THE ANALYSIS OF POPULATION-BASED
SURVEY EXPERIMENTS
Diana C. MutzUniversity of Pennsylvania
Analysis of Experiments 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!
The Basics1. Well measured Dependent Variable(s)2. Manipulation check (to ensure that the
Independent Variable was successfully manipulated by the experimental treatment)
Why Not More?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)
The Basics1. Well measured Dependent Variable2. Manipulation checks (to ensure that the
Independent Variable was successfully manipulated by the experimental treatment)
OPTIONAL:3. Potential Moderators/Contingent
conditions4. Covariates
An ExampleDoes Social Trust Influence Willingness to Engage in Online Economic Transactions?
CONTROLCONDITION
POSITIVESOCIALTRUST
NEGATIVESOCIALTRUST
1. Randomization checks/Balance tests2. Statistical models for analysis3. Weighting data to population parameters4. Use and misuse of covariates
Four Issues in Analyses
Two common errors: 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 population-based survey experiments often altogether ignore the fact that they are, indeed, experiments.
The Parameters
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.
The Parameters 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.
Part I. Balance tests?
Rationales for balance tests Credibility of findings Efficiency of analyses
Origins of this Practice? 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
Credibility of Findings 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.
Credibility of Findings “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.)
Credibility of Findings “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.
Efficiency Can balance tests profitably inform the
analyses of results? What should one do if a balance test
fails?
Three proposed “remedies” for failed balance tests
Inclusion of covariates Post-stratification Re-randomization
Inclusion of covariates 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?
Inclusion of covariatesNO! 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.
Inclusion 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.
Two-stage analysis:Balance test, then hypothesis test
Changes the appropriate p-value 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
Why are we doing randomization checks?
If they have no implications for the credibility of our findings…
If they cannot improve the efficiency of our analyses…
Why not? 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
Part II. Statistical models 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.”
Irrelevant factors often dictate model selection and analysis
“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.”
Regressions run amok with survey-experimental findings!
Five dummies for 6 conditions
EXAMPLE 2:
What’s the point? 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.
Four Issues in Analyses
1. Randomization checks/Balance tests2. Statistical models for analysis3. Weighting data to population parameters4. Use and misuse of covariates
Part III. Using Weights 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: Possibility of heterogeneous effects Power needs Emphasis on generalizability
Possible Weighting Options1. No use of weights2. Weighting sample as a whole to underlying
population parameters3. 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 .
Calculating the Loss 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:
If M1 =3000 and n=2000, then the equation will come out to .33.
¿1− 𝑛𝑀 1
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.
Calculating the Loss
¿1− 𝑛𝑀 1
Within-Condition Weights Calculate via same formula for within-
subject Compare loss of power in within versus
whole sample weighting
¿1− 𝑛𝑀 1
Weighting Recommendations Request both whole sample and within-
condition weights Decision can be made on basis of
importance of power relative to generalizability
Ultimately depends on expectations about heterogeneity of effects.
1. Randomization checks/Balance tests2. Statistical models for analysis3. Weighting data to population parameters4. Use and misuse of covariates
Four Issues in Analyses
Part IV. (In)appropriate Uses of Covariates
Because population-based survey experiments involve survey data, often analyzed as if they were observational studies
Mistaken use of unnecessary “control” variables
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
Part IV. (In)appropriate Uses of Covariates
Treatment effects and their interactions with other variables
EXAMPLE 3:
But then what are these? “Control variables”
Treatment effects and their interactions with other variables
Appropriate Uses of Covariates 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.
An Embarrassment of Riches
Too many available variables leads to sub-optimal 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.