Biometrics and Statistical Analysis of Data
What Is Biometrics?
In this lab exercise, you will learn more about using metric
system measurements for height and weight, how to read lab equipment and
interpolate digits, and how to calculate averages and standard deviations to
analyze data. Also, in this lab, humans (Homo sapiens) will be used as
an example to illustrate Darwin’s concept of intraspecific variation.
In biology, as in other sciences, gathering numerical data to
test one’s hypothesis and subsequently performing a statistical analysis on
those data are of utmost importance when interpreting the data and drawing
any conclusions from them. Due to a variety of factors, despite the most
careful observations, there will always be some variation in the data
collected, hence the necessity for a statistical analysis of those data.
Biometrics is the application of statistical methodology to analyze
biological data.
Interpolation of Data
In collecting data, it is important to know how to correctly
read the equipment being used. This frequently involves interpolation
to obtain the last digit of the data. Interpolation is “reading between the
lines” — for example, if you’re looking at a clock that only has 5-min.
markings on it and you read a time of 8:53, you are interpolating the “3” by
estimating how far between the “0” and the “5” the minute hand of the clock
is. Similarly, when reading the scale on a piece of scientific apparatus,
it is also necessary to interpolate, to read between the lines. For example,
in the illustration, above, if the numbered divisions represent grams, then
the marked divisions in between represent tenths of a gram. This scale must,
then, be read to the one-hundredths of a gram by envisioning ten divisions
in the white space in between the tenth-gram markings.
Also, in biology, as in other sciences, the metric system is used.
Thus, we measure an organism’s weight in grams or kilograms and its length
or height in centimeters or meters.
Statistical Analysis
To evaluate these numbers, it is necessary to employ several
statistical concepts. The mean or average
(X)
of a set of data is a measure of “central tendency” of a group of numbers,
such that the total of the deviations of the numbers above the mean is equal
to the total of the deviations of the numbers below the mean. For example,
for the numbers 1, 3, 5, 7, and 9, the mean is 5, so the deviations of each
of the numbers from that mean are –4, –2, 0, 2, and 4, respectively. Note
that the absolute values of |2 + 4| and |(–4) + (–2)| are equal. Further,
note that the sum of the deviations around a mean should always be 0. The
mean is the total of the values divided by the number of data points. This
is expressed mathematically as:
X = (ΣXi)/N.
Σ means sum, Xi means all the
individual values, and N means the number
of items. The closer the mean of a group of numbers is to the true value,
the more accurate that mean and group of numbers are.
Another concept that is sometimes used is that of the
median, which is the data point above and below which one-half of the
data points lie. That means that if there is an odd number of data points,
the median is the number that’s in the “middle” of the list, just by counting
in from both ends. If there is an even number of data points, the median is
the average of the middle two. For example, for the numbers 2, 6, 7, 14, and
56, the median is 7. For the numbers 2, 6, 7, 9, 14, and 56, the median is
(7 + 9)/2 = 8.
The mean is preferred over the median as a measure of central
tendency in a group of data, but there might be some situations where the
median would be a better indicator. If a distribution is symmetrical, the
mean and median should be about the same, but if a distribution is skewed,
then the median might be a better measure to use than mean. For example, if
a statistician was looking at family income in an area where four families
had incomes of under $20,000 while one family had an income of over
$1,000,000, then median would be a better indicator of “typical” family
income in that community. The median is less sensitive to extremes in the
data than the mean. For example, as pointed out above, the mean of the
numbers 1, 3, 5, 7, and 9 is 5, and so is the median. However, for the
numbers 1, 3, 5, 7, and 34, the median is still 5, but the mean is 10.
One other concept that is only used occasionally is that of
mode. The mode is the number that occurs with the greatest frequency.
For example, if 2 students get a score of 50 on a test, 3 students get 80,
and 1 student gets a 90, then the mode is 80 — the most students got that
score (by the way, since the middle score would be one of the 80s, that is
also the median, and the mean of those numbers would be 71.67). However, if
you are collecting data on some experiment which requires that you weigh
something three times, and you get three entirely different weights, the
concept of mode really doesn’t mean much.
When analyzing data, it is also useful to determine how
spread-out, how dispersed, those data are. One indication of this is the
range of the data, which is equal to the highest number (the
maximum) minus the lowest number (the minimum). This can be
expressed as range = Xmax – Xmin.
