilitates neonatal rotation within the inlet, allowing it to pass through and exit the

maternal body (Rosenberg and Trevathan 2002). However, despite these adaptations,

there is still a significant percentage of women who are unable to give birth naturally

because the neonate is too wide to squeeze through the confines of the pelvic inlet. This

condition is termed obstructed labor. Fatality of both mother and child is almost certain in

these situations, if a caesarean section is not performed. The Worldwide Health

Organization, or WHO, estimates that 529,000 maternal deaths occur annually,

worldwide (WHO 2005). Of these deaths, 8%, or 42,000 women, are due to obstructed

labor (WHO 2005). What is also crucial to note is that of the total maternal deaths

worldwide, only 1% occur in developed countries (WHO 2005). It is clear that the

development and popularization of modern medicine has been effective in reducing

mortality rates when complications arise during labor. The first cesarean sections were

performed during ancient Roman times, where the infant was cut from the womb of the

mother if she died before being able to give birth or was dying (Todman 2007). This was

a last resort technique that was infrequently used on living mothers unless it was a

particularly difficult birth (Todman 2007). The mother rarely survived the procedure

(Todman 2007).


2

This research aims to compare and analyze two samples from the United States

population to see if the introduction and spread of the cesarean section within modern

medicine has any correlations with changes in the female pelvic morphology.

The first sample will be from the Hamann-Todd collection of the Cleveland

Museum of Natural History. Approximately 104 females from around the introduction of

the cesarean section will represent the pre-cesarean pelves. The second sample will be

from the osteological collection at the University of Tennessee in Knoxville, which

serves to provide a representative look at pelves that likely have gone through multiple

generations where the female potentially gave birth via cesarean section. This will be

composed of approximately 124 individuals. Photographs of pelves from each sample

will be taken for reference.

The results show a significantly different pelvic canal, where most of the

dimensions have increased to create a larger canal. A t-test determined that all but 3

variables exhibited significantly different means between pre-cesarean and post-cesarean

samples. Overall, changes in the pelvic canal have occurred since the time that cesarean

sections have been introduced. While other environmental factors contribute to changes,

cesarean sections remove a selection pressure and have contributed to changes in the

pelvic inlet.


3

Chapter II

Background

Basic Pelvic Morphology

William Caldwell and Howard Moloy developed a classification of four basic

types to describe pelvic morphology in 1934. These four pelvic types include gynecoid,

platypelloid, android, and anthropoid. Gynecoid pelves have an inlet that is oval with a

greater transverse diameter (Caldwell and Moloy 1934). The interior walls of the canal

are straight and have a round greater sciatic notch. The sacrum has a backward incline

and a wide subpubic arch (Caldwell and Moloy 1934). This type best facilitates birth and

comprises about half of the women measured in the study that they conducted (Caldwell

and Moloy 1934). The platypelloid pelvis is characterized by a flattened shape that is

both wide transversely and anteriorly (Caldwell and Moloy 1934). The sacrum is short

and curves inward with a masculine sciatic notch. An android pelvis is a female pelvis,

yet is reminiscent of a masculine pelvis (Caldwell and Moloy 1934). This has a suite of

features, including a wedge or heart shaped pelvic inlet due to a triangularly shaped

anterior segment and a prominent sacrum. Caldwell and Moloy (1934) found this

category of pelvis in one third of white women and one sixth of non-white women. The

last classification is the anthropoid pelvis. An anthropoid pelvis has an oval shape that

has a greater diameter anteroposteriorly (Caldwell and Moloy 1934). The wall of the inlet

are straight with a reduced subpubic arch and a straighter sacrum. This accounts for 38%

pelves among all women (Caldwell and Moloy 1934).


4

The Primate Pelvic Shape from an Evolutionary View

The pelves of Miocene apes and other hominoids were of the anthropoid shape,

referring to a pelvis with a long anteroposterior diameter, also including a larger subpubic

angle and a deep greater sciatic notch (Lierse 1984). The first bipedal hominids include

Australopithecus afarensis, the most notable female fossil being AL 288-1 (Lucy).

Lucy’s pelvis was platypelloid, which has an ovular inlet, where the long axis is

transverse with a large anteroposterior diameter, making it extremely difficult for a

neonate to be able to fit through (Lierse 1984; Tague and Lovejoy 1986). The pelvis of an

anatomically modern female human is gynecoid, where the inlet is more rounded, with a

large subpubic angle and a wide greater sciatic notch (Lierse 1984). The inlet of the

gynecoid pelvis is derived from the platypelloid pelvis, making labor slightly less

problematic.

Labor and Maternal/Fetal Mortality

During the labor process in anatomically modern humans, the morphology of the

pelvis facilitates neonatal rotation within the inlet, allowing it to pass through and exit the

maternal body (Rosenberg and Trevathan 2002). The fetal head aligns its sagittal

diameter with the longest dimension of the pelvic inlet (Wittman and Wall 2007). Due to

the varying dimensions of each superior-inferior segments of the birth canal, the neonate

rotates within the canal, aligning itself with the sagittal plane of the pelvis. However,

despite these adaptations, there is still a significant percentage of women who are unable

to give birth naturally because the neonate is too wide to squeeze through the confines of

the pelvic inlet. This condition is termed obstructed labor. Fatality of both mother and


5

child is almost certain in these situations. The Worldwide Health Organization, or WHO,

estimates that 529,000 maternal deaths occur annually, worldwide (WHO 2005). Of these

deaths, 8%, or 42,000 women, are due to obstructed labor (WHO 2005). What is also

crucial to note is that of the total maternal deaths worldwide, only 1% occur in developed

countries (WHO 2005). It is clear that the development and popularization of modern

medicine has been effective in reducing mortality rates when complications arise during

labor.

Cesarean Sections

Cesarean sections provided a procedure to reduce both infant and maternal

mortality rates. The first cesarean sections were performed during ancient Roman times,

where the infant was cut from the womb of the mother if she died before being able to

give birth or was dying (Todman 2007). This was a last resort technique that was

infrequently used on living mothers unless it was a particularly difficult birth (Todman

2007). However, the mothers rarely survived the procedure (Todman 2007). Ferdinand

Kehrer was the first physician to perform the modern caesarean section in 1881. It is clear

that the development and popularization of modern medicine has been effective in

reducing mortality rates when complications arise during labor. It is logical to assume

that in order to give birth naturally without complications, a female must have a pelvis

that is within a certain range of shape and size. Before the introduction of cesarean

sections, obstructed labor led to much higher mortality rates than they do today. By

removing those females and their genes from the population, the assumption is that

pelves that successfully give birth and continue for subsequent generations would attempt


6

to create a specific range of pelvis size and shape that would facilitate natural,

unobstructed birth. However, the introduction of the cesarean section removes this

selection pressure from the population.

Davis-Floyd (1986) discusses the rates of cesarean sections in the United States

and also Brazil. The cesarean section rates nationwide hover around 33% percent in the

United States, but are much higher in teaching hospitals and private hospitals (Caughey et

al. 2014). In teaching hospitals, rates reach up to 50 percent and average 58 percent of

total births in non-teaching private hospitals (Davis-Floyd 1986). These rates also

differed by socioeconomic status: hospitals that were for profit, private, and also patients

with the best health insurance had the highest incidences of cesarean sections (Davis-

Floyd 1986). Federal, state, and local hospitals have the lowest rates of cesarean sections

(Davis-Floyd 1986). However, in other countries such as Brazil, the incidences of this

procedure skyrocket. Rates of cesarean section in the public teaching hospitals are as high

as 65 percent and average 95 percent in most private hospitals (Davis-Floyd 1986). These

are all based on hospitals in Sao Paulo and Rio. Such significantly high cesarean section

rates have roots in the culture, and has little to do with medical necessity. Middle and

upper-class Latina women place more value on scientific knowledge, control, and also

creating cultural distance from the lower class, reflected in the rate of cesarean sections

(Davis-Floyd 1986).

While the literature regarding changes in female pelvic morphology as a result of

modern medicine has expanded in the past decade, nothing specific has been published

explicitly discussing relatively recent skeletal changes in females residing in the United

States. The literature has either discussed the evolution of the pelvis, as outlined


7

previously in this section, or it focuses on muscle structure and changes as a result of

cesarean section procedures.

Secular Skeletal Changes in the United States

When discussing the factors that could possibly affect pelvic skeletal anatomy,

there are several that could possibly have affected pelvic and overall skeletal anatomy

between the time periods apart from the cesarean section. One of the more prominent

potential factors is nutrition. While the literature lacks data specific to nutritional trends

and its effect on skeletal morphology, there are a series with respect to secular skeletal

changes in the United States done by Jantz and Jantz. They point out that forces driving

secular changes in skeletal anatomy are typically associated with changes in the

environment with respect to nutrition and overall health (Jantz and Jantz 1999). However,

other forces can contribute to these changes, such as socioeconomic status and age (Jantz

and Jantz 1999).

