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Do the people want a tax cut? During the 2000 presidential campaign, the
candidates debated what to do with the large government surplus. The Pew
Research Center asked two questions of random samples of adults. Both
said that Social Security would be “fixed.” Here are the uses suggested for
the remaining surplus:
Should the money be used for a tax cut, or should it be used to fund newgovernment programs? Should the money be used for a tax cut, or should it be spent on programs foreducation, the environment, health care, crime-fighting and military defense? One of these questions drew 60% favoring a tax cut; the other, only 22%.
Which wording pulls respondents toward a tax cut? Why? Designing Experiments
A study is an experiment when we actually do something to people, animals,or objects to observe the response. Experiments are important tools forproduct development and improvement of processes and services. Our shortintroduction here concentrates on basic ideas at a level suitable for managers.
Statistically designed experiments are at the core of some large industries,especially pharmaceuticals, where regulations require that new drugs beshown by experiments to be safe and reliable before they can be sold.
Because the purpose of an experiment is to reveal the response of one variable to changes in other variables, the distinction between explanatoryand response variables is essential. Here is some basic vocabulary forexperiments.
SUBJECTS, FACTORS, TREATMENTS
The individuals studied in an experiment are often called subjects,
especially if they are people.
The explanatory variables in an experiment are often called factors.
A treatment is any specific experimental condition applied to the
subjects. If an experiment has several factors, a treatment is a
combination of a specific value (often called a level) of each of the
factors.
EXAMPLE 3.11
Absorption of a drug
Researchers at a pharmaceutical company studying the absorption of a drug into
the bloodstream inject the drug (the treatment) into 25 people (the subjects). The
response variable is the concentration of the drug in a subject’s blood, measured
30 minutes after the injection. This experiment has a single factor with only one
level. If three different doses of the drug are injected, there is still a single factor
(the dosage of the drug), now with three levels. The three levels of the single factor
are the treatments that the experiment compares.
CHAPTER 3 Ⅲ Producing Data
FIGURE 3.3 The treatments in the experimental design of Example 3.12.
Combinations of levels of the two factors form six treatments.
EXAMPLE 3.12
Effects of TV advertising
What are the effects of repeated exposure to an advertising message? The answer
may depend both on the length of the ad and on how often it is repeated. An
experiment investigates this question using undergraduate students as subjects.
All subjects view a 40-minute television program that includes ads for a digital
camera. Some subjects see a 30-second commercial; others, a 90-second version.
The same commercial is repeated either 1, 3, or 5 times during the program.
After viewing, all of the subjects answer questions about their recall of the ad,
their attitude toward the camera, and their intention to purchase it. These are the
This experiment has two factors: length of the commercial, with 2 levels; and repetitions, with 3 levels. The 6 combinations of one level of each factor form 6treatments. Figure 3.3 shows the layout of the treatments.
Examples 3.11 and 3.12 illustrate the advantages of experiments over observational studies. Experimentation allows us to study the effects ofthe specific treatments we are interested in. Moreover, we can control theenvironment of the subjects to hold constant the factors that are of nointerest to us, such as the specific product advertised in Example 3.12.
The ideal case is a laboratory experiment in which we control all lurkingvariables and so see only the effect of the treatments on the response. Likemost ideals, such control is not always realized in practice.
Another advantage of experiments is that we can study the combined interaction
effects of several factors simultaneously. The interaction of several factors
can produce effects that could not be predicted from looking at the effect
of each factor alone. Perhaps longer commercials increase interest in a
product, and more commercials also increase interest, but if we both make
a commercial longer and show it more often, viewers get annoyed and their
interest in the product drops. The two-factor experiment in Example 3.12
will help us find out.
APPLY YOUR
Sickle cell disease. Sickle cell disease is an inherited disorder of the red
KNOWLEDGE
blood cells that in the United States affects mostly blacks. It can cause severe KNOWLEDGE
pain and many complications. Bristol-Myers Squibb markets Hydrea—abrand name for the drug hydroxyurea—to treat sickle cell disease. Federalregulations allow the sale of a new drug only after statistically designedexperiments (called clinical trials in medical language) show that the drug issafe and effective. A clinical trial at the National Institutes of Health gavehydroxyurea to 150 sickle cell sufferers and a placebo (a dummy medication)to another 150. The researchers then counted the episodes of pain reportedby each subject. What are the subjects, the factors, the treatments, and theresponse variables? Sealing food packages. A manufacturer of food products uses package liners
that are sealed at the top by applying heated jaws after the package is filled.
