Transcript The Analysis of Population

Diana C. Mutz
University of Pennsylvania
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Simple, straightforward
No fancy statistical techniques required
Very few questions required
Comparison of means (analysis of variance)
Many problems result from using
observational analysis techniques on
experimental data
People make it more complicated than it needs
to be!
1.
2.
Well measured Dependent Variable(s)
Manipulation check (to ensure that the
Independent Variable was successfully
manipulated by the experimental treatment)
Causality requires meeting only 3 conditions:
1. Association (The easy part!)
2. Precedence in Time of Independent Variable
(We manipulate the Independent Variable)
3. Non-spuriousness of relationship
(Random assignment eliminates this problem)
1.
2.
Well measured Dependent Variable
Manipulation checks (to ensure that the
Independent Variable was successfully
manipulated by the experimental treatment)
OPTIONAL:
1. Potential Moderators/Contingent conditions
2. Covariates
Does Social Trust Influence Willingness to Engage
in Online Economic Transactions?
CONTROL
CONDITION
POSITIVE
SOCIAL
TRUST
NEGATIVE
SOCIAL
TRUST
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Randomization checks/Balance tests
Statistical models for analysis
Weighting data to population parameters
Use and misuse of covariates
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Randomization checks/balance tests: They
can’t tell us what we want to know, and they
can lead to inferior model choices
Statistical models for analyzing populationbased survey experiments often altogether
ignore the fact that they are, indeed,
experiments.
We assume….
 Researcher has control over assignment to
conditions
 Respondents do not undergo attrition
differentially as a result of assignment to a
specific experimental condition
 Researcher can ensure that those assigned
to a given treatment are, in fact, exposed
to treatment.
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If any one of those 3 requirements is not met,
then balance tests can make sense
If the randomization mechanism requires
pretesting, then balance tests make sense
Otherwise, not.
Rationales for balance tests
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Credibility of findings
Efficiency of analyses
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Lack of faith in or thorough understanding of
probability theory
Confusion between frequentist and Bayesian
paradigms
Mistakenly applying methods for
observational analyses to experimental results
Field experimental literature in which
exposure to treatment cannot always be
controlled
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What does it mean for a randomization to
“succeed”?
A well-executed random assignment to
experimental conditions does not promise to
make experimental groups equal on all
possible characteristics, or even a specified
subset of them.
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“Because the null hypothesis here is that the
samples were randomly drawn from the same
population, it is true by definition, and needs
no data.” (Abelson)
Randomization checks are “philosophically
unsound, of no practical value, and potentially
misleading.” (Senn)
“Any other purpose [than to test the
randomization mechanism] for conducting such
a test is fallacious.” (Imai et al.)
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“p<.05” already includes the probability that
randomization might have produced an
unlikely result
Thus experimental findings are credible
without any balance tests at all.
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Can balance tests profitably inform the
analyses of results?
What should one do if a balance test fails?
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Inclusion of covariates
Post-stratification
Re-randomization
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Is a failed balance test useful for purposes of
choosing covariates?
Covariates should be chosen in advance, not
based on the data.
Covariates are chosen for anticipated
relationship with the DV; balance tests
evaluate the relationship with the IV.
So is a balance test informative for model
selection?
NO!
 If inclusion of a variable as a covariate in the
model will increase the efficiency of an
analysis, then it would have done so, and to a
slightly greater extent, had it not failed the
balance test.
 Thus balance tests are uninformative when it
comes to the selection of covariates.
“Failed” randomization with respect to a
covariate should not lead a researcher to
include that covariate in the model. If the
researcher plans to include a covariate for the
sake of efficiency, it should be included in the
model regardless of the outcome of a balance test.
Changes the appropriate p-value
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Always excludes X: p1
Always includes X: p2
Not the same p-value that should result after
the 2-stage process
But most researchers simply report p1 or
p2
If they have no implications for the credibility of
our findings…
If they cannot improve the efficiency of our
analyses…
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They can’t tell us what we want to know
They can lead to inferior model choices
They can lead to unjustified changes in the
interpretation of findings
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Balance tests do not provide rationales for
including additional variables
Three examples of model and analysis choices
made for the wrong reasons
EXAMPLE 1: “In order to ensure that the experimental
conditions were randomly distributed—thus establishing the
internal validity of our experiment—we performed difference
of means tests on the demographic composition of the
subjects assigned to each of the three experimental
conditions.”
“Having established the random assignment of
experimental conditions, regression analysis
of our data is not required; we need only
perform an analysis of variance (ANOVA) to
test our hypotheses as the control variables
that would be employed in a regression were
randomly distributed between the three
experimental conditions.”
EXAMPLE 2:
Five dummies
for 6 conditions
Regressions run
amok with
surveyexperimental
findings!
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Regression versus analysis of variance is a red
herring. So are balance tests.
Especially in an experimental analysis,
everything needs a reason for being there.
True experiments should not have “control”
variables! (A few covariates are OK.)
The presence of unnecessary variables in a
statistical model should be viewed with
suspicion; they can hurt and bias results.
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2.
3.
4.
Randomization checks/Balance tests
Statistical models for analysis
Weighting data to population parameters
Use and misuse of covariates
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Should population-based experiments use
population weights supplied by survey
houses?
Some studies do, some don’t; no particular
rationale typically given
No one correct answer but need to consider:
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Possibility of heterogeneous effects
Power needs
Emphasis on generalizability
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No use of weights
Weighting sample as a whole to underlying
population parameters
Weighting formulated so that individual
experimental conditions reflect population
parameters
Either (1) or (2) benefits through increasing
generalizability to full population; (2) is better at
reducing noise due to uneven randomization
But all weighting sacrifices power .
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If all the full sample weights are squared for a
sample of size n, and then summed across all
subjects, this sum (call it M1) provides a sense
of just how much power is lost through
weighting:
𝑛
=1 −
𝑀1
If M1 =3000 and n=2000, then the equation
will come out to .33.
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Weighting in this example lowers power as if
we had reduced the sample size by one-third.
Instead of a sample of 2000, we effectively have
the power of a sample size of 1340.
𝑛
=1 −
𝑀1
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Calculate via same formula for within-subject
Compare loss of power in within versus whole
sample weighting
𝑛
=1 −
𝑀1
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Request both whole sample and withincondition weights
Decision can be made on basis of importance
of power relative to generalizability
Ultimately depends on expectations about
heterogeneity of effects.
1.
2.
3.
4.
Randomization checks/Balance tests
Statistical models for analysis
Weighting data to population parameters
Use and misuse of covariates
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Because population-based survey experiments
involve survey data, often analyzed as if they
were observational studies
Mistaken use of unnecessary “control”
variables
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Because population-based survey experiments
involve survey data, often analyzed as if they
were observational studies
Mistaken use of unnecessary “control”
variables
Not a cure for an unlucky randomization
(which isn’t necessary in any case)
But what’s the harm? Biased results
EXAMPLE 3:
Treatment
effects and their
interactions with
other variables
Treatment
effects and their
interactions with
other variables
But then what
are these?
“Control
variables”
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To improve efficiency when selected in
advance from pretest measures based on
advance knowledge of predictors of dependent
variable
Better yet, use blocking if equality across
conditions on that particular variable is THAT
important.
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Too many available variables leads to suboptimal data analysis practices.
Researchers need to rely more on the elegance
and simplicity of their experimental designs.
Equations chock full of “control” variables
demonstrate a fundamental misunderstanding
of how experiments work.
Failed randomization checks should never be
used as a rationale for inclusion of a particular
covariate.