Regarding the growth patterns of the human pelvis in males and females,

differences in the adult bony pelvis cannot be attributed to varying response of specific

bones to sex hormone (Coleman 1969). Males and females exhibit the most significant,

consistent sexual dimorphism in the pelvic inlet and sciatic notch, being more variable

due to dependencies on external anatomical systems which affect the end adult

morphological configuration (Coleman 1969). Overall, external dimensions in the

skeletal pelvis tend to be greater in men than in women, while internal dimensions

typically are larger in females than in males (Coleman 1969). Due to significant sexual

dimorphism in the pelvis, there are significantly different energetic costs in bipedalism


8

between the sexes. Leonard and Robertson (1995) reported that in tests of energetic costs

for men and women of different total body weights, males consistently had higher

energetic costs than females to walk bipedally. However, it is important to note that this

study was done with living test subjects, and reflects energetic costs of individuals today.

Moerman (1981) conducted an analysis of skeletal pelvic growth in females and

documented that on average, the growth of the pelvis after the age of 18 is less than 2 mm

per measurement. The only two measurements that significantly change after the age of 18

are the length of the linea terminalis and width of subpubic angle, neither of which

significantly affect the pelvic canal (Moerman 1981). Frisancho et al (1985) reported that

younger maternal age (15-18 years) is associated with lower birthweights, despite having

similar nutritional intake as those women who gave birth after the age of 18.

Nutrition, correlated with socioeconomic status, is another environmental factor

that affects the shape of the pelvic inlet during the growth and development of the

subject. Angel and colleagues (1978, 1987) have reported significant flattening of the

pelvic inlet. This is associated with poor nutrition and subpar growth patterns (Angel

1987). Regarding measurements that proportionally affect the pelvic canal, Moerman

(1981) found that only the anteroposterior diameter of the pelvic inlet and pubis length

were relative to body size.

The most relevant study published by Jantz and Jantz (1999) examined secular

changes in long bone proportion and length from 1800 to 1970. They examined white and

black individuals in the United States, also looking separately at males and females. The

results revealed the most significant change in white males, with changes in all six of the

long bones examined. Both black males and white females exhibited similar significant


9

patterns of change, while black females were the most stable group examined in this

study, with the femur being the only long bone exhibiting change (Jantz and Jantz 1999).

White males also had the greatest rates of change over any other group. When comparing

different groups, Jantz and Jantz (1999) found that differences between sexes were

greater than differences between ethnic groups, with males being more responsive to

environmental factors, whereas females tended to be more resistant to change (Stinson

1985). Therefore, significant changes in females that are greater than significant changes

in males would indicate a strong driving force that is only affecting women. This will be

explored in further detail in the discussion section.

Research Goals

This research aims to compare and analyze two samples from the United States

population to see if the introduction and spread of the caesarean section within modern

medicine has any correlations with changes in the female pelvic morphology. It will

specifically look for not only changes in the size and shape of the pelvic morphospace,

but will also compare levels of diversity between the two samples to determine whether

removal of this selection pressure increased levels of diversity.

Hypothesis: The use of the modern cesarean section in United States healthcare

eliminated the confines upon which the female pelvis can be shaped and still successfully

give birth naturally, without complications. Therefore, there will be a statistically

significant change in pelvic morphology between the two samples which trends towards a

greater range in all measured dimensions of the female pelvis.


10

Null Hypothesis: The use of the modern cesarean section in the United States had no

effect on the dimensional restrictions upon which the female pelvis can give birth

naturally, without complications. Therefore, there will not be a statistically significant

change between the two samples with regards to all measured dimensions of the female

pelvis.


11

Chapter III

Materials and Methods

Study Parameters

This research will be conducted through a series of documented measurements

and statistical analyses. One sample represented the female population before the

integration of the modern caesarean section and the other represented the population after

integration. In order to collect the most relevant data, all pelves assessed were females

between the ages of 18 and 70 years. This age range represents women who were most

likely to have given birth at some point within their lifetime. 18 years of age was the

youngest age, in order to best represent the adult pelvis at its final stage of growth. 70

years of age was the cutoff to prevent significant bone degradation (due to age and

pathologies) from skewing the data. While natural variation is inherent in any and all

populations, possible bias due to interracial differences in skeletal morphology was an

important consideration in this research. Therefore, only females of Caucasian racial

designation were used in this particular study.

The total pre-integration sample from the Hamann-Todd collection in the

Cleveland Museum of Natural History included 104 individuals, with a mean age of 43

years. The birth date ranges of the compiled sample fell between 1911 and 1938. The

post-integration sample was composed of 124 individuals from the William Bass

collection at the University of Tennessee in Knoxville, with an average age of 56.6 years.


12

Most of the individuals in this sample were born between 1932 and 1961, and none

before 1921.

Figure 3.1. Example of skeletal pathology (Scoliosis).


13

Figure 3.2. Example of Skeletal Pathology (Sacralized Lumbar and Fusion of

Vertebra).

Pre-Integration: Hamann-Todd Collection

The pre-integration sample comes from the Hamann-Todd collection in the

Cleveland Museum of Natural History. The collection was compiled between 1911 and

1938. By subtracting the average age of the sample from the dates of compilation, birth

year range estimates fall within 1868 and 1895, well before the modern caesarean section

was introduced, up to shortly thereafter. Since medical techniques take a considerable


14

amount of time to become commonplace in hospitals, it is unlikely that significant,

persistent changes would occur over a few generations.

Post-Integration: William M. Bass Collection

The post-integration sample comes from the William Bass collection at the

University of Tennessee in Knoxville. Most of the individuals in this sample were born

between 1932 and 1961, and none before 1921. This sample is representative of

individuals who were born at least 40 years after the caesarean section was integrated into

the health practices of the US medical system.

Methodology

The pelvis of each individual was reconstructed and held together with a matrix of

rubber bands. Digital calipers and an osteometric board were used to take a set of 14

different measurements (adapted from Tague 1989), listed in in Table 1 and illustrated in

Figures 1-4.

Photographs of pelves from each sample will be taken for reference. Since the

collections are both of modern origin, the pelvis should still be intact to be able to obtain

the following measurements* for the statistical analyses explained later in this section:

1. Bi-Iliac Breadth: Maximum distance across the right and left iliac blades

2. Inlet A-P: Sacral promontory to dorsomedial superior pubis

3. Inlet M-L: Maximum distance between linea terminalis


15

4. Inlet Posterior: Curved length of linea terminalis from INML to apex of

auricular surface

5. Inlet Anterior: Curved length of linea terminalis from INML to dorsomedial

superior pubis

6. Midplane A-P: From junction of 4th and 5th sacral vertebrae to dorsomedial

superior pubis

7. Midplane M-L: Between ischial spines

8. Midplane posterior: S4-S5 junction to ischial spine

9. Midplane anterior: Ischial spine to dorsomedial inferior pubis

10. Outlet A-P: Apex of 5th sacral vertebrae to dorsomedial inferior pubis

11. Outlet M-L: Distance between inner margins of transverse ridge of ischial

tuberosities

12. Outlet Posterior: Apex of S5 to transverse ridge of ischial tuberosity

13. Outlet Anterior: Transverse ridge of ischial tuberosity to dorsomedial inferior

pubis

14. Canal Depth: Apex of auricular surface to transverse ridge of ischial

tuberosity

*Measurements taken from Tague (1989), Franciscus and Holliday (1992), and

Buikstra and Ubelaker (1994).


16

Figure 3.3. Superior View of Pelvis (A. Inlet A-P, B. Inlet M-L, C. Inlet Posterior, D.

Inlet Anterior)

Figure 3.4. Inferior View of Pelvis (F. Midplane M-L, J. Outlet M-L)


17

Figure 3.5. Medial View of Pelvis (E. Midplane A-P, I. Outlet A-P, M. Canal Depth)

Figure 3.6. Medial View of Pelvis, Continued (G. Midplane Posterior, H. Midplane

Anterior, K. Outlet Posterior, L. Outlet Anterior)


18

The data are collected using calipers in order to ensure precision and each

measurement is taken twice (once initially, and a second at the end of the week) to check

for consistency. There are a few factors that may have influenced the results; however,

precautions were taken to mitigate any error or bias. At the end of each week of collecting

data from each skeletal collection, measurements of the first samples taken were repeated,

to ensure consistency. If the second set of measurements did not match up with the original

set of data, then additional measurements were taken until they did match.

An osteometric board was used in Cleveland for the bi-iliac breadth versus

spreading calipers in Knoxville. However, this was the only difference in methodology

between data obtained from the two skeletal collections, and the results showed that there

was no significant difference in bi-iliac breadth between pre-cesarean and post-cesarean

samples. Lastly, when measuring individuals, it was extremely important to look at the rest

of the individual, rather than just focus on the pelvis. Significant pathologies can have a

significant effect on pelvic skeletal morphologic development, so the rest of the skeleton

for each individual sampled was examined for pathologies. Individuals that exhibited

lesions, such as scoliosis, were not included in the data analysis.

