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We reviewed sample surveys in a previous video Introduction to Sampling.
Researchers use a variety of terms to describe who is measured. The generic term unit
is used to indicate a single individual or object being measured. When the units are
people, they are usually called subjects or participants.
The two groups: subjects who ate an apple a day and those who ate less than 1 apple a week
might differ in more ways that effect the number of new cavities than just the
explanatory variable (apple eating frequency) when confounding is present.
The key to identifying a possible confounding variable is to explain how it is linked
to both the explanatory variable and the response variable in a way that also explains the
observed association.
Both explanations – “eating an apple a day” and “eating fewer sugary snacks” are consisted
with a reduction in cavities. In this study, we have no way of separating out the effects
of “eating an apple a day” from the effects of “eating fewer sugary snacks” on our response
variable, number of new cavities. We may say that eating an apple a day is
associated with fewer new cavities but we cannot say that eating an apple a day causes
fewer new cavities. Don’t get the idea that Observational Studies are useless. It is
sometimes impossible or unethical to conduct a randomized experiment. Consider
the relationship between smoking and lung cancer. Numerous studies over the years
have shown a strong association between smoking and lung cancer. It would be unethical
to conduct an experiment in which one group of volunteers was instructed to smoke a
certain number of cigarettes each day and another group instructed to refrain from
smoking. Many case-controlled studies conducted to determine the relationship between
smoking and lung cancer have led to increased awareness of the harmfulness of smoking in
addition to restrictions on sale of tobacco products to minors. In a case-control study
case-subjects and controls should differ only with respect to disease status and exposure
to the agent under investigation. In the 1920s, health care workers in Great
Britain first began to suspect a relationship between cigarette smoking and lung
cancer. The suspicion was based on the fact that many patients who acquired lung cancer were
also smokers. Although this was an astute observation, these workers lacked the scientific
evidence to justify their position. As a result, between 1930 and 1960, numerous
epidemiologic studies were undertaken to try to quantify the relationship between
cigarette smoking and lung cancer. Two of these studies, one in 1947 by Sir Richard Doll
and one in 1951 by A.B. Hill, are considered classics. Doll used the case-control study
method and compared the smoking history of a group of hospitalized patients with lung
cancer with the smoking history of a similar group without lung cancer. Hill used a cohort
study, categorizing a group of British physicians according to their smoking histories and
then analyzing the causes of death among those who died, to see whether cigarette smokers
had the highest incidence of lung cancer.
But sometimes it can give us a pretty big hint that a relationship truly does exist!
Randomly assigning experimental units or subjects to the different treatment groups
tends to balance out all the other variables between the groups. Any variables that
could have an effect on the response should be equalized between the groups and
therefore should not be confounding. If an observed difference in the groups is too
large to be expected to happen by the random chance inherent in the random assignment process,
then a plausible explanation for the observed differences is the treatment received and we can
assign a cause-and-effect relationship between the explanatory and response
variables.
We already looked at the role randomization plays in an experiment. In order to
determine whether or not our treatment had an effect on the response variable we are
measuring, we need to know what would have happened to the response variable if the
treatment had not been applied. To do this experimenters create control groups which are
treated identically in all respects except for the treatment received. A control
group may receive a standard or existing treatment that is compared to a new drug or they
may receive a placebo, a drug that looks like the treatment but has no active ingredients.
Comparison of two or more treatments is the simplest form of control. Replication
more subjects that are used in an experiment, the more likely that randomization will create
groups that are alike on average. Then, when differences are averaged out, only the
effects of the different treatments or random chance (as a result of chance assignment)
remain.
To summarize, a well-designed experiment must have both random assignment of
experimental units to treatments and a control or comparison group that is
compared to the group receiving the treatment of interest. Replication is the random
assignment of the same treatment to different experimental units. Each
treatment is randomized to enough experimental units to provide adequate assessment of
how much the responses from the same treatment vary. When these key elements are present, the
experiment is called a randomized comparative experiment.
In order for the control and treatment groups to be treated exactly the same except for the
treatment they receive, both the subjects and the person administering the treatment
should be “blind”. In a blind experiment, the subject does not know which treatment they
are receiving. In a double-blind experiment, neither the subject or the
person administering the treatment has knowledge of which treatment the subject
received. In a double-blind experiment, the treatments are typically coded with a number
that only the researching analyzing the final results knows the group to which the
treatment belongs.
A diagram is not necessary, but it can help us organize the components of a well-designed
experiment. If you decide to use a diagram, you should follow it up with a written
explanation of the experimental design. You do not need to explain the randomization
technique you will use unless specifically asked. This is often a part (b) follow-up
question. You may want to review the different ways to choose a random sample in the
Introduction to Sampling video.
Individuals in a block should be as homogeneous (or similar) as possible with respect to what we
are measuring and different blocks should be different with respect to the response
variable.
In summary, in the words of the esteemed *** Scheaffer, the first chief reader for the AP
Statistics exam. Blocking is used to control for anticipated variability by creating blocks
that are enough alike that you expect them to have a similar response to any
treatment. Randomization balances out factors that we couldn’t control for by
creating treatment groups that are as similar as possible except for the treatment being
imposed.
The top dotplot is the graph of the individual differences in pulse rates (standing –
sitting) for each student in the class. We can see that one student had a sitting and
standing pulse rate that was the same (difference=0), but the rest of the students had
standing pulse rates that were higher than their sitting pulse rates (difference were
positive). The matched-pairs design controlled for the person- to-person variability in
pulse rates making it clear that standing pulse rates tend to be higher than sitting pulse
rates.
The class data was entered into StatKey and a simulated sampling distribution of the difference
in pulse rates (stand-sit) when any effect of position in which the pulse rate was taken, was
removed by randomly shuffling the students’ pulse rates and assigning half to the sit group
and the other half to the stand group. The differences (stand- sit) were recorded and
the mean difference calculated. This simulation was then repeated for a total of 1000
trials.
Technically, if the experimental units are not randomly selected from the population, we can say
attribute a cause-and-effect relationship but any inference is limited to only the
experimental units included in the study. This is very limiting, and in reality,
researchers try to justify a larger population that their experimental units are likely
representative of in order to broaden the scope of interest.
In an experiment, researchers manipulate something and measure the effect of the
manipulation on some outcome of interest. Randomized experiments are experiments in
which the participants are randomly assigned to participate in one condition or
another. The different conditions are called the “treatments”.