The customer peels the sealed pieces apart to open the package. What effect
does the temperature of the jaws have on the force needed to peel the liner?
To answer this question, engineers prepare 20 pairs of pieces of package
liner. They seal five pairs at each of 250Њ F, 275Њ F, 300Њ F, and 325Њ F.
Then they measure the force needed to peel each seal.
(a) What are the individuals studied?
(b) There is one factor (explanatory variable). What is it, and what are its
An industrial experiment. A chemical engineer is designing the production
process for a new product. The chemical reaction that produces the product
may have higher or lower yield, depending on the temperature and the
stirring rate in the vessel in which the reaction takes place. The engineer
decides to investigate the effects of combinations of two temperatures
(50 C and 60Њ C) and three stirring rates (60 rpm, 90 rpm, and 120 rpm)on the yield of the process. She will process two batches of the product ateach combination of temperature and stirring rate.
(a) What are the individuals and the response variable in this experiment?(b) How many factors are there? How many treatments? Use a diagram like that in Figure 3.3 to lay out the treatments.
(c) How many individuals are required for the experiment? Comparative experiments
Experiments in the laboratory often have a simple design: impose the
treatment and see what happens. We can outline that design like this:
Subjects-y Treatment-y Response
In the laboratory, we try to avoid confounding by rigorously controllingthe environment of the experiment so that nothing except the experimentaltreatment influences the response. Once we get out of the laboratory,however, there are almost always lurking variables waiting to confound us.
When our subjects are people or animals rather than electrons or chemicalcompounds, confounding can happen even in the controlled environment ofa laboratory or medical clinic. Here is an example that helps explain whycareful experimental design is a key issue for pharmaceutical companies andother makers of medical products.
CHAPTER 3 Ⅲ Producing Data
EXAMPLE 3.13
Gastric freezing to treat ulcers
“Gastric freezing” is a clever treatment for ulcers. The patient swallows a deflated
balloon with tubes attached, then a refrigerated liquid is pumped through
the balloon for an hour. The idea is that cooling the stomach will reduce its
production of acid and so relieve ulcers. An experiment reported in the Journal
of the American Medical Association showed that gastric freezing did reduce acid
production and relieve ulcer pain. The treatment was widely used for several years.
The design of the experiment was
Subjects-y Gastric freezing-y Observe pain relief
This experiment is poorly designed. The patients’ response may be due to the placebo effect
placebo effect. A placebo is a dummy treatment. Many patients respond favorably
to any treatment, even a placebo, presumably because of trust in the doctor and
expectations of a cure. This response to a dummy treatment is the placebo effect.
A later experiment divided ulcer patients into two groups. One group was treated by gastric freezing as before. The other group received a placebo treatmentin which the liquid in the balloon was at body temperature rather than freezing.
The results: 34% of the 82 patients in the treatment group improved, but so did38% of the 78 patients in the placebo group. This and other properly designedexperiments showed that gastric freezing was no better than a placebo, and its use The first gastric-freezing experiment was biased. It systematically favored gastric freezing because the placebo effect was confounded with the effectof the treatment. Fortunately, the remedy is simple. Experiments shouldcompare treatments rather than attempt to assess a single treatment inisolation. When we compare the two groups of patients in the secondgastric-freezing experiment, the placebo effect and other lurking variablesoperate on both groups. The only difference between the groups is theactual effect of gastric freezing. The group of patients who receive a sham control group
treatment is called a control group, because it enables us to control the
effects of lurking variables on the outcome.
Randomized comparative experiments
The design of an experiment first describes the response variables, the factors
(explanatory variables), and the layout of the treatments, with comparison
as the leading principle. The second aspect of design is the rule used to
assign the subjects to the treatments. Comparison of the effects of several
treatments is valid only when all treatments are applied to similar groups
of subjects. If one corn variety is planted on more fertile ground, or if
one cancer drug is given to less seriously ill patients, comparisons among
treatments are biased. How can we assign individuals to treatments in a way
that is fair to all the treatments?