Data Analysis

Principal component analysis allowed for the exploration of size and shape

variation among and within the samples. Also, an F-test was used to compare levels of

diversity in pelvic morphology between the two samples. This tested for equality of

variances in the multivariate variance of the total model morphospace. The morphospace


19

of the pelvic girdle is represented by the 14 measurements outlined earlier in this chapter

(Kurki 2013).

After complete collection of the data, a master excel workbook combined the data

from both samples. The initial multivariate analysis of variance, or MANOVA, using the

program MiniTab 17, was applied to the collected data in order to test the proposed

hypothesis. A MANOVA test looks at the 14 different response variables as a mean

vector total, between pre and post-cesarean section samples (Warne 2014). It assumes

normal distribution, basically testing if the mean vector either supports or rejects the null

hypothesis (Warne 2014). If the MANOVA rejects the null hypothesis, individual tests of

each response variable will elucidate which precise variables contributed to the

conclusion (Warne 2014).

With the master dataset, f-tests were performed on each of the 14 measurements

taken. The f-test was a simple equation done in Excel to determine whether the

measurement values between the pre-cesarean and post-cesarean samples were of equal

or unequal variance, looking at variability within each sample and then compared the

variability between the two samples (Box 1953). If the p-value was greater than 5%, then

the variance of the measurement between samples was equal (not significant) (Box

1953). If not, then it was listed as unequal (significant) (Box 1953). Table __ lists the

measurements and the results of the f-test. The f-test then was used to compare levels of

diversity in pelvic morphology between the two samples. This tested for equality of

variances in the multivariate variance of the total model morphospace (Kurki 2013).

Significant differences in each of the 14 variables between pre- and post-introduction

samples were then tested for using the student’s t-test.


20

Once the variance for each measurement was determined, a t-test was applied to

the data in Excel to see whether the mean of each measurement between samples was

significantly different (Press et al. 1992). The results of the f-test determined the type of

t-test to use. If the measurement was of unequal variance, then the t-test: two sample

assuming unequal variance was used. If the measurement was of equal variance, then the

t-test: two sample assuming equal variance was used (Press et al. 1992). A p-value of less

than .05 but greater than .01 denotes statistical significance. Any values less than .01

were of high significance, while any p-values greater than .05 meant that the difference

between the mean values were not statistically significant (Press et al. 1992).

Linear discriminant analysis was used to analyze the complete dataset to create a

function to classify any pelvis that has each of the 14 measurements into one of the two

samples, along with the rate of accuracy for classification. The function essentially

predicts which group the pelvis would be classified under, using the 14 different variables

(Friedman 1989). This is done by entering measured values into two different functions;

one for pre-cesarean and one for post-cesarean (Friedman 1989). The higher value of the

two outputs indicates which sample the pelvis is likely from. This test also created a

function and tested it with cross-validation. Cross-validation is the method of building a

discriminant function with all of the data except for one observation in this case, one

pelvis (Friedman 1989). The program then uses the function to predict the values of the

missing observation and compares it with the actual missing values to determine accuracy

of the function (Friedman 1989).

The MiniTab 17 program will be used to also create residual versus fits plots,

Tables for test and confidence interval for two variances, and normal probability plot of


21

residuals for each of the pelvic measurements. The residual versus fits plots show the

spread for both pre-cesarean and post-cesarean section sample data, relative to the

response variable being examined. A roughly equal spread, save for one or a few outliers,

between the two samples would support to clear evidence of unequal variances. However,

a formal test is also performed with these plots, which is shown in the tables for test and

confidence intervals for two variances. The normal probability plot of residuals is also

created alongside the residual versus fit plots. These normal probability plots create a best

fit line with the points. Ideally, the points should be roughly linear, with no standard

deviation from the line. This would support the results of the residual versus fit plots.

The two plots that are created with each of the response variables are also

accompanied by the formal test results. Formal test results include three different plots:

one that show the 95 percent confidence interval for post-cesarean versus pre-cesarean,

one that shows the 95 percent confidence interval for standard deviations, and a boxplot

of the response variable versus the two different samples. The most important plot is the

95 percent confidence interval for post-cesarean versus pre-cesarean section samples. If

the lines include the value of 1, we do not reject the null hypothesis that the two variances

are equal. This is reflected in the p-values that are included in the formal tests. A large p-

value indicates that the means of the two samples are of equal variances.

MiniTab 17 was used to perform the MANOVA and discriminant analysis, and

Excel was used to calculate f-test and t-test results.


22

Chapter IV

Results

F-Test Results

Of the 14 measurements, seven of the variables (measurements) did not have

significant differences in variation, while the other seven variables were found to have

significant differences in variation between the two samples. Table 4.1 shows the

measurements that showed a statistically significant difference.

Table 4.1. Results of f-test

Measurement p-value

Bi-iliac Breadth NS

Inlet A-P *

Inlet M-L *

Inlet Posterior NS

Inlet Anterior *

Midplane A-P NS

Midplane M-L **

Midplane Posterior NS

Midplane Anterior NS

Outlet A-P **

Outlet M-L **

Outlet Posterior NS

Outlet Anterior NS

Canal Depth **

* .01 < p < .05

** p < .01

NS = not significant


23

T-Test Results

Table 4.2 shows that four out of the 14 measurements exhibited no significant

difference in average measurements between pre and post-cesarean section samples. The

medio-lateral inlet increased by 4.12 mm. However, the medio-lateral midplane average

decreased by 5.52 mm. Table 4.2 shows the measurements that were to be determined to

be of significance, with p-values less than .01. There is a 4.57 mm increase in the antero-

posterior inlet, while the inlet anterior average decreased by 17.06 mm. All of the highly

significant midplane measurement averages increased. The antero-posterior midplane

aspect of the pelvic canal increased by 6.31 mm, midplane posterior by 5.38 mm, and

midplane anterior lengthened by 4.31 mm. The overall outlet medio-lateral mean

shortened by 11.51 mm, whereas outlet posterior expanded by 7.49 mm. Lastly, canal

depth deepened by a total of 6.37 mm between pre and post-cesarean section samples.


24

Table 4.2. t-test results by measurement, with pre- and post-cesarean mean values

Measurement

Pre-Cesarean Post-Cesarean p

(mm) (mm)

Biiliac Breadth 266.54 266.01 NS

Inlet A-P 114.12 118.69 **

Inlet M-L 129.33 133.45 *

Inlet Posterior 21.813 22.911 NS

Inlet Anterior 134.8 117.74 **

Midplane A-P 126.41 132.72 **

Midplane M-L 103.27 97.753 *

Midplane Posterior 70.596 75.971 **

Midplane Anterior 90.998 95.305 **

Outlet A-P 114.21 126.51 NS

Outlet M-L 111.77 100.26 **

Outlet Posterior 81.673 89.158 **

Outlet Anterior 85.533 87.1 NS

Canal Depth 111.314 117.68 **

* .01 < p < .05

** p < .01

NS = not significant


25

Linear Discriminant Analysis

The following tables detail the results of the linear discriminate analysis. This includes a

summary of classification with cross-validations, the squared distance between groups,

and the linear discriminant function for groups.

Table 4.3. Linear Discriminate Analysis Results: Summary of Classification with Cross-

Validations

True Group

Put into Group Post-Cesarean Pre-Cesarean

Post-Cesarean 118 1

Pre-Cesarean 2 100

Total Number 120 101

Number Correct 118 100

Proportion 0.983 0.99

Table 4.4. Linear Discriminate Analysis Results: Squared Distance Between Groups

Post-Cesarean Pre-Cesarean

Post-Cesarean 0 25.6299

Pre-Cesarean 25.6299 0

The squared distance between groups in the linear discriminate analysis results,

shown above in Table 4.4, shows how many standard deviations away the mean of one

sample is from the mean of the other sample. This table shows squared distance of the

two samples, relative to each sample.


26

Table 4.5. Linear Discriminate Analysis Results: Linear Discriminant Function for

Groups

Post-Cesarean Pre-Cesarean

Constant -215.34 -216.17

Bi-iliac Breadth 0.44 0.43

Inlet A-P 0.46 0.13

Inlet M-L -0.14 -0.25

Inlet Posterior -0.46 -0.58

Inlet Anterior 0.02 1.04

Midplane A-P 0.14 0.12

Midplane M-L 0.16 0.16

Midplane Posterior 0.23 0.05

Midplane Anterior 1.01 0.46

Outlet A-P -0.09 0.08

Outlet M-L 0.05 0.17

Outlet Posterior 0.15 0.02

Outlet Anterior 0.41 0.29

Canal Depth 0.8 0.67

The linear discriminant analysis produced two different results for the linear

method: one using all of the dataset and another that includes cross-validation. A total of

221 cases were used, 101 cases from the pre-cesarean section and 120 cases from the

post-cesarean section. In the summary of results that did not include cross-validation, 220

of the 221 cases were classified in the correct group. This calculates to a 99.5 percent rate

of accuracy. The results of the linear discriminant analysis with cross-validation produced

slightly less accurate results. Of the 221 total cases examined, 218 cases were classified

into the correct group, with a total accuracy rate of 98.6 percent.


