Control in the Design of an Experiment
Dr. Penelope Nicholls is interested in exploring a possible connection between
high plasma homocysteine (a toxic amino acid created by the body as
it metabolizes protein) levels and cardiac hypertrophy (enlargement of the
heart) in humans. She realizes that, because there are many complex relationships
among human characteristics, it will be difficult to answer her
research question unambiguously because there is a significant risk that
confounding factors will cloud her inferences. She wants to be as sure
as possible that any differences in cardiac hypertrophy are due to
high plasma homocysteine levels and not to other hidden factors. Consequently,
she needs to design her experiment carefully, so that she controls lurking
variables to the extent possible. Therefore, she decides to design a
two-sample experiment with independent sampling—one of the groups will
be the experimental group, the other a control group. Knowing that there are
many factors that can affect the degree of cardiac hypertrophy (the response
variable), Dr. Nicholls controls these factors by randomly assigning the experimental
units to the experimental or control group. She hopes the randomization
will result in both groups having similar characteristics. By controlling the
data collection environment and procedures, she also hopes to minimize any
situational contaminants within her experimental design.
In her preliminary literature review, Dr. Nicholls uncovered an article
in which the authors hypothesized that there might be a relationship between
high plasma homocysteine levels in patients with end-stage renal disease
(ESRD) and cardiac hypertrophy. As her assistant, she has asked you
to review this article and to write a brief report detailing your findings.
Upon reading the article, you discover that the authors employed a
nonrandom process to select a control and an ESRD group. The researchers
enlisted 75 stable ESRD patients into their study. All of these patients
were on hemodialysis for between 6 and 312 months. The control
group was composed of 57 nonuremic members. Nonuremic subjects were
chosen so as to eliminate any intergroup differences in terms of mean blood
pressure (BP) and gender. Any individuals taking vitamins and any individuals
with any type of specified heart-related ailments were excluded from
the study. In an effort to minimize situational contaminants, all physical and
biochemical measurements were made after an overnight fast. The results
of the clinical characteristics and the biochemical findings for the control
and ESRD groups are reproduced in the following tables.
Clinical Characteristics (Mean Standard Deviation)
Parameters Controls ESRD Subjects
1n = 572 1n = 752
Sex (M/F ratio)
Body Surface Area (m2)
Body Mass Index (kg/m2 )
Systolic BP (mmHg)
Diastolic BP (mmHg)
Mean BP (mmHg)
Pulse Pressure (mmHg)
Heart Rate (beats/min) 63.0 ; 8.0 70.0 ; 9.0
59.4 ; 15.5 68.6 ; 24.3
104.5 ; 14.2 103.6 ; 17.4
85.0 ; 14.8 80.2 ; 14.3
145.0 ; 15.5 148.8 ; 29.7
26.0 ; 4.70 23.7 ; 3.90
1.85 ; 0.25 1.67 ; 0.20
1.4 ; 0.50 1.4 ; 0.50
49.2 ; 14.7 57.3 ; 15.1
SullStatCH10_Fpp592-653 11/20/02 1:06 PM Page 650
Which type of sampling method, independent or dependent, was used
in this experiment? Explain.
Using the appropriate hypothesis-testing procedure, ascertain whether
the control and ESRD groups have equivalent population means for each
of the various clinical and biochemical parameters. Dr. Nicholls requires
that you indicate those parameters that have P-values less than 0.05 and
those less than 0.01.
Detail any assumptions, and the rationale behind making them, that
you made while carrying out your analysis. Is there any additional information
that you would like to have? Explain. Are there any additional statistical
procedures that you think might be useful for analyzing these data?
Based on your findings, does it appear that the control and ESRD
groups have similar initial clinical characteristics and biochemical findings?
Does it appear that the authors of this article were successful in reducing
the likelihood that a confounding effect would obscure their results?
Even though Dr. Nicholls does not wish to restrict her research to patients
with end-stage renal disease, how might the information presented
for this research assist her in designing her own experiment?
Write a report for Dr. Nicholls that outlines all of your findings and recommendations.
Biological Findings (Mean Standard Deviation)
Parameters Controls ESRD Subjects
1n = 572 1n = 752
Total Cholesterol (mmol/L)
HDL Cholesterol (mmol/L)
Serum Albumin (g/L)
Plasma Fibrinogen (g/L)
Plasma Creatinine (mmol/L)
Blood Urea (mmol/L)
Source: Jacques Blacher, et al. “Association between Plasma Homocysteine
Concentrations and Cardiac Hypertrophy in End-Stage Renal Disease.”