Our answer is the same as in sampling: let impersonal chance make the assignment. The use of chance to divide subjects into groups is called randomization
randomization. Groups formed by randomization don’t depend on any
characteristic of the subjects or on the judgment of the experimenter. An randomized
experiment that uses both comparison and randomization is a randomized
comparative
comparative experiment. Here is an example.
experiment
EXAMPLE 3.14
Testing a breakfast food
A food company assesses the nutritional quality of a new “instant breakfast”
product by feeding it to newly weaned male white rats. The response variable is a
rat’s weight gain over a 28-day period. A control group of rats eats a standard diet
but otherwise receives exactly the same treatment as the experimental group.
This experiment has one factor (the diet) with two levels. The researchers use 30 rats for the experiment and so must divide them into two groups of 15. To dothis in an unbiased fashion, put the cage numbers of the 30 rats in a hat, mix themup, and draw 15. These rats form the experimental group and the remaining 15make up the control group. Each group is an SRS of the available rats. Figure 3.4outlines the design of this experiment.
We can use software or the table of random digits to randomize. Label the rats 01 to 30. Enter Table B at (say) line 130. Run your finger along this line (andcontinue to lines 131 and 132 as needed) until 15 rats are chosen. They are the ratslabeled These rats form the experimental group; the remaining 15 are the control group.
Completely randomized designs
The design in Figure 3.4 combines comparison and randomization to arrive
at the simplest statistical design for an experiment. This “flowchart” outline
presents all the essentials: randomization, the sizes of the groups and which
treatment they receive, and the response variable. There are, as we will
see later, statistical reasons for generally using treatment groups that are
about equal in size. We call designs like that in Figure 3.4 completely
COMPLETELY RANDOMIZED DESIGN
In a completely randomized experimental design, all the subjects are
allocated at random among all the treatments.
FIGURE 3.4 Outline of a randomized comparative experiment, for
Example 3.14.
CHAPTER 3 Ⅲ Producing Data
Completely randomized designs can compare any number of treatments.
Here is an example that compares three treatments.
EXAMPLE 3.15
Conserving energy
Many utility companies have introduced programs to encourage energy conservation
among their customers. An electric company considers placing electronic indicators
in households to show what the cost would be if the electricity use at that moment
continued for a month. Will indicators reduce electricity use? Would cheaper methods
work almost as well? The company decides to design an experiment.
One cheaper approach is to give customers a chart and information about monitoring their electricity use. The experiment compares these two approaches(indicator, chart) and also a control. The control group of customers receivesinformation about energy conservation but no help in monitoring electricity use.
The response variable is total electricity used in a year. The company finds 60single-family residences in the same city willing to participate, so it assigns 20residences at random to each of the 3 treatments. Figure 3.5 outlines the design.
To carry out the random assignment, label the 60 households 01 to 60. Enter Table B (or use software) to select an SRS of 20 to receive the indicators. Continue inTable B, selecting 20 more to receive charts. The remaining 20 form the control group.
Examples 3.14 and 3.15 describe completely randomized designs that compare levels of a single factor. In Example 3.14, the factor is the dietfed to the rats. In Example 3.15, it is the method used to encourageenergy conservation. Completely randomized designs can have more thanone factor. The advertising experiment of Example 3.12 has two factors:the length and the number of repetitions of a television commercial. Theircombinations form the six treatments outlined in Figure 3.3 (page 190).
A completely randomized design assigns subjects at random to these sixtreatments. Once the layout of treatments is set, the randomization neededfor a completely randomized design is tedious but straightforward.
APPLY YOUR
Gastric freezing. Example 3.13 describes an experiment that helped end the
KNOWLEDGE
use of gastric freezing to treat ulcers. The subjects were 160 ulcer patients.
KNOWLEDGE
(a) Use a diagram to outline the design of this experiment, following the information in Example 3.13. (Show the size of the groups, the treatmenteach group receives, and the response variable. Figures 3.4 and 3.5 aremodels to follow.) FIGURE 3.5 Outline of a completely randomized design comparing
three treatments, for Example 3.15.