27

Table 4.6. MANOVA Results

Criterion Test Statistic F Num Denom P

Wilks' 0.1348 94.439 14 206 0

Lawley-Hotelling 6.4182 94.439 14 206 0

Pillai's 0.8652 94.439 14 206 0

Roy's 6.4182

The MANOVA results show the p-values, or significance, of the data by using

four different criteria. For all of the criteria, the p-value was 0, meaning that the data was

highly significant.


28

Chapter V

Discussion

MANOVA and its Significance

The results of the MANOVA are the most important factors in determining the

extent to which we can examine the data for significant changes. Minitab 17 calculated

the MANOVA output for four different criteria: Wilks', Lawley-Hotelling, Pillai's, and

Roy's. Regardless of the criteria, the results all showed the same P value of 0.000. This

means that the p-value is so small that we must reject the null hypothesis, which states

that the means of all of the variables are not significantly different.

Linear Discriminate Analysis

The results of the linear discriminate analysis showed whether or not there were

differences in the overall variation by each individual variable measured in the pelvic

anatomy. Of the 14 measurements, 50% of the variables did not show any significant

change overall in the variation within each sample, between pre-cesarean and post-

cesarean section samples. These variables include: bi-iliac breadth, inlet posterior,

midplane a-p, midplane posterior, midplane anterior, outlet posterior, and outlet anterior.

Despite the elimination of the selection pressure (necessity to be able to give birth

naturally) with the introduction and popularization of the modern cesarean section, the

amount of variation does not change significantly between pre and post-cesarean

samples. However, the rest of the variables did exhibit a significant difference in


29

variation between pre and post-cesarean samples. These include inlet a-p, inlet m-l, inlet

anterior, midplane m-l, outlet a-p, outlet m-l, and canal depth.

The results of the linear discriminate analysis also provided a calculation of how a

pelvis could be categorized into either pre-cesarean or post-cesarean samples. Based on

the samples already taken, the linear discriminate analysis summary of classification

correctly categorized 220 out of a total 221 pelves. Taking the testing of classification,

including cross validation into account, the results showed that 218 of the total 221

samples were correctly classified, with 98.6 percent accuracy.

The classification results provide an accurate method of determining the

timeframe (pre-cesarean and post-cesarean) during which the pelvis existed. With larger

sample sizes and documented birth and death dates, this method shows the possibility of

being developed into an accurate method of classification with more specific ranges of

dates.

Overall Changes in the Female Birth Canal

Overall, there is significant expansion of the pelvic canal, both mediolaterally and

anteroposteriorly in the post-caesarean sample. This varies with each segment of the

canal, consisting of the inlet, midplane, and outlet (in order from superior to inferior).

Increases are seen in the inlet a-p, inlet m-l, midplane a-p, midplane posterior, midplane

anterior, and outlet posterior dimensions. The additional space that these variables

provide facilitate the natural birthing process, allowing the neonate to pass through the

canal with more ease than the slightly more constricted canal of the pre-caesarean

sample.


30

However, there are three variables that are problematic and do not contribute to

the overall expansion of the pelvic canal, detailed in the following paragraphs. The most

significant changes in the morphology of the pelvic canal occurred in the inlet anterior

and mediolateral outlet dimensions.

The mean anterior border of the inlet decreased by 17 mm. This difference would

reduce the superior anterior circumference of the canal. For the circumference of the

pelvic inlet to fit around the increases in the inlet a-l and m-l variables, the shape of the

inlet will shift. The posterior border of the inlet has not significantly changed, so it will

retain the rounded shape consistent with the Caldewell and Moloy (1934) definition of

the gynecoid pelvis. However, the anterior border will exhibit less curvature in order to

accommodate the reduction in border size and increase in the anteroposterior and

mediolateral dimensions of the inlet. This creates a slightly more pear shaped opening,

with the more constricted end being oriented anteriorly. In a sense, this post-cesarean

pelvic inlet has become more android like, with its pear-shaped opening that now has a

triangular anterior border.

With regards to the midplane portion of the pelvic inlet, there was an average

constriction of the midplane mediolaterally by 5.5 mm. This reduction, coupled with the

expansion of the midplane, anteroposteriorly, exaggerated the characteristics of the

midplane shape, which is more ovular, with elongation anteroposteriorly. The ovular

shape of the midplane contrasts with the inlet of the canal, where the elongation of the

opening was distinctly mediolateral, facilitating the neonatal rotation within the canal that

is consistent with the modern labor process. Despite the mediolateral constriction, there is


31

an expansion of the midplane posterior and anterior borders, expanding the overall

surface area of the space in the canal.

The other significantly negative trend was seen in the mediolateral length of the

outlet, with a difference of 11.5 mm between the pre- and post-cesarean samples. This

further complicates the birthing process by shape deformation and overall area reduction

of the outlet. Even with the shape deformation, the posterior border of the outlet

increased by 7.5 mm, increasing overall canal space.

While most of the variables in the pelvic morphospace increased overall, the

significant reduction of the variables discussed caused shape shifts that create issues for

neonates trying to fit within these differently shaped levels of the pelvis inlet. However,

for neonates that do fit within the canals, these shifts from elongated inlet m-l to

midplane a-p further facilitate rotation within the canal that is part of the modern labor

process. The combination of these changes encourages fit and rotation of the neonate,

thereby facilitating natural labor.


32

Chapter VI

Conclusion

Between pre-cesarean and post-cesarean samples, there is significant overall

expansion of the pelvic canal. Even though multiple factors likely influenced this

expansion, what is important to focus on is the significant reduction in some of the

measurements. These reductions happen to exaggerate the shape of the pelvic canal in a

way that encourages neonatal rotation necessary for natural birth. Overall, these changes

lend itself to a pelvis that is better adapted to natural labor. While it is not known to what

extent cesarean section in the United States affected pelvic anatomy, there is a clear

correlation between female skeletal pelvic morphology and the timespan during which

the cesarean section was introduced. This medical technique eliminated the selection

pressure on the female population for a specifically shaped pelvis to facilitate natural

labor processes.

Nutrition, Maternal Age, and Bipedalism

There is not one sole factor that factors into the changes documented in this study.

However, it is important to acknowledge environmental influences such as nutrition and

maternal age. Average maternal age increased over the past century, which in turn

corresponded to higher birthweights in neonates. Lower birthweights often result in

stunted skeletal growth, which would factor into the overall smaller pelvic canal in the

pre-cesarean sample. Also, different standards for nutrition and less advanced medical


33

practices would have contributed to the reduced average measurements of the pelvic

canal in the pre-cesarean sample. The increase in average maternal age, more advanced

nutrition, and medical practices all contribute to the larger pelvic canal in the post-

cesarean populations.

As previously mentioned, modern, post-cesarean females are more energetically

efficient than males with regards to bipedalism. There is not any literature on energetic

costs for sexes throughout the centuries, so it is difficult to determine how costs have

changed recently. However, with the elimination of the selection pressure that labor

placed on females, we can hypothesize that the female pelvic anatomy would shift to

better adapt to costs of bipedalism, reflected in the study reviewed in the literature

review.

Future Research

There are a number of avenue for expansion in this study to further explore the

changes within the pelvic morphospace in recent centuries. One of the ways to reduce the

likelihood of other environmental factors, such as nutrition, affecting pelvic anatomy is to

repeat the parameters of this study, but with white males. By collecting data from the

same skeletal collections (Hamann-Todd collection at the Cleveland Museum of Natural

History and William M. Bass collection at University of Tennessee-Knoxville), we can

get two male sample populations that are of similar provenience, age, race, and class,

comparable to the female samples collected. The study would apply the same statistical

analyses, including t-tests, f-tests, MANOVA, and discriminate analysis. These results

are key in eliminating the probability that the changes in the female pelvic anatomy were


34

due to environmental changes. Based on the studies with secular long bone changes done

by Jantz and Jantz (1999), the results would provide valuable insight. As mentioned

earlier, men exhibit the most sensitivity and greatest amount of change in response to

environmental changes. A greater change in male pelvic anatomy would indicate that

these changes in females were more likely to have been due to environmental factors and

would not support the hypothesis. However, significantly higher rates of change in

females than males would decrease the likelihood that these changes in females were

solely due to environmental factors, such as nutrition. While the literature reviewed in

this study sheds light on how nutrition affects ontology in humans, another investigation

with male samples from the same collections would elucidate the issues with some of the

results from this study.

