Transcript Lecture 7: Designing Experiments

Lecture 7: Designing
Experiments
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Units: Subjects, patients, animals
Treatment: A specific experimental
condition applied to the units.
Explanatory variables in a designed
experiment are often called factors
We want to see the changes in the
response as the factor changes
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The specific values of a factor are often
called the levels
treatments are often formed by combining
different levels of different factors.
Example: A drug is injected into 30 people.
After half an hour the blood level of the drug
is measured. Factor: drug with one level.
Example: Three doses of the drug injected to
three groups of 10 people each. Factor: drug
with three levels.
Two factor experiment
Suppose in the previous experiment three
doses of the drug were given to 10 people , 5
after meal and 5 before meal. Then meal
time is another factor along with drug.The
layout of the design looks like:
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Before meal After meal
Dose 1
5
5
Dose 2
5
5
Dose 3
5
5
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The 3X2=6 possible level combinations are
called treatments.
 Example 2: Gastric freezing: A treatment for
ulcer was reported to be an effective
treatment as many people treated by this
method reported relief. It was used for a few
years.
 Later a designed study showed
Gastric freezing : 82 patients 34% reported
improvement
Placebo: treated with liquid at body
temperature : 78 patients 38% reported
improvement
Use of gastric freezing was abandoned.
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Randomized comparative
experiments:
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First step to design an experiment: Specify
response, factors and their levels, layout of
the treatments, comparisons of interest
Second step is to allocate units randomly to
treatments
Comparison is valid only if treatments are
applied unbiasedly to homogeneous groups of
units.
comparing two drugs by giving one to
seriously ill patients, another to not so
seriously ill patients confounds the real effect
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The use of chance or randomness to divide
experimental units into groups is called
randomization.
An experiment which uses both
randomization and comparison is called a
randomized comparative experiment.
Example: One wants to compare a new
training program for pharmacists. A group of
20 pharmacists volunteered. All were given a
pre test. Their names were then mixed in a
hat and 10 were drawn randomly.
Those 10 were offered the new training
program, remaining 10 were trained by
standard method. A post test was given. Pre
and post scores were compared for the two
groups.
Completely Randomized
Design
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Units are randomly allocated to the
treatments, usually equal number of units per
treatment.
Example: three fertilizers are randomly
assigned to 10 plants each. Growth was
measured at 2 days, 10 days, a month.One
can think about many randomization
strategies to accomplish this.
Why need designing:
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random assignment of subjects forms groups
that should be similar in all respects before
the treatment is applied, so controls the
effects of lurking variables on the response.
Influences other than the treatment occur
uniformly on each group.
Differences in average response must be due
either to the treatments or to the play of
chance in random assignments.
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We should use enough units in each group to
reduce variations due to chance so that the
effects of the treatments are clearly
pronounced.
Control, Randomization and Replication are
the three fundamental prinicples of
experimental design.
Statistical significance: An observed effect so
large that it would rarely occur by chance is
called statistically significant
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We can use laws of probability to give a
mathematical description of chance behaviour
and assess the likelihood of what differences
we may see if only chance was operating.
A well-designed randomized comparative
experiment produce data which is capable of
indicating a good causal relationship.
If results from such a study are statistically
significant, one may rely on the strength of
evidence.
Cautions about
experimentation:
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One must be careful that the random
assignment is really fair and unbiased.
To prevent any bias from any side often the
experiments are double blind, the subject and
the investigator do not know which treatment
the subject is receiving until the experiment is
complete.
Attention should be given to uniformity of
experimental conditions for each patient.
Matched Pair designs
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Completely randomized designs are
often the easiest design but may not be
so efficient.
Matching the subjects can produce
more precise results than
randomization.
Matched pairs design compares only
two treatments
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Choose pairs of subjects as similar as
possible.
Toss a coin, if it is a head give treatment A
to subject 1 and B to subject 2.
Sometimes “pair” is only one subject..give
him one treatment..wait a while..give him the
other treatment
the order in which treatment is applied (AB
or BA ) is decided by a coin toss.
This way a subject serves as its own control.
Example: Coke vs.Pepsi
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subjects drink two colas , the order of tasting
was chosen randomly for each subject.
More than half coke drinkers chose pepsi
Coke glasses were marked Q , pepsi glasses
were marked M.
Coke said people just like M better than Q..
To have a full proof experiment, they should
have made the drinkers blindfolded or the
glasses visibly identical…
Block Designs:
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A block is a group of experimental
units which are known to be similar in
some way that is expected to affect the
response to the treatments. Units within
a block are as homogeneous as
possible. Units between blocks are
expected to be heterogeneous.
Treatments are randomly assigned to
units within a block.
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Blocking controls for the outside blocking
factor.
Example: Want to assess a new welfare
system’s impact on family income. Present
family income has strong influence of future
family income. So families with same level of
current income were used as blocks. Then
they were randomly assigned to the new and
existing welfare system. Comparison within
blocks removes variation due to current
income.
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The principle of blocking is a very
crucial principle in statistical design.
Blocking eliminates variation due to the
blocking factor and leads to more
precise estimate of treatment
differences.
A wise experimenter will choose his
blocking factor very carefully.
Summary
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Recognize a study to be observational or
experimental
Identify response, factors and levels,
treatments, units
Draw the design layout
Carry out the actual random allocation either
by using Table B or software.
Be aware of lurking variables confounding
treatment effect
Realise when matched pairs or block designs
are appropriate
Be aware of placebo effect, need for doubleblind experiments.