(b) The 82 patients in the gastric-freezing group are an SRS of the 160 subjects. Label the subjects and use Table B, starting at line 131, tochoose the first 5 members of the gastric-freezing group.
Sealing food packages. Use a diagram to describe a completely randomized
experimental design for the package liner experiment of Exercise 3.30. (Show
the size of the groups, the treatment each group receives, and the response
variable. Figures 3.4 and 3.5 are models to follow.) Use software or Table B,
starting at line 120, to do the randomization required by your design.
Does child care help recruit employees? Will providing child care for em-
ployees make a company more attractive to women, even those who are
unmarried? You are designing an experiment to answer this question. You
prepare recruiting material for two fictitious companies, both in similar
businesses in the same location. Company A’s brochure does not mention
child care. There are two versions of Company B’s material, identical except
that one describes the company’s on-site child-care facility. Your subjects
are 40 unmarried women who are college seniors seeking employment. Each
subject will read recruiting material for both companies and choose the one
she would prefer to work for. You will give each version of Company B’s
brochure to half the women. You expect that a higher percentage of those
who read the description that includes child care will choose Company B.
(a) Outline an appropriate design for the experiment.
(b) The names of the subjects appear below. Use Table B, beginning at line
131, to do the randomization required by your design. List the subjectswho will read the version that mentions child care.
The logic of randomized comparative experiments
Randomized comparative experiments are designed to give good evidence
that differences in the treatments actually cause the differences we see in the
response. The logic is as follows:
Ⅲ Random assignment of subjects forms groups that should be similar in all respects before the treatments are applied.
Ⅲ Comparative design ensures that influences other than the experimental treatments operate equally on all groups.
Ⅲ Therefore, differences in average response must be due either to the treatments or to the play of chance in the random assignment of subjectsto the treatments.
CHAPTER 3 Ⅲ Producing Data
That “either-or” deserves more thought. In Example 3.14, we cannot say that any difference in the average weight gains of rats fed the two diets mustbe caused by a difference between the diets. There would be some differenceeven if both groups received the same diet, because the natural variabilityamong rats means that some grow faster than others. Chance assigns thefaster-growing rats to one group or the other, and this creates a chancedifference between the groups. We would not trust an experiment with justone rat in each group, for example. The results would depend on whichgroup got lucky and received the faster-growing rat. If we assign many ratsto each diet, however, the effects of chance will average out and there willbe little difference in the average weight gains in the two groups unless thediets themselves cause a difference. “Use enough subjects to reduce chancevariation” is the third big idea of statistical design of experiments.
PRINCIPLES OF EXPERIMENTAL DESIGN
1. Control the effects of lurking variables on the response, most
simply by comparing two or more treatments.
2. Randomize—use impersonal chance to assign subjects to
treatments.
3. Replicate each treatment on enough subjects to reduce chance
variation in the results.
We hope to see a difference in the responses so large that it is unlikely to happen just because of chance variation. We can use the laws of probability,which give a mathematical description of chance behavior, to learn if thetreatment effects are larger than we would expect to see if only chance wereoperating. If they are, we call them statistically significant.
STATISTICAL SIGNIFICANCE
An observed effect so large that it would rarely occur by chance is
called statistically significant.
If we observe statistically significant differences among the groups in a comparative randomized experiment, we have good evidence that thetreatments actually caused these differences. You will often see the phrase“statistically significant” in reports of investigations in many fields of study.
The great advantage of randomized comparative experiments is that theycan produce data that give good evidence for a cause-and-effect relation-ship between the explanatory and response variables. We know that ingeneral a strong association does not imply causation. A statistically sig-nificant association in data from a well-designed experiment does implycausation.
APPLY YOUR
Conserving energy. Example 3.15 describes an experiment to learn whether
KNOWLEDGE
providing households with electronic indicators or charts will reduce their KNOWLEDGE
electricity consumption. An executive of the electric company objects to including a control group. He says, “It would be simpler to just compareelectricity use last year (before the indicator or chart was provided) withconsumption in the same period this year. If households use less electricitythis year, the indicator or chart must be working.” Explain clearly why thisdesign is inferior to that in Example 3.15.