The results from the proposed study would also be important in determining

morphological differences and similarities between sexes. As previously discussed in the

literature review section of this thesis, studies by Jantz and Jantz have discussed the

significant differences between male and female skeletal anatomy. Since the selection

pressures for labor have been removed with the introduction and popularization of the

cesarean section, one topic of exploration is to look at morphologies between sexes both

before the introduction of the cesarean section and post-introduction to see not only what

differences exist, but also what similarities the post-cesarean samples share. If the need

for a certain type of pelvis is removed, then a hypothesis could be made that the female

pelvis would then be better adapt itself for obligate bipedalism. This evolution would

shift female pelvic anatomy towards a pelvis that is biomechanically more efficient.


35

In the repetition of this study within the scope of the United States and even globally,

it is important to take into consideration the effect that stature has on the morphospace of

the pelvic canal, and what biases it may introduce into the sample datasets.

To take these studies globally would provide valuable insight regarding to what

degree cesarean sections affect the morphology in females. This could be determined by

repeating the study with populations who have rates of cesarean section much lower than

the United States’ average, similar to the Zuni-Ramah Native Americans. The Zuni-

Ramah reported a cesarean section rate of 7.3% in 1996 (Wagner p. 49). Studies of

Native Americans would be extremely difficult due to many cultural barriers and

NAGPRA laws, but a population that has similar cesarean section rates would be an

effective sample. It is also important to conduct this research with populations that have

significantly higher rates of cesarean sections than the United States, such as Brazil,

where rates in private hospitals have reached as high as 95% of all births. Comparing the

results of these types of populations to the results of the United States study could help

support the hypothesis that cesarean sections significantly impact female pelvic anatomy,

and in a short number of generations. Hypothetically, populations with lower rates of

cesarean section would exhibit either non-significant or very small amounts of change in

the 14 dimensions measured, while populations with higher rates of cesarean sections

would not only demonstrate high significant differences, but also the greatest amount of

change between pre and post-introduction. However, results that deviate from the

proposed hypothesis could indicate either greater influences by nutrition and

environment, or that the cesarean section was not a significant influence on female pelvic

anatomy.


36

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38

Appendix A

Pre-Cesarean Sample Data (Hamann-Todd Collection, Cleveland, Ohio)