The standard deviation, s, is one of the most
commonly-used measures of the dispersion of the data, in other words, a
measure of how far from the mean the data are scattered. Thus, the smaller
the standard deviation is, the more precise, the closer to agreement
with each other, the data are. In many cases, if the standard deviation is
as large as or greater than the mean, that would indicate that the
experimenter needs to re-examine his/her experimental technique! If the means
of two groups of data are not farther apart from each other than the standard
deviation of each group, then one cannot draw the conclusion that there is a
statistically-significant difference between the two groups (to really be
sure, one should do a “t-test” on the data). Standard deviation is expressed
mathematically as
.
In other words, first subtract the mean from each of the data points to get
the deviation of each number. Then, square each of those deviations (that
“gets rid of” the negative signs). Next, add up all those squared deviations
and divide by the number of data points to get an “average”. Finally,
calculate the square root of that “average.”
For example, for the numbers 1, 3, 5, 7, and 9 from above
(remember, we said the average is 5):
| Number |
Xi – X |
deviation2 |
| 1 |
1 – 5 = –4 |
–42 = 16 |
| 3 |
3 – 5 = –2 |
–22 = 4 |
| 5 |
5 – 5 = 0 |
02 = 0 |
| 7 |
7 – 5 = 2 |
22 = 4 |
| 9 |
9 – 5 = 4 |
42 = 16 |
| Σ = 25 |
|
Σ = 40 |
| 25 ÷ 5 = X = 5 |
|
40 ÷ 5 = 8 |
| |
|
s = √8 = 2.828 |
Initially (i. e., for this lab), you should practice
doing these calculations “by hand” so that you understand what these numbers
represent and how to do the calculations. Once you have mastered and
understand these calculations, they can easily be done on a calculator or
computer. Since so many people use the mean and standard deviation to
analyze data, most calculators and spreadsheet software [@avg() and @std()
work in most spreadsheet programs I’ve used] have built-in functions to do
those calculations.
 |
 |
To more easily visualize statistical data, often a
histogram is constructed. A histogram is a bar graph in which the
X-axis represents the range of possible values divided into discrete
categories, and the Y-axis represents the number of individuals who “fit
into” each category (frequency of individuals observed at each value).
Given a large-enough sample size, the histograms for weight and
height for adult humans should look like “bell” curves, with fewer people
in the highest and lowest weight/height categories, and more people in the
middle categories.
How to Collect Your Data
For this lab, you should work in groups of 5 to 7
students.
- Please do not form a group of less
than 5 people. Including at least 5 people will both increase the accuracy
of your numbers and calculations and give you adequate practice doing these
calculations. If you do not have enough people, split up and join other
groups. While a group of more than 7 people would increase the accuracy
of your data, that would also increase the number of required calculations.
Get your lab notebook set up to gather data.
- Set up a chart similar to
this in your lab notebook, and record the names and ages of all the
students in your group.
Use the medical balance to determine your height.
- With the help of a lab partner from
your group, use the medical balance in the biology lab to determine your
height in centimeters (to the nearest 0.1 cm) and your weight in
kilograms (to the nearest 0.01 kg). You may wish to remove your shoes
to obtain a more accurate height measurement. Make sure you obtain readings
with the correct number of decimal places, and make sure that you record your
data (and those of your group members) directly into your lab notebook.
- To determine your height, raise the
height “bar” on the medical balance to approximately the height of your
head, then stand on the balance. Someone else should adjust the height
bar (up or down) until its arm sits flat on your head (make sure it is
pointing straight sideways and not slightly up or down).
- Read your height
in the middle of the bar where the top piece slides into the bottom piece,
and make sure to use the metric scale. For example, the height shown in
these photos is 160.3 cm (not 5 ft 3⅛ in!). Also, remember to read
your height to the nearest 0.1 cm, and remember to record your data in your
lab notebook.
Use the medical balance to determine your weight.
- When obtaining your weight, it is
important to notice that the beams on the medical balance have two
scales (metric and English) and two sets of notches intermixed. Begin
with the weighs on both beams set at 0.
- First, adjust the weight on the lower
beam. You need to make sure that the weight is in a notch for one of the
metric system numbers, not one of the notches for an English system number
(notice the difference, here between the 40-kg and 100-lb notches). Adjust
the weight so that it is in the last metric notch that’s “too light.”
- Then, carefully slide the weight
on the top beam over to adjust the balance such that the needle swings the
same amount up and down. Do not wait for the needle to stop swinging because
friction may cause it to stop somewhere else.
