Obtaining data

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Obtaining data

• Available data are data that were produced in the
  past for some other purpose but that may help
  answer a present question inexpensively. The
  library and the Internet are sources of available
  data.
• Government statistical offices are the primary
  source for demographic, economic, and social data
  (visit the Fed-Stats site at www.fedstats.gov).
• Beware of drawing conclusions from our own
  experience or hearsay. Anecdotal evidence is
  based on haphazardly selected individual cases,
  which we tend to remember because they are
  unusual in some way. They also may not be
  representative of any larger group of cases.
• Some questions require data produced specifically
  to answer them. This leads to designing
  observational or experimental studies.

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Observational study Record data on individuals
without attempting to influence the responses. We
typically cannot prove cause effect this
way. Example Based on observations you make in
nature,you suspect that female crickets choose
theirmates on the basis of their health. ?
Observehealth of male crickets that mated.
Experimental study Deliberately impose a
treatment on individuals and record their
responses. Lurking variables can be
controlled. Example Deliberately infect some
males with intestinal parasites and see whether
females tend to choose healthy rather than ill
males.
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• a sample is a collection of data drawn from a
  population, intended to represent the population
  from which it was drawn a census is an attempt
  to sample every individual in the population.
• an experiment imposes a so-called treatment on
  individuals in order to observe their responses.
  This is in opposition to an observational study
  which simply observes individuals and measures
  variables of interest without intervention
• go over Examples 3.4-3.6 on p. 176-177 (Chapter
  3, Introduction)

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Terminology of experiments

• The individuals in an experiment are the
  experimental units. If they are human, we call
  them subjects.
• In an experiment, we do something to the subject
  and measure the response. The something we do
  (explanatory variable) is a called a treatment,
  or factor. The values of the factor are called
  its levels. Sometimes a treatment is a
  combination of levels of more than one factor.
• The factor may be the administration of a drug
  the different dosages are its levels.
• One group of people may be placed on a
  diet/exercise program for six months (treatment),
  and their blood pressure (response variable)
  would be compared with that of people who did not
  diet or exercise. Two levels here on diet, not
  on diet

5

• Go over example 3.8 on page 179 (3.1, 1/8) and
  below an example of a designed experiment with
  two factors and six treatments. Also see Ex.
  3.9, p. 180 (3.1, 2/8) for an example of an
  experiment not designed well... The lack of a
  control group causes the problem...

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• If the experiment involves giving two different
  doses of a drug, we say that we are testing two
  levels of the factor.
• A response to a treatment is statistically
  significant if it is larger than you would expect
  by chance (due to random variation among the
  subjects). We will learn how to determine this
  later.

• In a study of sickle cell anemia, 150 patients
  were given the drug hydroxyurea, and 150 were
  given a placebo (dummy pill). The researchers
  counted the episodes of pain in each subject.
  Identify
• The subjects
• The factors / treatments
• And the response variable

• (patients, all 300)

• 1 factor, 2 levels (hydroxyurea and placebo)

• (episodes of pain)

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• In principle, experiments can give good evidence
  for causation through what we call randomized
  controlled comparative experiments.
• The need for comparative experiments is shown in
  Example 3.9 on p. 180 a control group is needed
  so the experimenter can control the effects of
  outside (lurking) variables
• The use of randomization is illustrated in
  Example 3.10 (3.1, 3/8) a chance mechanism is
  used to divide the experimental units into groups
  to prevent bias.

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• The logic behind randomized comparative
  experiments is given on p. 183 (3.1, 4/8)
• Randomization produces groups of subjects that
  should be similar in all respects before the
  treatments are applied
• Comparative design ensures that influences other
  than the treatment operate equally on all groups
• Therefore, differences in the response must be
  due either to the treatment or to chance in the
  random assignment of subjects to the groups.
• This lead to three basic principles of
  experimental design on page 183-184

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• Control the effects of lurking variables on the
  response, usually by comparing two or more
  treatments
• Randomize use a chance mechanism to assign
  experimental units to treatments. See the Table
  B of random digits discussed on the later slides
• Repeat each treatment on many units to reduce
  chance variation in the results
• Then if you see differences in the response they
  are called statistically significant if they
  would rarely occur by chance

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Caution about experimentation
The design of a study is biased if it
systematically favors certain outcomes.
The best way to exclude biases in an experiment
is to randomize the design. Both the individuals
and treatments are assigned randomly.
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• Other ways to remove bias
• A double-blind experiment is one in which neither
  the subjects nor the experimenter know which
  individuals got which treatment until the
  experiment is completed. The goal is to avoid
  forms of placebo effects and biases in
  interpretation.
• The best way to make sure your conclusions are
  robust is to replicate your experimentdo it
  over. Replication ensures that particular results
  are not due to uncontrolled factors or errors of
  manipulation.