Age

Bi-Iliac Breadth

(mm) Inlet A-P Inlet M-L Inlet

Posterior Inlet

Anterior Midplane

A-P Midplane

M-L

35 258 120.01 114.84 25.41 140.26 123.48 37.96

20 239 131.04 169.46 31.42 151.88 127.84 54.45

38 114.87 143.06 28.09 137.18 138.89 45.91

45 281 115.41 148.02 19.13 138.23 147.09 40.77

38 257.17 106.85 122.68 18.12 131.35 120.05 103.92

27 256.19 115.37 131.9 16.88 132.33 117.42 110.44

38 285.49 115.87 126.13 24.68 139.56 121.34 100.12

50 286.07 122.06 138.25 29.3 146.48 136.14 116.31

65 289.02 102.27 137.06 14.79 128.41 133.79 108.53

40 276.03 114.37 134.09 23.95 138.66 134.06 117.65

40 252.94 104.33 125.58 22.7 129.57 117.13 106.53

50 265.12 104.2 126.15 23.86 137.3 120.03 99.74

35 260.99 105.57 131.87 18.59 130.75 111.84 98.92

25 265.24 121.12 136.75 35.36 162.45 144.84 119.68

53 316.09 116.57 144.33 21.9 142.11 128.66 117.74

34 280.39 118.05 127.88 20.87 135.03 117.03 98.23

56 294.71 102.05 145.9 18.14 138.04 127.38 119.76

43 264.23 111.09 127.02 23.93 133.61 126.98 103.9

38 290.77 120.55 136.27 19.7 135.56 130.53 103.17

72 290.71 117.95 135.18 27 141.62 130.97 105.14

60 269.72 93.41 136.82 20.88 130.3 114.76 107.9

49 262.68 107.42 140.18 22.68 137.08 119.2 119.38

25 271.54 109.06 131.26 19.54 129.1 105.52 108.55

51 273.69 89.98 130.62 16.94 119.35 100.89 103.01

23 236.22 106.89 109.85 19.13 119.73 109.65 88.46

40 294.19 103.27 139.43 19.55 130 122.95 110.37

18 257.68 101.07 121.42 20.78 133.61 121.14 99.67

38 271.05 95.71 131.47 12.45 116.57 121.68 106.9

43 266.05 105.23 138.68 25.63 140.08 118 90.56

62 262.14 85.64 131.89 16.83 127.14 113.83 109.2

35 267.33 116.18 118.47 13.43 125.23 108.7 99.58

30 261.42 117.27 131.7 18.01 137.44 125.02 103.73

16 246.42 115.44 118.92 30.11 133.17 124.69 85.98


39

30 271.14 117.39 119.19 18.95 133.25 121.98 104.64

60 272.15 119.94 134.68 22.31 138.09 121.82 106.63

36 281.56 121.24 141.67 24.42 143.13 137.98 126.05

35 292.11 112.33 138.33 18.01 137.42 113.92 109.66

36 246.95 110.75 117.76 20.14 131.92 130.49 99.73

29 284.76 113.37 130.16 14.81 123.96 117.78 105.12

27 250.93 115.64 106.97 23.81 130.23 127.22 90.51

39 204.62 96.52 108.65 23.51 126 120.85 102.03

47 253.31 131.87 129.96 33.99 153.62 140.06 103.89

40 246.1 125.07 125.96 20.24 142.4 141.02 103.31

50 279.78 125.34 126.18 20.57 139.18 145.01 103.21

38 269.48 104.95 119.66 21.51 125.99 126.96 105.68

23 279.62 124.89 133.88 22.53 140.91 143.71 107.2

54 285.06 116.07 124.86 18.1 126.88 139.85 91.91

71 239.2 122.03 119.91 26.96 139.44 125.08 94.83

38 272.02 116.01 127.53 22.5 139.05 130.39 101.79

32 269.42 115.02 127.48 23.8 141.3 128.45 104.74

51 232.18 104.67 125.02 20.29 125.62 114.58 125.41

55 261.78 113.7 132.05 27.03 143.58 142.61 117.26

43 287.41 117.81 135.98 21.97 142.15 116.64 107.21

31 253.31 100.81 130.86 21.14 130.62 130.37 107.69

40 253.71 118.85 124.88 25.39 138.08 139.15 102.1

51 258.61 93.94 115.75 17.15 117.73 107.12 113.78

65 275.65 106.83 129.54 17.88 132.72 129.1 90.74

31 283.95 119.29 133.39 16.07 140.92 136.71 104.7

35 280.34 104.43 133.11 16.61 132.12 127.06 107.09

25 246.86 115.82 121.88 21.09 134.79 140.62 106.87

28 294.8 96.84 140.28 19.78 128.87 114.52 116.76

71 283.9 133.74 117.88 23.96 142.74 135.43 94.1

68 277.72 115.42 132.28 20.08 135.47 119.35 106.36

19 253.29 124.06 127.35 17.31 129 121.71 101.54

31 228.23 96.22 112.83 18.67 122.58 113.49 107.83

55 292.11 120.14 135.59 19.89 141.28 137.62 95.27

44 258.18 108.92 135.7 29.25 138.81 119.35 110.56

39 267.57 132.4 125.7 26.21 140.3 140.2 101.82

47 258.42 126.8 136.78 27.94 144.48 133.27 107.32

43 255.03 103.92 121.47 22.6 129.3 127.63 97.84

28 269.29 132.76 136.02 28.59 149.7 136.99 107.42

25 238.6 110.38 114.98 24.09 120.94 116.57 93.05

60 263.7 121.53 122.35 27.79 136.7 129.62 88.74

45 251.76 102.12 114.6 18.82 117.83 121.82 95.91


40

54 281.43 115.6 132.11 20.44 137.77 115.8 108.35

30 278.54 124.66 129.46 19.9 140.94 122.76 99.05

48 254.44 116.65 118.53 16.38 126.52 116.6 91.7

33 265.49 120.46 119.44 21.29 127.09 126.11 98.21

34 247.04 115.71 132.26 18.76 137.97 124.98 109.77

48 266.53 113.62 128.93 21.18 137.63 136.13 102.85

40 234.53 106.78 127.31 26.8 131.64 117.25 105.77

61 259.78 103.98 124.07 23.08 126.6 131.75 97.71

54 245.2 120 115.08 24.14 126.97 115.19 91.74

60 274.87 102.27 137.22 17.79 127.23 132.53 117.25

56 266.52 123.26 117.39 15.79 124.66 122.01 79.31

45 296.42 132.91 151.34 21.48 153.04 134.19 120.73

53 280.12 107.41 129.58 22.13 134.89 124.46 95.73

65 263.87 130.03 123.43 23.01 140.41 126.53 107.93

27 242.59 129.06 116.15 25.63 131.62 126.84 97.86

48 275.25 123.77 136.01 25.22 139.93 130.03 113.37

47 238.3 120.81 125.3 23.62 128.05 110.41 115.97

49 277 130.15 124.52 24.5 134.95 133.05 87.08

50 289.06 109.27 142.25 13.89 131.14 130.42 106.75

33 266.96 120.25 143.39 17.7 141.48 125.52 220.73

42 259.25 114.54 131.85 19.97 132.64 139.23 120.05

36 235.03 132.21 117.44 19.06 134.77 130.03 96.45

50 268.53 122.22 127.84 23.17 134.63 135.63 118.75

50 289.93 115.09 130.69 28.51 140.44 151.46 108.5

61 300.82 136.45 150.82 23.85 159.61 142.69 123.07

64 255.76 98.8 129.42 22.77 131.22 111.7 98.59

37 259.2 101.91 130.32 12.44 123.38 126.16 101.14

41 292.5 128.48 138.87 25.82 147.72 140.06 102.26

62 248.1 102.02 117.73 22.92 121.31 114.87 89.67

Midplane Posterior

Midplane Anterior

Outlet A-P

Outlet M-L

Outlet Posterior

Outlet Anterior

Canal Depth

68.67 92.56 96.35 85.78 78.28 82.93 112.77

76.84 93.63 118.02 115.58 91.91 90.94 126.38

76.95 96.42 124.1 105.16 90.84 93.04 112.69

79.45 97.15 134.99 68.34 82.03 89.88 120.51

72.18 90.25 109.83 109.19 80.34 77.67 111

67.25 89.72 95.63 128.82 69.12 94.6 104.59

70.43 93.66 107.31 123.63 83.74 90.3 123.89

87 91.79 113.92 120.88 92.19 85.63 121.3

85.13 99.35 112.02 117.18 83.8 83.43 108.05


41

82.67 95.03 114.53 118.3 85.39 82.22 114.25

74.47 89.42 106.34 111.39 81.43 82.55 109.77

70.5 88.99 102.23 112.95 74.23 82.74 103.22

64.54 90.64 94.25 108.12 66.89 82.95 111.12

80.31 98.07 128.09 121.27 87.02 84.47 124.22

77.07 98.93 122.14 118.79 85.59 85.2 113.95

63.37 91.52 109.21 106.75 66.32 83.25 104.72

75.03 96.64 124.63 121.46 84.84 97.38 106.82

70.07 96.81 115.02 111.37 75.12 86.73 112.42

67.87 98.95 110.98 112.7 67.99 91.78 116.65

68.37 100.37 99.44 113.03 53.07 87.36 122.9

69.25 91.37 111.92 113.05 76.78 82.97 104.5

80.34 94.89 104.81 133.79 88.76 93.44 113.77

55.07 87.22 87.28 121.71 73.56 83.02 116.81

64.44 73.16 84.72 101.52 65.33 64.37 94.83

63.4 79.04 102.82 105.19 77.8 74.55 106.6

66.84 98.01 113.88 120.11 82.91 85.31 106.32

73.11 89.56 110.71 113.68 79.28 83.62 112.55

79.31 87.92 123.16 106.69 88.62 83.06 98.26

60.54 93.23 108.51 95.52 75.37 85.52 115.32

61.26 95.27 100.85 118.36 75.74 88.88 105.46

55.85 90.8 96.65 111.92 60.71 89.47 104.37

61.95 99.6 110.52 116.89 72.1 90.08 102.76

68.84 85.62 127.81 86.32 83.52 80.36 116.16

68 91.09 92.31 119.5 63.52 86.39 111.88

73.13 89.8 110.1 108.15 80 81.73 105.69

86.01 98.73 128.73 134.69 103.94 93.49 123.94

66.97 91.05 110.44 116.3 69.93 87.94 118.9

71.18 87.2 117.68 103.92 86.49 79.09 105.93

71.23 87.3 108.6 114.99 85.43 110.3 110.3

56.43 93.25 113.48 99.07 76.26 70.6 108.8

71.67 83.94 116.41 119.57 93.7 75.64 105.9

77.52 97.65 111.68 119.53 80.08 95.06 134.73

71.9 97.51 121.67 113.65 85.66 86.07 115.66

73.87 95.1 130.61 121.99 87.08 93.15 112.1

74.61 88.17 122.45 118.88 96.2 76.86 99.87

88.67 90.64 133.25 122.65 98.43 92.13 116.92

80.49 85.94 131.23 105.85 90.87 81.69 112.03

65.61 87.74 111.2 102.35 76.03 79.4 106.04

73.55 87.72 113.46 110.47 79.45 84.28 111.05

72.98 88.74 113.92 114.86 80.33 85.38 113.2


42

73.61 91.57 100 127.11 76.38 86.23 92.36

78.47 95.73 117.05 124.4 89.43 92.24 118.74

63.24 95.65 111.19 106.75 73.48 94.75 108.47

73.65 90.8 121.5 121.93 92.99 89 110.25

78.58 89.37 127.41 102.13 88.41 83.23 107.41

66.93 79.72 91.17 121.27 66.16 74.86 89.33

63.56 86.19 91.75 83.16 117.8

74.93 97.15 131.56 118.02 96.59 87.64 115.37

65.55 94.28 111.72 112.76 79.89 88.43 110.33

76.46 88.25 129.36 115.94 91.39 83.48 113.51

67.3 90.46 110.41 129.26 96.98 85.75 119.44

63.42 94.19 125.61 110.79 84.45 85.06 121.06

72.43 91.8 104.87 112.59 78.42 83.92 118.94

58.29 88.03 108.64 110.96 74.85 85 108.68

65.83 83.65 94.9 109.74 79.89 80.02 105.62

67.93 95.36 116.22 98.74 74.97 86.04 123.04

64.46 95.52 98.81 109.72 65.31 84.87 103.88

73.29 92.93 124.24 112.56 91.61 87.47 113.06

69.61 93.58 114.31 119.79 86.24 84.92 118.7

70.8 89.71 117.67 110.3 76.44 88.35 99.75

77.7 94 128.15 127.04 98.85 95.31 123.83

54.98 84.56 108.91 102.77 72.62 83.2 104.62

64.96 85.86 116.53 81.01 82.19 79.92 117.52

68.15 78 115.98 100.64 79.56 76.99 104.39

63.29 92.08 102.53 112.97 74.95 91.51 114.58

63.87 86.93 107.14 106.27 77.61 83.53 102.41

53.28 89.13 107.06 105.26 65.43 87.26 110.12

68.89 85.7 114.24 107.74 84.45 80.2 111.74

71.79 89.75 109.26 128.08 84.48 83.94 107.77

67.11 96.9 132.16 111.14 89.23 89.19 116.87

68.08 81.34 119.15 109.58 90.46 78.77 111.24

72.16 89.25 118.14 93.7 87.3 80.46 111.11

57.66 85.81 108.05 97.88 66.52 82.04 105.12

78.58 95.95 123.48 118.91 84.91 95.51 105.82

55.54 86.71 118.74 83.27 72.46 76.74 112.02

82.52 100.81 125.14 124.61 89.55 95.02 117.96

57.8 93.02 113.52 106.01 77.94 87.36 121.89

72.22 87.28 107.98 108.98 82.27 78.85 110.96

79.61 78.82 126.53 111.03 92.67 83.33 110.21

76.29 94.61 125.1 130.57 93.77 94.78 111.77

64.55 85.35 99.44 115.97 79.9 82.39 110.45


43

69.68 89.98 121.67 85.44 78.58 81.06 115.2

76.59 89.4 121.84 104.36 83.46 88.32 104.03

75.04 99.33 120.98 121.08 81.18 93.56 112.16

82.1 92.21 130.73 123.09 98.53 85.37 106.2

70.55 83.89 121.55 110.79 92.78 82.64 108.17

85.98 90.33 110.84 130.92 87.61 81.33 111.57

80.36 97.29 145.87 113.09 97.69 91.76 105.1

82.93 101.48 129.51 127.38 81.08 98.53 121.37

61.68 82.11 107.67 103.18 80.1 80.43 104.7

61.03 86.72 109.14 116.35 83.16 83.98 102.69

76.78 90 127.84 112.05 92.58 85.56 114.41

59.08 87.11 107.78 93.09 68.83 77.69 109.75


44

Appendix B

Post-Cesarean Sample Data (William M. Bass Collection, Knoxville, Tennessee)