- Also, remember to read your weight
to the nearest 0.01 kg. This balance is at 14.15 kg, so added to the 40 kg
from the bottom beam, that person’s total weight would be 54.15 kg.
- Remember to write all the measurements
for everyone in your group in your lab notebook.
Determine your pulse.
- Locate the tendon that runs just to
the “thumb-side” of the middle of the wrist.
- Use your same hand (right-right
or left-left) as your “patient.” Support
the person’s hand/wrist on the palm of your hand, and reach up and around with
your fingers, such that your fingers line up along, and to the outside
(thumb-side) of the tendon. (Do not use your thumb because you have a
“pulse point” in the end of your thumb.) Gently, but firmly, press down with
your fingers to feel the pulse in the radial artery.
- Use a stopwatch to time for 30 sec.
as you count the number of pulse beats you feel with your fingers. Multiply
that number by two to determine the person’s pulse in beats per minute (BPM).
- Do this three times — obtain three
separate pulse readings — and average the readings to calculate the person’s
average pulse.
Determine your blood pressure.
with pressure of 140, no blood flow
with pressure of 120, flow when beating
with pressure of 80, normal flow
- Like barometric pressure, blood
pressure is designated in terms of how tall of a column (in mm) of mercury
(Hg) that much pressure could support. Thus, the units used are
“mm Hg.”
- A blood pressure reading consists of
two numbers. The first, higher number is called the
systolic pressure,
and represents the pressure on the blood while the heart is actively contracting
(and therefore putting enough pressure on the blood that it is able to
overcome the resistance of the cuff and flow under it). The sounds you will
hear at that point are the sounds of the
brachial artery
slapping
shut as the heart relaxes and ceases to put pressure on the blood. Thus,
you will need to listen (and watch the sphygmomanometer dial) for when you
first hear a “beating” sound.
- The second, lower number is called the
diastolic pressure,
and represents the residual pressure in the
artery while the heart is relaxed (in between a beat). At that point, the
pressure in the cuff is low enough that the blood can easily flow underneath.
Thus you will need to listen (and watch the dial) for when the sound becomes
muffled.
- You will be using a
sphygmomanometer
attached to a blood-pressure cuff to determine blood pressure. Become familiar
with this equipment and the proper way to put the cuff on a person’s arm.
Learn which is the inside and which is the outside, which is the top and which
is the bottom, and in what “configuration” it is to be placed on someone’s
arm.
- First, closely examine (and
draw)
the dial of the sphygmomanometer. Notice what divisions are marked
on the dial, and what each of those divisions represents.
- Also, examine and try out the
bulb of the sphygmomanometer, and practice turning the screw that
controls the valve (remember “righty-tighty, lefty-loosey”).
- The cuff should be wrapped
snugly around the person’s upper arm, a little above the elbow. Many cuffs
have a label indicating which area of the cuff should be lined up with the
center-front of the person’s arm. Depending on where it is most visible,
the sphygmomanometer may be clipped onto the cuff, as shown here, or removed
and placed somewhere nearby.
- You will also need to use a
stethoscope
to hear the sounds of the blood flowing past the cuff. Note that with no
cuff on the person’s arm (or the cuff in place but totally deflated, you
will not hear a sound because the blood flow is unimpeded.
- Before you insert the earpieces
of the stethoscope into your ears, you need to insure that they are
clean. Since
these stethoscopes are used by numerous students, you need to squirt some
70% alcohol onto a Kimwipe® and use that to clean the earpieces before and
after you use them.
- The bell of the stethoscope is
placed slightly under the bottom edge of the cuff, above the elbow, on roughly
the center front of the arm. It may be held in place with a finger or two,
not your thumb (again, because of the pulse point in your thumb, you might
hear your own pulse, instead). Also, remember that with the cuff deflated
and the blood flowing freely through the brachial artery, you won’t hear
anything.
- There is actually, a correct way to
insert the earpieces into your ears. Notice that the tips
do not face straight toward each other, but rather are “slanted” or “angled”
in one direction.
Because your ear canals are angled forward (toward your
face), the correct way to insert the stethoscope earpieces is also facing
forward (toward your face) to enable you to better hear the sound. Be
careful not to hit the bell of the stethoscope on anything while the earpieces
are inserted in your ears — the noise will be VERY loud!
- Close the valve, but not so tightly
that it gets stuck. Pump up the cuff — unless the person knows (s)he has
hypertension (high blood pressure), going to about 140 mm Hg or so should be
sufficient for most people.