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Designing controlled experiments
Sir Ronald FisherThe father of statistics He
was sent to Rothamsted Agricultural Station in
the United Kingdom to evaluate the success of
various fertilizer treatments.

• Fisher found the data from experiments going on
  for decades to be basically worthless because of
  poor experimental design.
• Fertilizer had been applied to a field one year
  and not in another in order to compare the yield
  of grain produced in the two years. BUT
• It may have rained more, or been sunnier, in
  different years.
• The seeds used may have differed between years as
  well.
• Or fertilizer was applied to one field and not to
  a nearby field in the same year. BUT
• The fields might have different soil, water,
  drainage, and history of previous use.
• ? Too many factors affecting the results were
  uncontrolled.

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Fishers solution
Randomized comparative experiments

• In the same field and same year, apply fertilizer
  to randomly spaced plots within the field.
  Analyze plants from similarly treated plots
  together.
• This minimizes the effect of variation within the
  field in drainage and soil composition on yield,
  as well as controlling for weather.

F F F F F F
F F F F F F F F
F F F F F
F F F F F F F F
F F F F F
F F F F
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A Table of Random Digits can be used to Randomize
an Experiment

• any digit in any position in the table is as
  equally likely to be 0 as 1 as 2 as as 9
• the digits in different positions are independent
  in the sense that the value of one has no
  influence on the value of any other
• any pair of random digits has the same chance of
  being picked as any other (00, 01, 02, 99)
• any triple of random digits has the same chance
  of being picked as any other (000, 001, 999)
• and so on

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• Now use Table B to randomly divide the 40
  students in Ex. 3.10 into the two groups (control
  group and experimental group)
• Step 1 Label the experimental units with as few
  digits as possible
• Step 2 Decide on a protocol for how you will
  place the chosen units into the groups
• Step 3 Start anywhere in the Table and begin
  reading random digits. Matching them with
  labeled experimental units and following the
  protocol creates the groups.
• Go over example 3.11 on page 185ff (3.1, 5/8) in
  detail until you understand!

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• EX.3.10 We need to randomly divide the 40
  students into two groups of 20-the cell phone
  talking while driving and the driving group only.
• List and number (label) all available subjects
  (the group of 40).
• Decide that the first 20 students chosen go to
  the experimental group the remainder to the
  control group (this is the protocol)
• Scan Table B in groups of numbers that are two
  digits long. Match the digits with the labels and
  follow the protocol to form the groups.

45 46 71 17 09 77 55 80 00 95 32 86
32 94 85 82 22 69 00 56
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• There are many types of experimental designs in
  use today in the sciencesread about these on p.
  189-191 (3.1, 7/8 8/8)
• Completely randomized all experimental units
  are allocated at random among all treatments (Ex.
  3.10)
• Block designs A block is a group of experimental
  units or subjects known in advance to be similar
  in some way that is expected to affect the
  response to the treatments. Knowing this, the
  experimenter can create a block design, in which
  the random assignment of units is carried out
  separately within each block. See examples
  3.18-3.20 for some examples
• Matched pairs This is a common design in which a
  block design is used to compare just two
  treatments. Sometimes each subject receives both
  treatments (acts as its own control), or there is
  a before-after design.

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Completely randomized designs
Completely randomized experimental
designs Individuals are randomly assigned to
groups, then the groups are randomly assigned to
treatments.
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Block designs
In a block, or stratified, design, subjects are
divided into groups, or blocks, prior to the
experiment to test hypotheses about differences
between the groups. The blocking, or
stratification, here is by gender.
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Matched pairs designs
Matched pairs Choose pairs of subjects that are
closely matchede.g., same sex, height, weight,
age, and race. Within each pair, randomly assign
who will receive which treatment. It is also
possible to just use a single person, and give
the two treatments to this person over time in
random order (before/after). In this case,
the matched pair is just the same person at
different points in time. Pre/post testing of a
new teaching method is another example...
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• Read the Introduction Section 3.1. Watch the
  StatTutors - I'll assign them officially on the
  StatsPortal. Pay particular attention to all the
  Examples. Make sure you understand the
  terminology and the sketches of the types of
  designs... Also, make sure you can use Table B
  to perform a completely randomized design.
• Do 3.3, 3.4, 3.6, 3.7, 3.9, 3.11, 3.12, 3.18,
  3.19, 3.21, 3.26, 3.27-3.29, 3.35, 3.39
• Test 1 will cover Chapters 1-3 and some parts of
  Ch.4. Start getting ready for it!