Journal of Nephrology 12, 4 (July–August, 1999): 248–255. Article available at
1.03 ; 0.21 1.88 ; 0.38
2.46 ; 0.08 2.45 ; 0.12
6.10 ; 1.20 24.3 ; 2.00
0.10 ; 0.01 0.90 ; 0.13
3.21 ; 0.78 4.75 ; 1.04
44.7 ; 2.60 39.9 ; 3.00
1.39 ; 0.63 1.90 ; 1.02
1.38 ; 0.39 1.07 ; 0.38
5.28 ; 1.04 4.91 ; 1.06
SullStatCH10_Fpp592-653 11/20/02 1:06 PM Page 651
Where Should I Invest?
Suppose that you have just received an inheritance of $10,000 and you decide
that you should invest the money rather than blow it on frivolous
items.You have decided that you will invest the money in one of two types
of mutual funds. The first type you are considering follows a “large value”
approach to investing.This means that the mutual fund invests only in large,
established companies that are considered to be a good bargain.The second
type of mutual fund you are considering follows a “large growth” approach
to investing. This means that the mutual fund invests in large companies
that are experiencing solid sales growth.
In order to make an informed decision, you decide to research the rate
of return of the past three years for each of these types of mutual funds.The
mutual fund must have a Morningstar rating of four or five stars.The Morningstar
mutual-fund rating system ranks mutual funds, using one to five
stars.The stars divide the mutual-fund performance into quintiles—that is, a
mutual fund with a one-star rating is in the bottom 20% of mutual funds in
its category, a mutual fund with a two-star rating has an investment performance
between the and percentile, and so on. These data can be
found at www.morningstar.com or http://screen.yahoo.com/funds.html.
(a) Obtain a simple random sample of at least 15 mutual funds for each investment
category. Determine the three-year rate of return for each of
(b) Verify that the three-year rates of return come from a population that
is normally distributed.Also, verify that the data have no outliers. If the
data do not come from a population that is normally distributed, you’ll
have to increase the sample size so that the Central Limit Theorem can
(c) Construct a boxplot for the rate of return of each fund category, using
the same scale.Which investment category, if any, seems superior?
(d) Obtain a 95% confidence interval for the difference between the mean
rates of return. Interpret the interval.
(e) Write a report that details which investment category seems to be superior.
SullStatCH10_Fpp592-653 11/20/02 1:06 PM Page 652
The High Cost of Convenience
(d) To test the claim, we used Minitab (release 13.1)
to perform a two-sample t-test. The results are
Using the Minitab output, determine the value of
the test statistic.What is the P-value of the test?
For a recent article, Consumer Reports (December
2001) was interested in comparing a name brand paper
towel with a new version packaged in a box.The towels
in the box, which cost nearly twice as much as the traditional
roll, are marketed for their convenience. Given
the difference in cost, one might wonder if the boxed
version performs better than the traditional roll. To
help answer this question, technicians at Consumers
Union subjected both types of towels to 5 physical
tests: absorption time in water, absorption time in oil,
absorption capacity in water, absorption capacity in oil,
and wet strength. For brevity, we will discuss only the
results of the absorption time in water test.
The absorption time in water was defined as the
amount of time necessary for a single sheet to absorb
a predetermined amount of water. In order to compare
the absorption times of the two types of towels,
we tested six randomly selected sheets of paper towels.
To avoid potential sources of bias, the individual
sheets were taken from different samples of the
products and the tests were conducted in a randomly
The claim being tested is that the water absorption
time for the boxed version is less than the water
absorption time for the traditional roll.
(a) Write the null and alternative hypotheses, letting
mbox represent the mean absorption time for the
boxed version and represent the mean absorption
time for the roll version.
(b) Normal probability plots of the water absorption
times for the two products are shown below.
Based on the normal probability plots, is it reasonable
to conduct a two-sample hypothesis test?
Note to Readers: In many cases, our test protocol and analytical
methods are more complicated than described in these examples.
The data and discussions have been modified to make the material
more appropriate for the audience.
Two-Sample T-Test and CI: Absorption Time In Water, CU
Difference = mu (Box) - mu (Roll)
Estimate for difference: -0.0483
95% upper bound for difference: 0.0320
T-Test of difference = 0 (vs <): T-Value = -1.09 P-Value = 0.150 DF = 10
Both use Pooled StDev = 0.0767
Two-sample T for Absorption Time In Water
Although they are not discussed here, the other
physical tests provided similar results. Write an
article that states your conclusion and any recommendations
that you would make regarding the
purchase of the two products.
(c) A boxplot of the water absorption times for the
two products is shown below.
Does the data set have any outliers? Based on the
boxplots, do you think that the absorption times
for the boxed version are lower than the absorption
times for the roll?
SullStatCH10_Fpp592-653 11/20/02 1:06 PM Page 653
Sampling Method Used;
Independent sampling as two samples selected from the same population, that have no effect on one another. The outcome for the control group is assumed to