Exercise and heart attacks. Does regular exercise reduce the risk of a heart
attack? Here are two ways to study this question. Explain clearly why the
second design will produce more trustworthy data.
1. A researcher finds 2000 men over 40 who exercise regularly and have
not had heart attacks. She matches each with a similar man who doesnot exercise regularly, and she follows both groups for 5 years.
2. Another researcher finds 4000 men over 40 who have not had heart attacks and are willing to participate in a study. She assigns 2000 ofthe men to a regular program of supervised exercise. The other 2000continue their usual habits. The researcher follows both groups for 5years.
Statistical significance. The financial aid office of a university asks a sample
of students about their employment and earnings. The report says that “for
academic year earnings, a significant difference was found between the sexes,
with men earning more on the average. No significant difference was found
between the earnings of black and white students.” Explain the meaning of
“a significant difference” and “no significant difference” in plain language.
Cautions about experimentation
The logic of a randomized comparative experiment depends on our ability to
treat all the subjects identically in every way except for the actual treatments
being compared. Good experiments therefore require careful attention to
details. For example, the subjects in both groups of the second gastric
freezing experiment (Example 3.13, page 192) all got the same medical
attention over the several years of the study. The researchers paid attention
to such details as ensuring that the tube in the mouth of each subject was
cold, whether or not the fluid in the balloon was refrigerated. Moreover,
double-blind
the study was double-blind—neither the subjects themselves nor the medical
personnel who worked with them knew which treatment any subject had
received. The double-blind method avoids unconscious bias by, for example,
a doctor who doesn’t think that “just a placebo” can benefit a patient.
lack of realism
The most serious potential weakness of experiments is lack of realism.
The subjects or treatments or setting of an experiment may not realisticallyduplicate the conditions we really want to study. Here are two examples.
EXAMPLE 3.16
Response to advertising
The study of television advertising in Example 3.12 showed a 40-minute videotape
to students who knew an experiment was going on. We can’t be sure that the
results apply to everyday television viewers. The student subjects described
their reactions but did not actually decide whether to buy the camera. Many
experiments in marketing and decision making use as subjects students who know
they are taking part in an experiment. That’s not a realistic setting.
CHAPTER 3 Ⅲ Producing Data
EXAMPLE 3.17
Center brake lights
Do those high center brake lights, required on all cars sold in the United
States since 1986, really reduce rear-end collisions? Randomized comparative
experiments with fleets of rental and business cars, done before the lights were
required, showed that the third brake light reduced rear-end collisions by as much
as 50%. Alas, requiring the third light in all cars led to only a 5% drop.
What happened? Most cars did not have the extra brake light when the experiments were carried out, so it caught the eye of following drivers. Now thatalmost all cars have the third light, they no longer capture attention.
Lack of realism can limit our ability to apply the conclusions of an experiment to the settings of greatest interest. Most experimenters want togeneralize their conclusions to some setting wider than that of the actualexperiment. Statistical analysis of the original experiment cannot tell us howfar the results will generalize. Nonetheless, the randomized comparativeexperiment, because of its ability to give convincing evidence for causation,is one of the most important ideas in statistics.
APPLY YOUR
Does meditation reduce anxiety? Some companies employ consultants to
KNOWLEDGE
train their managers in meditation in the hope that this practice will relieve KNOWLEDGE
stress and make the managers more effective on the job. An experimentthat claimed to show that meditation reduces anxiety proceeded as follows.
The experimenter interviewed the subjects and rated their level of anxiety.
Then the subjects were randomly assigned to two groups. The experimentertaught one group how to meditate and they meditated daily for a month.
The other group was simply told to relax more. At the end of the month,the experimenter interviewed all the subjects again and rated their anxietylevel. The meditation group now had less anxiety. Psychologists said thatthe results were suspect because the ratings were not blind. Explain whatthis means and how lack of blindness could bias the reported results.
Frustration and teamwork. A psychologist wants to study the effects of
failure and frustration on the relationships among members of a work team.
