BDIMS

download.file("http://www.openintro.org/stat/data/bdims.RData",
              destfile = "bdims.RData")
load("bdims.RData")

Renaming Variables and Creating Subsets

sex <-bdims$sex
age <-bdims$age
hgt <-bdims$hgt #height of each participant in centimeters
wgt <-bdims$wgt #weight of each participant in kilograms
elb.di <-bdims$elb.di #elbow diameter in centimeters
wri.di <-bdims$wri.di #wrist diameter in centimeters
kne.di <-bdims$kne.di #knee diameter in centimeters
ank.di <-bdims$ank.di #ankle diameter in centimeters
sho.gi <-bdims$sho.gi #shoulder girth in centimeters
che.gi <-bdims$che.gi #chest girth in centimeters
wai.gi <-bdims$wai.gi #waist girth in centimeters
hip.gi <-bdims$hip.gi #hip girth in centimeters
thi.gi <-bdims$thi.gi #thigh girth in centimeters
bic.gi <-bdims$bic.gi #bicep girth in centimeters
for.gi <-bdims$for.gi #forearm girth in centimeters
kne.gi <-bdims$kne.gi #knee girth in centimeters
cal.gi <-bdims$cal.gi #calf girth in centimeters
ank.gi <-bdims$ank.gi #ankle girth in centimeters
wri.gi <-bdims$wri.gi #wrist girth in centimeters

fh <-subset(hip.gi, sex =="0") #Female hip girth
mh <-subset(hip.gi, sex =="1") #Male hip girth

Exploring Relationships in Body Dimensions

Introduction

The following data provides the body girth measurements and skeletal diameter measurements, as well as age, weight, height and gender,for 507 physically active individuals - 247 men and 260 women. Much of the data supports the hypothesis that body build (skeletal) variables and height predict scale weight substantially better than height alone. Similar data is often used in forensic and ergonomic studies to discover how a variety body dimensions can be used to predict the height and weight of a person. Specifically, forensic science will use girth and diameter measurements to determine the appearance and gender of a victim.

Data Introduction

Trunk and limb girths were measured at twelve well-defined sites for 247 men and 260 women. The sites included shoulder, chest, waist, navel, hip, thigh, bicep, forearm, calf. Fixed girths were also included like the wrist, knee, and ankle.

Nine skeletal measurements (diameter measurements) were included in the study. A broad-blade anthropometer was used to measure the biacromial, biiliac, bitrochanteric , and chest diameters along the trunk and a smaller version of this anthropometer was used for the four skeletal measurements along the limbs - the elbow, wrist, knee, and ankle diameters. These measurements typically remain fixed through adulthood.

In addition to the skeletal and girth measurements, recorded in centimeters (cm), each subject had his or her age (years), weight (kg), height (cm), and gender recorded.

The individuals involved in the study were primarily in their twenties and early thirties, with a scattering of older men and women, all physically active (several hours of exercise a week). The data set does not constitute a random sample from a well-defined population.

Side-by-side histograms for the sampling distributions

par(mfrow=c(1,2))
hist(fh, main = "Female Hip Girth", xlab = "Hip Girth in centimeters", col = "pink")
hist(mh, main = "Male Hip Girth", xlab = "Hip Girth in centimeters", col = "lightblue")

summary(fh)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   78.80   90.75   94.95   95.65   99.50  128.30

summary(mh)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   81.50   93.25   97.40   97.76  101.55  118.70

Comparative Histogram Analysis The female hip girth distribution is uni modal and symmetric with a center of approximately 95. The male hip girth distribution is uni modal and symmetric with a center of 97.76.

One of the most defining qualities of a women is the hips and pelvic breadth. This led me to assume that the average woman would have a larger hip size than a man, so I was surprised when the data revealed that the average man in this study had larger hips than the average woman. However, I believe that the difference between waist and hip girth will be larger among women.

fw <-subset(wai.gi, sex =="0") #creates a new value that seperates males and females by waist girth
mw2 <-subset(wai.gi, sex =="1")

par(mfrow=c(1,2))
hist(fw, main = "Female Waist Girth", xlab = "Waist Girth in centimeters", col = "pink")
hist(mw2, main = "Male Waist Girth", xlab = "Waist Girth in centimeters", col = "lightblue")

summary(fw)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   57.90   64.75   68.30   69.80   72.75  101.50

summary(mw2)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   67.10   77.90   83.40   84.53   90.00  113.20

Comparative Histogram Analysis There is a larger difference between the average female’s waist and hips than a man’s. The distribution of female waist girths is uni modal and skewed right with a center of 68.30 centimeters. Male waist girth has a slight skew right, is uni modal, and has a center of 83.40 centimeters. The difference between a the average female’s hips and waist is approximately 26.65 centimeters. Where the difference between a males waist and hips is approximately 14 centimeters.

Comparing Scatterplots

plot(fh, fw, main= "Female Waist and Hips Girths", xlab = "female hip girth", ylab = "female waist girth", col = "pink2")

plot(mh, mw2, main= "Male Waist and Hips Girths", xlab = "male hip girth", ylab = "male waist girth", col = "blue2")

The males in the study have a greater variability than the females because there is a much larger range. However, both scatter plots reveal that as hip size increases, waist size increase. Reinforcing the idea shown in the histograms above, there is greater disparity between female waist and hip size because the data is condensed in the lower left corner of the scatter plot.

Inferential Statistics

Gathering Samples

HYPOTHESES Null hypothesis: There is no relation between female hip and waist size. Alternative hypothesis: Females have significantly smaller waists than hips

set.seed(53019) #allows the code chunk to be ran repeatedly without changing
fwmeans <- rep(0,50)
for (i in 1:50) {
  sam <-sample(fw, 10)
  fwmeans[i] <- mean(sam)#creates a new sample that allows for a T-test to be ran
}

t.test(fh,fwmeans)

## 
##  Welch Two Sample t-test
## 
## data:  fh and fwmeans
## t = 48.626, df = 236.11, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  25.12153 27.24305
## sample estimates:
## mean of x mean of y 
##  95.65269  69.47040

The p-value is essentially 0, therefore I will reject the null. There is sufficient evidence that female waist and hip size is related.

Confidence Intervals for the TRUE mean difference of female waist and hip size

I am 95% confident that the TRUE mean difference of female’s waists and hips in this sample is between 25.12 centimeters and 27.24 centimeters.

Conclusion

By examining data collected on body dimensions, I wanted to highlight the differences between male and female body proportions. I focused primarily on the hips and waist dimensions because I believed I would find the greatest difference there. Males on average have bigger hips than females (typically because all of their body proportions are bigger than females). However, the difference between waist and hip size is much greater in females than it is in men. With more time, I would have liked to explore some of the more tedious measurements, like the wrists, ankles, knees, etc., to see if there is any outstanding difference in skeletal measurements between men and women.