Math 1530 - Chapter 4
GATHERING DATA
Chapter 4
Learning Objectives:
1.
2.
3.
4.1 Experiment or Observe?
Population versus
Sample
Types of Studies:
Experimental and
Observational
Comparing
Experimental and
Observational Studies
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Population and Samples
Population: Subjects of
interest
Sample: Subset for whom
we have data
Often want answers
about large group but
can’t measure all, so a
subset is chosen
Use statistical techniques
to make conclusions
Observational Study
Merely observe values of
response and
explanatory variables
without doing anything
to the subjects
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Math 1530 - Chapter 4
Sample Survey
Experiment
Select sample
and interview
Observational
study
Census is survey
of entire
population
Imposes certain
conditions and
observes outcomes
Experimental
conditions =
explanatory
variable values =
treatments
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Experiments and Observational Studies
Experiment reduces lurking
variables and thus outside
influences
Experiments establish cause
and effect, unlike
observational studies
Some experiments
impractical because of
ethics, time, money, etc.
4.2 What are Good and Poor Ways to Sample?
www.purbeck.gov.uk
Learning Objectives:
1.
2.
3.
4.
5.
6.
7.
Sampling Frame &
Sampling Design
Simple Random Sample
Random number table
Margin of Error
Convenience Samples
Types of Bias in Sample
Surveys
Key Parts of Sample
Survey
Sampling Frame & Sampling Design
Sampling frame – list of
subjects in (hopefully
total) population
Sampling design
determines how sample
is selected
www.nedarc.org
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Math 1530 - Chapter 4
Simple Random Sampling (SRS)
Random Sampling –
best way to get
representative sample
Simple Random Sample
– each possible sample
of set size n has equal
chance of being
selected
SRS: Table of Random Numbers
Pg. A6 of text
1.
2.
3.
Number subjects
Select numbers from random number table or
random number generator
Include subjects with random numbers selected
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Margin of Error for Population Percentages
Example: Margin of Error
Margin of Error –
how well sample
predicts population
With n subjects in
SRS, margin of error
is about
A survey result
states: “The
margin of error
is plus or minus
3 percentage
points”
1
×100%
n
2010 British PM Election
i.telegraph.co.uk
Convenience Samples: Poor Ways to Sample
Convenience Sample:
survey sample that’s
easy to get
† Unlikely to represent
population
† Often severe biases
† Results apply only to
observed subjects
Convenience Samples: Poor Ways to Sample
Volunteer Sample:
most common
convenience sample
where subjects
volunteer – not
representative
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Math 1530 - Chapter 4
Types of Bias in Sample Surveys
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Key Parts of a Sample Survey
Bias: Favoring parts of population
1. Sampling Bias: from
sampling method (e.g.,
nonrandom samples)
2. Nonresponse bias: some
subjects cannot be reached
or decline
3. Response bias: subject gives
incorrect response or
question is misleading
Identify entire
population
2.
Construct sampling
frame
3.
Random sampling
design to get n subjects
from frame
4.
Avoid sampling bias
1.
Cross-stitch Sampler
www.vam.ac.uk
Learning Objectives:
1.
2.
3.
4.
4.3 What are Good and Poor Ways to Experiment?
5.
6.
Elements of an Experiment
Experimental units:
Subjects
Treatment: Conditions
imposed on subjects
Explanatory variable:
Defines groups and
treatments
Response variable:
Outcome
Identify elements of
experiment
Experiments
3 components of good
experiments
Blinding the study
Statistical Significance
Generalizing results of
the study
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Experiments
Impose treatments on
subjects to observe
responses
Goal: compare effects of
treatments on response
Randomized experiments –
subjects randomly
assigned to treatments
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Math 1530 - Chapter 4
Placebo effect
3 Components of a Good Experiment
Placebo – fake
treatment; sugar
pill
Control or Comparison Group
Randomization
Replication
Placebo effect –
improving not from
real treatment but
from belief that he
or she should
improve
pages.cs.wisc.edu
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Principle 1: Control or Comparison Group
Control or Comparison Group
Helps analyze
effectiveness of
primary treatment
Placebo removes
lurking variables
Control group gets
placebo
† Clinical
trials may
compare new
treatment with existing
Experiments should
compare treatments
rather than effect of
single treatment
Example: 400
volunteers asked to quit
smoking with some
taking and some not
taking antidepressant
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Principle 2: Randomization
1.