Age Bi-Iliac Breadth

Inlet A-P

Inlet M-L

Inlet Posterior

Inlet Anterior

Midplane A-P

Midplane M-L

53 244 102.5 103.5 20.2 111.2 105.9 64.2

64 242 124 118.2 15.1 123.7 132.7 104.6

62 247 126.1 123 20.65 115.2 116.3 115.1

52 285.5 112.9 135.4 15.24 107.1 128 108.6

61 280 126.4 154.36 21.3 121.9 136.2 116.7

61 259 116.1 109.7 24.2 112.9 118.6 98.04

55 305 121.6 127.7 27.6 126 132.6 111.2

66 277 119.9 142.32 23.5 129 78.68

60 290 112.7 136.7 13.1 126.1 132.2 91.4

58 265 115.4 127.3 25 111.3 120 94.4

68 269 121 140.6 20.5 123.2 120.3 99.2

53 264 121.1 143.4 29 108.4 126.8 97.5

62 28.2 111.8

67 257 111.1 125.8 15.8 113.2 117.7 106.28

62 256 107.5 137.7 26.1 123.5 136.6 112.1

62 256 116.9 134.4 22.7 117.3 124 95.3

69 255 118 137 23.5 123.2 125.5 104.6

50 260 112.3 145.6 18.1 116.2 128.5 92.5

64 261 106.1 117.8 17.1 109.9 118.3 92

57 306 124.5 159.1 20 131.3 135.8 84.2

66 286 101 149.9 18.3 120.4 137.8 83

57 250 115.8 116.7 20.6 100.9 127 81.1

43 278 129 140.9 20.59 127.1 133 85.8

64 295 108.7 137.5 29.3 115.4 137.4 107.2

54 292 113.6 150.9 27.7 127.2 126.7 106.4

57 263 114.4 131.6 25.2 120.8 139.4 74.7

50 289 112.1 135.6 19.35 123.7 141.7 84.7

50 264 116.8 125.3 27.1 111.9 133.4 89.4

60 289 128.7 146.7 24.8 118.4 136.8 91.8

60 287 108.4 134.3 12.5 120.5 126.7 82.7

56 257 113.2 132.7 20.8 118.8 140.4 106.9

50 257 138.9 130.5 21.7 127.2 142 92.4


45

64 255 125.8 128.7 24.1 115.2 130 94.6

58 286 124.3 162.2 22.7 124.2 137.5 112.7

42 259 126.3 157 30.8 120.7 141 102

68 252 115.4 124.7 27.7 118.9 140.9 95.3

70 277 117.4 145.1 20.8 112.61 155 96.5

54 252 108.5 129.3 24.3 107.9 129.7 95.5

52 279 118.9 107.8 23.3 118 138.6 80.9

69 275 123.9 124.6 19.7 118.1 131.4 106.9

49 299 116.6 156.5 22.3 133.7 148.9 93.3

69 265 103.5 126.7 21.6 108.8 116.4 97.3

46 258 115.9 132.7 27 112.3 123.8 107.2

54 255 118.5 116.6 24.8 112.3 128.3 96.2

60 244 107.9 139.2 21.4 115.7 125.9 134

50 297 141.4 141.7 36.1 132 150.7 96.8

64 269 115.2 141 28.9 114.7 134.6 109.6

51 278 129.3 148.5 20.9 122.3 139.2 94.2

67 285 105.3 149.2 21.3 116.5 135.8 114.3

49 290 126.4 141.3 25.9 124.4 134.4 106.4

60 256 119.8 137.2 13.6 120.8 132.7 84.8

48 270 122.6 122.7 22.6 117.4 141.1 105.5

69 290 109.4 146.8 14.7 118.1 123.3 88.2

58 280 102.1 145.9 15.2 110.4 123.1 92.9

69 245 97.7 112.2 21.6 102.6 127.6 91.5

51 272 121.8 143.9 25.1 111.6 139.1 104.3

58 262 120.8 124.8 29.5 113.8 129.3 121.6

58 260 111.8 136 21.5 114 147.3 108.5

50 274 128.1 138.2 17.9 122.5 146.5 89.3

48 254 109.6 133.5 19.8 111.5 128.2 94.3

60 264 121 128.2 15 116.7 122.9 82.4

44 246 121.4 141.7 25.3 112.8 135.7 110.6

62 259 127.4 133.5 23.6 117.7 132.8 116.6

63 274 118.2 137.1 16.5 117.9 119.5 110.7

65 235 112.8 109.8 21.9 116.5 136 98.9

59 280 126.6 140 26.9 124.8 129.8 75.6

51 271 122.7 112.9 25.2 111.8 130.9 73.1

44 264 129.2 138.8 35.4 123 137.7 95.7

67 255 111.1 123.9 22.1 109.1 126.2 69

64 255 114.4 131.3 16.4 110.1 135.6 107.4

63 254 126.3 124.9 19.9 121.4 132.2 83.2

58 241 113.4 125.1 25.8 107 121.6 102.5

45 284 120.3 134.4 19.7 115 134.9 92.1


46

38 247 117.7 147.8 24.4 115.1 138.3 102.2

61 285 124.1 136.4 25.2 120.5 138.7 99.4

57 256 120.2 114.6 32.8 122.1 142.4 95.8

45 254 125.6 138.1 21.6 122.4 120.6 91.9

59 244 116.7 66.2 17.9 126.4 107.4 108.5

66 293 131.2 136.4 25.6 128.2 138.1 118.7

69 261 122.4 120.6 20.8 121.8 140.8 82.3

31 246 125.2 117.8 28.1 122.4 142.2 90.1

51 251 118.7 128 16.8 115.9 119.3 100.2

67 255 114.5 120.5 19.2 115.1 133 101.1

39 270 112.9 113.5 26.5 112.6 140.8 92.9

51 258 141.1 145.2 36.6 126 149.7 99.4

70 273 105.8 148.7 11.7 116.8 131.7 91.1

29 210 96.5 114 28.4 101.3 119.8 79.2

67 223 112.7 110.7 24.6 105.3 135.7 82.3

66 274 109.5 144.6 17.5 113.6 132.7 118.3

55 264 109.6 131.3 27.1 126.9 128.2 96.8

67 279 138.9 135.2 31.8 128 153.7 85.9

46 285 129.2 144.7 28 132 143.9 86.1

57 270 129.3 123.2 25.1 119.4 145.2 94.62

36 273 134.1 130.1 29.2 123.6 142.8 101.5

52 270 116.9 137.7 19.7 121.6 133 87

63 242 112.1 107.6 26.9 108.4 126.9 79.8

58 236 121.2 114.2 24.4 114.9 126.6 82.2

60 270 114.7 137.8 26.4 120.5 134.4 100.9

69 255 110.4 131.1 23.6 109.4 125.9 88.6

56 286 128.4 155.6 26.5 129.5 135 113.3

55 282 115.1 141 30.1 123.4 140.5 107.2

65 234 112.4 124.6 15.4 107.2 125 103.4

56 257 132.2 103.8 32.2 116.7 125.8 108.2

68 277 119.5 155.9 27.5 121.6 139.2 101.4

44 283 137.9 152.6 26.9 118.9 136.3 117.3

67 252 117.2 137.6 24.8 119.9 128.9 101.9

47 280 132.1 164.2 22.4 132.5 150.2 114.2

50 272 118.5 152.2 20.4 116.2 127.5 88.7

67 259 127.5 155.5 20.9 112.2 128.5 104.6

60 253 125.4 136.9 25 123.1 143.8 93.9

54 264 110.9 155.3 25.9 124.06 139 122.2

66 271 113.7 135.4 24.5 119.3 136.6 110.9

51 262 121.8 142.2 22.6 116.7 139.9 93.5

57 270 127.8 129.6 27.2 120.4 135.6 87


47

60 284 117.5 133.3 21.6 117.3 145.1 103.2

58 275 109 127.5 15.7 109.4 125.6 94.6

34 273 109.3 142.5 15.4 116.5 148.3 116.8

51 269 117.2 126.7 20.5 116.1 125.9 88.3

55 254 112.5 122.8 16.7 108.5 114.3 107.9

52 270 126.2 132.7 18.9 118.6 132 94.2

58 271 132.6 147.1 22.7 120.1 140.5 122.8

42 262 125.1 136.5 24.1 115.2 131.7 107.7

31 244 112.9 125.9 16.6 99.1 118.3 80.8

Midplane Posterior

Midplane Anterior

Outlet A-P

Outlet M-L

Outlet Posterior

Outlet Anterior

Canal Depth

67.5 77.3 99.4 64.4 86.3 66.6 114.3

80.9 100.7 123.4 126.56 97.7 101.8 111

68.37 93.6 111.7 126.14 81.03 95 119.5

73.4 96.7 130.1 114.6 84.6 93.6 103.6

80.9 96.3 127.8 163.1 97.3 105.2 104.9

76.2 94.3 124.5 120 99.8 95.4 106.3

85.5 97.6 130.5 118.4 100.5 102.3 118.7

105.7 113.3 100 107.5

77.1 97.5 112.5 103.76 83.3 107.7 106.4

75.8 92.4 96.33 106.9 68.4 92 92.9

68.1 99 111.4 105.8 81.4 94.9 111.8

87.9 86.7 109.6 105.4 83.3 90.3 112.4

95.5 88 112.1