- Then, open the valve slightly to
slowly let air out. As the pressure drops, watch the dial of the sphygmomanometer
and listen for any sounds. When you first hear sounds, make a mental note
of that reading, and as the pressure continues to drop, make a mental note
of when the sounds become muffled. Open the valve to TOTALLY RELEASE THE
PRESSURE and let the person’s arm “rest.” Record the systolic and
diastolic pressure numbers in your lab notebook.
- Repeat this twice more so you have
three sets of numbers. Average the three systolic readings and average the
three diastolic readings to calculate the person’s average blood pressure.
Submit your data online.
- Go to the
(Biometrics Data Web page
and enter the requested data, including your name or initials, sex, age (to
the nearest 0.5 yr), height in centimeters (to the nearest 0.1 cm),
weight in kilograms (to the nearest 0.01 kg), your three pulse readings,
and your three blood pressure readings on that
page. Note: that page contains JavaScript code that is checking to see if
the right number of decimal places were entered, so if a message box pops
up, READ IT and do what it is asking you to do. When everyone has entered
his/her data, use the link to the
class data
at the bottom of that page to view and print a copy of the class results.
How to Analyze Your Data
- Calculate what percentage of your
group are males, and what percentage are females.
As a reminder,
# males + # females = total #
# males ÷ total # × 100 = % males
# females ÷ total # × 100 = % females
Remember to record all your calculations and final numbers directly
into your lab notebook. Do not use a separate sheet of “scratch
paper” first, then recopy your numbers.
- Calculate the mean age of your
group. As a reminder, add all the ages, then divide by the number of people.
Round your answer to the nearest 0.1 years. For example, if you wanted to
find the mean (average) of the ages 19.0, 17.5, 22.5, 30.0, and 21.5, the
total of those numbers would be 110.5, so since there are 5 numbers, the mean
would be 110.5 ÷ 5 = 22.1 years.
- Calculate the standard deviation for
the age of your group. As explained above, for these 5 numbers, the calculations
would look like,
| Number |
Xi – X |
deviation2 |
| 19.0 |
19.0 – 22.1 = –3.1 |
–3.12 = 9.61 |
| 17.5 |
17.5 – 22.1 = –4.6 |
–4.62 = 21.16 |
| 22.5 |
22.5 – 22.1 = 0.4 |
0.42 = 0.16 |
| 30.0 |
30.0 – 22.1 = 7.9 |
7.92 = 62.41 |
| 21.5 |
21.5 – 22.1 = –0.6 |
–0.62 = 0.36 |
| Σ = 110.5 |
|
Σ = 93.70 |
| 110.5 ÷ 5 = X = 22.1 |
|
93.70 ÷ 5 = 18.74 |
| |
|
s = √18.74 = 4.3 |
and thus, the mean ± standard deviation for this group would be expressed
as 22.1 ± 4.3 years.
- Similarly, calculate the means and
standard deviations for the heights and weights of your group.
- For pulse, calculate the group average
two different ways — based on all three individual numbers for each person
(thus averaging a total of 15 to 21 numbers) and based on each person’s
average pulse (thus averaging a total of 5 to 7 numbers) — and compare to
see if it makes a difference in the results.
- For pulse, calculate the group
standard deviation based on each person’s average pulse. For blood pressure,
(remember, systolic and diastolic numbers must be calculated separately)
calculate the group mean and standard deviation based on each person’s
“average” blood pressure.
- While histograms really work better
with larger sets of data, to save time while simultaneously introducing
you to how they are constructed, you are asked to plot histograms of your
group’s data as follows.
- First,
as explained in the protocol, make a list of 2.5-year-span age
categories, such as:
under-15
15.0-17.4
17.5-19.9
20.0-22.4
22.5-24.9
25.0-27.4
27.5-29.9
30.0-32.4
32.5-34.9
35.0-37.4
37.5-39.9
40-and-over,
including enough categories to cover the ages of all group members.
Then determine how many people’s ages fall into each of those categories.
For example, for the ages in the above example, this would look
like:
AGE NUMBER
17.5-19.9 2
20.0-22.4 1
22.5-24.9 1
25.0-27.4 0
27.5-29.9 0
30.0-32.4 1
- Secondly,
make a similar list of height by 5 cm categories (for example: 135.0-139.9,
140.0-144.9, etc.), including enough of those categories to include
the heights of all group members. Then, determine how many people’s
heights fall into each of those categories.