2.
Eliminates bias
from researcher
assigning
subjects
Balances groups
on known and
lurking variables
Principle 3: Replication
1.
2.
Reduces
difference due
to ordinary
variation or
chance
Increases
chance that
results show
true difference
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Math 1530 - Chapter 4
Blinding the Experiment
Statistical Significance
Blind – subjects unaware
of which treatment used
Double-Blind Experiment
- Neither subjects nor
investigators know which
treatment
† Controls bias from
respondent and
experimenter
Statistically Significant
Difference –
Observed
difference is larger
than expected from
chance
gridskipper.com
Generalizing Results
Goal of
Experimentation –
Analyze association
between treatment
and response for
entire population
Generalize only to
population
represented by study
4.4 Other Ways to Conduct Experimental and
Observational Studies
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Learning Objectives
Sample Surveys: Random Sampling Designs
Understand basic principles
of the following:
1.
Sample Surveys
2.
Two Types of
Observational Studies
3.
Multifactor Experiment
4.
Matched Pairs Design
5.
Randomized Block
Design
Alternative to
experiments
1. Simple Random
Sampling
2. Cluster Random
Sampling
3. Stratified
Random
Sampling
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Math 1530 - Chapter 4
Cluster Random Sample
1.
2.
3.
Divide population
into large
number of
clusters, such as
city blocks
Select simple
random sample
of clusters
Use all subjects in
clusters as sample
Cluster Random Sample
Advantages
† Sampling
frame
unavailable
† Cost
Disadvantage
† Need larger
sample size
for same
reliability
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Stratified Random Sample
Stratified Random Sample
www.smh.com.au
1.
2.
3.
Divide the
population into
groups, strata
Select SRS from
each strata
Combine samples
from each for total
sample
Advantage
Ensures stratum
representation
Disadvantage
Need sampling
frame and to
which stratum
each subject
belongs
www.nedarc.org
Comparing Random Sampling Methods
Types of Observational Studies
Sample Survey:
current
2. Retrospective
Study: past
3. Prospective Study:
future
Cause not proven,
but studies can
support beliefs
1.
Back to the Future
youtube.com/watch?v=c8Rngy90Q14
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Math 1530 - Chapter 4
Retrospective Case-Control Study
Prospective Case-Control Study
Retrospective
Prospective
Studying sunlight
exposure and multiple
sclerosis connection…
Cases – have MS
Controls or don’t
Explanatory variable –
low sun or not
www.lisisoft.com
Studying
effects of
vegetarian
diet on heart
disease…
Cases – have heart disease
Controls or don’t
Explanatory variable –
vegetarian or not
www.dubaiinternetmarketing.com
Multifactor Experiments
Single experiment
analyzes two or more
factors
Learn more since
combinations may
affect response
Matched Pairs Design
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Subjects are somehow
matched
† Husband/wife, two plots in
same field, etc.
† Same individual – crossover
design
Randomly assign or randomize
order of treatments
Reduces effects of lurking
variables
www.marshallhammondwedding.info
Randomized Block Design
Block – subjects with common characteristics
Randomized Block Design, RBD – within each block,
randomly assign to treatments
Image Sources
Statistics: The Art and Science of Learning from Data, 2nd Edition, Agresti
and Franklin
http://www.consumersenergy.com/uploadedImages/CEWEB/YOUR_BUSI
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http://creativejuice.files.wordpress.com/2007/10/voyeur.jpg
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_0_0_7037531_300.jpg
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70b-800wi
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ford2.jpg
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http://www.youtube.com/watch?v=c8Rngy90Q14
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ges/subsetPopulation.gif
http://www.purbeck.gov.uk/images/bird%20watching.jpg
http://www.youthnoise.com/Assets/Image/Gill%27s%20images/coin_fli
p.jpg
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ay_1630464c.jpg
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http://www.stlouiscenterforclinicalresearch.com/slccrtest_files/volunteer_g
roup.jpg
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http://colorectal.surgery.ucsf.edu/media/1160745/randomization.gif
http://www.scientificamerican.com/media/inline/placebo-effect-a-curein-the-mind_1.jpg
http://www.redicecreations.com/ul_img/6999placebo_big.jpg
http://www.gpaulmckinneyjr.com/Files/images/quit_smoking.gif
http://www.clinplus.com/Portals/53286/images/iStock_000005903700
XSmall-resized-600.jpg
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