71.6 94.3 109.3 116.5 78.8 89.7 104

77 95.4 130 130.84 103.3 88.4 112

71 87.9 103 87.6 57.5 90.6 103.8

71.9 97.6 114.7 107.6 82.9 92.8 102.6

86 91.5 121.1 98.4 85.3 95.4 104.8

62.4 88.3 97.9 82.8 64.9 82.7 107.2

71.6 100.2 138.5 90.9 92.3 93.6 103.5

80.7 100.5 121.4 89.2 89.4 94.5 99.3

71.6 94.4 116 87.8 84.1 95.3 104.33

75 94.1 117.7 97.8 89.4 85.7 126.1

82.3 95.8 121.5 126.8 93.8 91.8 120.4

75.5 99.6 116 123.8 93.5 97.5 130.1

78.5 100.5 133.1 101.4 105.1 91.4 125.4

82.9 102 130.2 91.2 99.9 99.2 113

81.9 96.4 124.2 105.1 93.6 89.9 114.4

80 101.2 124.5 114.3 85.2 99.2 112.4


48

72.4 100 122.1 70.2 82.8 90.7 109.6

77.3 98.2 115.8 118.1 92.8 88.2 116.7

83.3 95.7 137.1 92.6 107.9 87.1 124.2

71.2 94.7 101.9 85.7 74.7 86.2 119

73.6 97.6 112.8 127.2 78.9 91.2 114.5

79.9 101.6 125.3 101.9 92.6 88.5 113.3

84.6 95 116.9 65 95.4 80.8 121.5

96.6 98.6 147 104.8 101.8 101.4 116.3

70 94.3 117.6 102.2 79.7 86.7 108.6

88.7 95.7 122.1 67 89.5 86.7 118.9

85.6 89.5 119.4 109.9 71.3 90.4 110.5

86.5 101.1 119.2 109.3 85.5 92.6 124.8

77.1 88.2 94.3 107.1 66.3 82.5 110.8

78.1 86.7 102.1 119.7 76.5 73.3 122.2

77.7 86.5 106.2 93.1 77.8 85.8 113.9

82.4 99.7 111.6 155 101.8 81.9 113.5

72.8 105.4 135.2 88.8 89.2 90.9 144.1

77.9 92.6 116.1 97.5 89.2 86.5 121.8

68 104.1 126.3 91.5 90.1 84.2 126.5

74.6 101.8 123.3 116.5 90 90.1 103.7

77.8 99.8 136.7 101.4 104.5 91.1 135.4

67.7 93.4 117.1 90.6 85.4 87.2 118.8

84 101.1 124.6 98 89.3 91.3 121.1

64.8 97.3 97.7 73.8 80.3 92.2 116.7

76.8 85.7 120.3 91.5 91.9 76.9 108.3

75.8 90.8 92.7 96.2 73.4 85.1 112.2

78.4 89.8 114.2 110.8 86.5 81.1 110.5

78.6 88.3 1001.1 117.1 74.8 83.4 120

85.8 98.1 143.3 110.9 106.6 88.8 114.4

79.2 100.5 139 83.8 91.4 84.5 129.1

70.4 90.7 113.5 86.3 82.8 79.9 120.8

54.3 93 105.7 97.7 60.5 90.8 107.3

80 93.9 106.2 102.5 84 85.3 127.8

82.3 97.4 120.2 109.5 106.5 84.1 133.4

73.1 92.7 110.5 113.9 87.6 81.2 118.5

82 92.5 125.5 68.1 101.5 75.2 119.3

74.3 101 121.3 65 84.1 89.8 118.3

66.1 89.2 111.3 68.4 74.8 74.6 119

84.7 104 117.2 87.9 89.7 85.2 137.7

70.6 88.8 116.9 78.8 72.4 82.2 121.2

76.1 96.3 110.8 115.1 81.2 89.9 118.1


49

75.2 92 117.5 83.1 94.8 76.3 117.2

66.7 81.7 104.4 111.9 67.6 78.9 101.7

80.8 92.5 122.5 92.7 95.8 82.6 126.6

74.7 88.5 126.3 120.6 94.4 84.4 116.5

85.7 95.1 127.6 100.4 106 94.8 131.2

80.9 102.4 131.6 86.5 88.9 87.7 124.1

62.4 92.7 104.9 48.9 76.4 83.4 119.7

56.6 86.2 93.3 102.8 55 83.4 109.1

74.6 100.1 121.2 125.7 86.4 92.7 129.3

83.7 86.7 119.8 81.4 87.2 81.1 123.6

77.1 93.9 127.5 99.1 96.5 81.7 133.4

61.3 96.4 107.7 97.3 83.1 85.8 111

70.3 97.3 130.1 116.5 94.8 88.6 127.3

76.6 96.4 139.2 93.2 99 87.1 116.8

75.8 99.5 131.7 97.2 98.5 89.4 124.2

68.3 92.2 115.5 63.5 84.2 81.9 109.7

75.3 84.3 114.4 80.2 97.3 74.8 113.2

72.5 94 129.6 83 90.5 80.9 116.9

75 96.9 128.9 106.1 98.5 88 123.4

79.1 97.6 116.3 96.7 102.6 85 125.6

85.8 100.3 123.2 104.7 76.3 92 127.9

77 96.4 118.1 89.2 89.6 87 134.5

86.6 89.1 132.1 101.3 104.4 78.8 119.7

84.5 94.4 120.4 113.1 99.3 84.7 134.5

68.7 100.7 119.3 89.5 99.3 85.2 130.2

67.8 93.2 116.7 73.9 81.4 85.7 120.6

60.7 93.6 106.7 104.1 83.3 78.6 120.8

73.8 104.1 113.1 100.5 94.9 92 127.6

65.5 93.3 109.8 99.8 83.1 80 119.4

77.3 107.9 125.5 104.1 101.5 85.4 134.6

82.8 104.2 122.5 114.9 95.7 88.8 130.2

71.2 86.6 111.5 89.6 80.4 77.9 105.5

69.2 110.1 111.7 93.8 84.7 92 115.5

71.8 101.1 130.4 91.1 96.3 85.3 118.9

77.3 93.7 124.8 113.8 92.6 80.5 124.1

72.3 97.5 122 91.4 93.1 85.8 118.9

79.3 116.6 137.5 129.4 109.2 109.7 141.8

67.7 88.6 106.3 76.2 83.1 77.5 123.3

61 85.9 103.1 118.7 86.5 80 110

81.8 93.3 133.2 99.8 103 85.1 123.3

81.2 96.9 119.8 96.8 97.8 80.1 125.6


50

67.7 101.6 117.8 110.4 93.7 89.9 108.9

87 91.5 96.5 84.6 125

81.8 99.9 120.5 96.5 92 91.7 129

86.4 94.1 135.9 119.9 105.8 79 115.6

84.2 92.9 121.4 100.2 105.1 82.3 116.3

89.9 95.8 135.4 112.1 107.3 90.1 110.1

76.3 89.9 114.7 64 77.5 85.2 112.4

61.9 91.3 108 114.7 83.9 78.8 109.5

79 90.2 127.6 91 97 74.6 111.8

84.7 96.4 120.2 118.7 102.4 81 121.7

67.5 99.7 125 121.1 98.1 83.5 111.9

67.5 81 122.7 93.1 97.6 76 108.6


51

Appendix C

F-Test Results

F-Test Two-Sample for Variances

Midplane A-P

Variable

1 Variable

2

Mean 126.4079 132.7248

Variance 105.9351 86.50705

Observations 103 121

df 102 120

F 1.224584

P(F<=f) one-tail 0.142645

F Critical one-tail 1.366584


Midplane M-L

Variable

1 Variable

2

Mean 103.2699 97.75344

Variance 355.1938 156.5422


df 102 121

F 2.268998

P(F<=f) one-tail 8.68E-06



Midplane Posterior

Variable

1 Variable

2

Mean 70.59573 75.97083

Variance 62.82312 56.96087


df 102 120

F 1.102917




52


Midplane Anterior

Variable

1 Variable

2

Mean 95.30488 90.99816

Variance 35.99391 30.06821


df 122 102

F 1.197075




Outlet A-P

Variable

1 Variable

2

Mean 126.5111 114.2076

Variance 6603.443 130.1203


df 119 101

F 50.74876




Outlet M-L

Variable

1 Variable

2

Mean 100.2582 111.773

Variance 333.5613 138.5471


df 121 102

F 2.407567




53


Outlet Posterior

Variable

1 Variable

2

Mean 89.15858 81.67255

Variance 125.7994 91.53871


df 119 101

F 1.374275




Outlet anterior

Variable

1 Variable

2

Mean 87.1 85.53252

Variance 52.17869 40.73619


df 122 102

F 1.280893




Canal Depth

Variable

1 Variable

2

Mean 117.6848 111.3142

Variance 88.46179 54.96813


df 122 102

F 1.609329




54

Appendix D

Normal Probability Plot of Residuals


55


56


57


58


59


60


61


62

Appendix E

Residuals versus fit plots


63


64


65


66


67


68


69


70

Appendix F

Test and Confidence Intervals for Two Variances


71


72


73


74


75


76


77

Popularization of the Modern Cesarean Section in the United States and its Effects on Female Pelvic Morphology

Documents