- Thirdly,
make a similar list of weight by 10 kg categories (for example: 40.00-49.99,
50.00-59.99, etc.), and determine how many people’s weights fall into
each of those categories.
- Similarly,
list average pulse in 5 BPM categories (for example, 75.0-79.9 BPM),
and average systolic and diastolic blood pressures (list separately)
in 5 mm Hg categories. Determine how many of your group members fall
into each of those categories.
- Set up a histogram (graph)
for each set of numbers (age, height, etc.). Each
“block” on the X-axis should represent one category (for example, on
the height histogram, one of the units on the X-axis would represent
the 150.0-154.9 cm group, the next would represent the 155.0-159.9 cm
group, etc.). The Y-axis represents the number of people in
each category (for example, if 12 people were in the 60.00-69.99 kg
category, that bar would be 12 blocks tall). For each category listed
on the X-axis, draw a bar the appropriate height to represent the
number of people in that category. Refer to the graphing protocol and
graphing Web page
for information on proper graphing technique, and make sure to
properly title your graph and label the axes.
- For
each graph except the one for sex distribution, on the X-axis,
indicate where the mean would be located. Also calculate and indicate
the position of the mean + one standard deviation unit and the
position of the mean – one standard deviation unit (for example, if
X = 5.00 and s = 0.20,
those two points would be at 5.20 and 4.80, respectively), as well as
the mean ± two standard deviation units (which would be 5.40 and 4.60
for this example).
- You
should end up with histograms for sex, age, height, weight, pulse,
systolic, and diastolic blood pressure distributions for your group
(a total of 7 graphs).
- After you print out the
class data,
compare your histograms with those for the class data. How are they similar?
Different? Are the means in the same places? How similar or dissimilar are
the standard deviations? Do any of the histograms form a bell curve?
- Based on your statistical analysis of
the data, do there appear to any statistically-significant differences
in either age, height, weight, pulse, systolic, or diastolic blood pressure
when comparing males vs. females? Do there appear to be any
statistically-significant differences when comparing people who are
under 25 with those who are 20 and over? For example, if you have the
following two groups of data:
| Group |
Mean |
Standard Deviation |
Mean +
Std Dev |
Mean –
Std Dev |
| Group 1 |
25a |
3 |
28 |
22a |
| Group 2 |
22b |
4 |
26b |
18 |
those groups of data would not be different from each other. While
there is a “fancy” statistical calculation called a t-test that could be
done to determine whether these groups are different or not, for our
purposes, since
25a – 3 = 22a (higher average – its standard deviation), and
22b + 4 = 26b (lower average + its standard deviation),
and those numbers are overlapping (22a = 22b and 26b > 25a),
it can be concluded that there is not
a statistically-significant difference between these numbers.
If you were doing an experiment and obtained these data for your control and
experimental groups, you would conclude that there is no difference between
the groups, the factor being tested in/on the experimental group had no
effect as compared to the control group. Thus, when stating your conclusions,
it is important to cite the actual numbers upon which those conclusions are
based.
- Before looking at the data, which
would you have expected to be more different between the under/over 25
groups: weight, height, pulse, or blood pressure? Why? Do the actual data
support or refute this hypothesis?
- Complete the statistics practice
problems in the lab protocol. Show all your work in your lab notebook.
Things to Include in Your Notebook
Make sure you have all of the following in your lab notebook:
- all handout pages (in separate protocol book)
- all notes you take as you read through this Web page and/or
during the introductory mini-lecture
- all notes and data you gather as you perform the experiment
- your personal and group data
- print-out of class data (available online)
- all requested calculations and graphs
- answers to all discussion questions, a summary/conclusion in your
own words, and any suggestions you may have
- evidence that you have at least tried to work the practice
problems
- drawing of the medical balance used to obtain your height and
weight, including detail of exactly what the markings on the beams
actually look like
- drawings of the dial of the stopwatch and dial of the
sphygmomanometer, again including detail of exactly what the markings
actually look like
- drawings of the stethoscope and blood-pressure cuff with all parts
clearly shown and labeled
- any returned, graded pop quiz
Copyright © 2010 by J. Stein Carter. All rights reserved.
Based on printed protocol Copyright © 2000 J. L. Stein Carter.
Chickadee photograph Copyright © by David B. Fankhauser
This page has been accessed 
times since 23 Jun 2011.