She forms a team of students, brings them to the psychology laboratory,
and has them play a game that requires teamwork. The game is rigged so
that they lose regularly. The psychologist observes the students through a
one-way window and notes the changes in their behavior during an evening
of game playing. Why is it doubtful that the findings of this study tell us
much about the effect of working for months developing a new product that
never works right and is finally abandoned by your company?
Matched pairs designs
Completely randomized designs are the simplest statistical designs for ex-
periments. They illustrate clearly the principles of control, randomization,
and replication of treatments on a number of subjects. However, completely
randomized designs are often inferior to more elaborate statistical designs. In
particular, matching the subjects in various ways can produce more precise
results than simple randomization.
One common design that combines matching with randomization is the matched pairs
matched pairs design. A matched pairs design compares just two treatments.
design
Choose pairs of subjects that are as closely matched as possible. Assign oneof the treatments to each subject in a pair by tossing a coin or readingodd and even digits from Table B. Sometimes each “pair” in a matchedpairs design consists of just one subject, who gets both treatments one afterthe other. Each subject serves as his or her own control. The order of thetreatments can influence the subject’s response, so we randomize the orderfor each subject, again by a coin toss.
EXAMPLE 3.18
Coke versus Pepsi
Pepsi wanted to demonstrate that Coke drinkers prefer Pepsi when they taste both
colas blind. The subjects, all people who said they were Coke drinkers, tasted both
colas from glasses without brand markings and said which they liked better. This
is a matched pairs design in which each subject compares the two colas. Because
responses may depend on which cola is tasted first, the order of tasting should be
chosen at random for each subject.
When more than half the Coke drinkers chose Pepsi, Coke claimed that the experiment was biased. The Pepsi glasses were marked M and the Coke glasseswere marked Q. Aha, said Coke, this just shows that people like the letter Mbetter than the letter Q. A careful experiment would in fact take care to avoid any distinction other than the actual treatments.
Block designs
Matched pairs designs apply the principles of comparison of treatments, ran-
domization, and replication. However, the randomization is not complete—
we do not randomly assign all the subjects at once to the two treatments.
Instead, we only randomize within each matched pair. This allows matching
to reduce the effect of variation among the subjects. Matched pairs are an
example of block designs.
BLOCK DESIGN
A block is a group of subjects that are known before the experiment
to be similar in some way expected to affect the response to the
treatments. In a block design, the random assignment of individuals
to treatments is carried out separately within each block.
A block design combines the idea of creating equivalent treatment groups by matching with the principle of forming treatment groups at random.
Blocks are another form of control. They control the effects of some outsidevariables by bringing those variables into the experiment to form the blocks.
The following is a typical example of a block design.
CHAPTER 3 Ⅲ Producing Data
EXAMPLE 3.19
Men, women, and advertising
Women and men respond differently to advertising. An experiment to compare
the effectiveness of three television commercials for the same product will want to
look separately at the reactions of men and women, as well as assess the overall
response to the ads.
A completely randomized design considers all subjects, both men and women, as a single pool. The randomization assigns subjects to three treatment groupswithout regard to their sex. This ignores the differences between men and women.
A better design considers women and men separately. Randomly assign the womento three groups, one to view each commercial. Then separately assign the men atrandom to three groups. Figure 3.6 outlines this improved design.
A block is a group of subjects formed before an experiment starts.
We reserve the word “treatment” for a condition that we impose on thesubjects. We don’t speak of 6 treatments in Example 3.19 even thoughwe can compare the responses of 6 groups of subjects formed by the 2blocks (men, women) and the 3 commercials. Block designs are similar tostratified samples. Blocks and strata both group similar individuals together.
We use two different names only because the idea developed separately forsampling and experiments. The advantages of block designs are the sameas the advantages of stratified samples. Blocks allow us to draw separateconclusions about each block—for example, about men and women in theadvertising study in Example 3.19. Blocking also allows more precise overallconclusions because the systematic differences between men and women canbe removed when we study the overall effects of the three commercials.
The idea of blocking is an important additional principle of statisticaldesign of experiments. A wise experimenter will form blocks based on themost important unavoidable sources of variability among the experimental FIGURE 3.6 Outline of a block design, for Example 3.19. The blocks consist of male and
female subjects. The treatments are three television commercials.
subjects. Randomization will then average out the effects of the remainingvariation and allow an unbiased comparison of the treatments.
Like the design of samples, the design of complex experiments is a job for experts. Now that we have seen a bit of what is involved, we will usuallyjust act as if most experiments were completely randomized.
APPLY YOUR
Does charting help investors? Some investment advisors believe that charts
KNOWLEDGE
of past trends in the prices of securities can help predict future prices. Most KNOWLEDGE
economists disagree. In an experiment to examine the effects of using charts,business students trade (hypothetically) a foreign currency at computerscreens. There are 20 student subjects available, named for convenience A,B, C, . . ., T. Their goal is to make as much money as possible, and the bestperformances are rewarded with small prizes. The student traders have theprice history of the foreign currency in dollars in their computers. They mayor may not also have software that highlights trends. Describe two designsfor this experiment, a completely randomized design and a matched pairsdesign in which each student serves as his or her own control. In both cases,carry out the randomization required by the design.
Comparing weight-loss treatments. Twenty overweight females have agreed
to participate in a study of the effectiveness of 4 weight-loss treatments: A,
B, C, and D. The company researcher first calculates how overweight each
subject is by comparing the subject’s actual weight with her “ideal” weight.
The subjects and their excess weights in pounds are
The response variable is the weight lost after 8 weeks of treatment. Becausea subject’s excess weight will influence the response, a block design isappropriate.
(a) Arrange the subjects in order of increasing excess weight. Form 5 blocks of 4 subjects each by grouping the 4 least overweight, then the next 4,and so on.
(b) Use Table B to randomly assign the 4 subjects in each block to the 4 weight-loss treatments. Be sure to explain exactly how you used thetable.
3.2 SUMMARY
Ⅵ In an experiment, we impose one or more treatments on the subjects.
Each treatment is a combination of levels of the explanatory variables,
which we call factors.
Ⅵ The design of an experiment describes the choice of treatments and the
manner in which the subjects are assigned to the treatments.
CHAPTER 3 Ⅲ Producing Data
Ⅵ The basic principles of statistical design of experiments are control,
randomization, and replication.
Ⅵ The simplest form of control is comparison. Experiments should
compare two or more treatments in order to avoid confounding of the
effect of a treatment with other influences, such as lurking variables.
Ⅵ Randomization uses chance to assign subjects to the treatments.
Randomization creates treatment groups that are similar (except for
chance variation) before the treatments are applied. Randomization and
comparison together prevent bias, or systematic favoritism, in experiments.
Ⅵ You can carry out randomization by giving numerical labels to the
subjects and using a table of random digits to choose treatment groups.
Ⅵ Replication of each treatment on many subjects reduces the role of
chance variation and makes the experiment more sensitive to differences
among the treatments.
Ⅵ Good experiments require attention to detail as well as good statistical
design. Many behavioral and medical experiments are double-blind. Lack
of realism in an experiment can prevent us from generalizing its results.
Ⅵ In addition to comparison, a second form of control is to restrict
randomization by forming blocks of subjects that are similar in some
way that is important to the response. Randomization is then carried out
separately within each block.
Ⅵ Matched pairs are a common form of blocking for comparing just two
treatments. In some matched pairs designs, each subject receives both
treatments in a random order. In others, the subjects are matched in pairs
as closely as possible, and one subject in each pair receives each treatment.
SECTION 3.2 EXERCISES
3.42
Public housing. A study of the effect of living in public housing on the income
and other variables in poverty-level households was carried out as follows.
The researchers obtained a list of all applicants for public housing during
the previous year. Some applicants had been accepted, while others had
been turned down by the housing authority. Both groups were interviewed
and compared. Is this study an experiment or an observational study? Why?
What are the explanatory and response variables? Why will confounding
make it difficult to see the effect of the explanatory variable on the response
variables?
Effects of price promotions. A researcher studying the effect of price pro-
motions on consumers’ expectations makes up a history of the store price
of a hypothetical brand of laundry detergent for the past year. Students in a
marketing course view the price history on a computer. Some students see
a steady price, while others see regular promotions that temporarily cut the
price. Then the students are asked what price they would expect to pay for
the detergent. Is this study an experiment? Why? What are the explanatory
and response variables?

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