The Analysis of Population-Based Survey Experiments

1. The Analysis of Population-Based Survey Experiments Diana C. Mutz University of Pennsylvania

2. 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!

3. The Basics • Well measured Dependent Variable(s) • Manipulation check (to ensure that the Independent Variable was successfully manipulated by the experimental treatment)

4. 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)

5. The Basics • Well measured Dependent Variable • Manipulation checks (to ensure that the Independent Variable was successfully manipulated by the experimental treatment) OPTIONAL: • Potential Moderators/Contingent conditions • Covariates

6. An Example Does Social Trust Influence Willingness to Engage in Online Economic Transactions?

7. Four Issues in Analyses • Randomization checks/Balance tests • Statistical models for analysis • Weighting data to population parameters • Use and misuse of covariates

8. 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.

9. 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.

10. 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.

11. Part I. Balance tests? Rationales for balance tests • Credibility of findings • Efficiency of analyses

12. 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

13. 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.

14. 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.)

15. 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.

16. Efficiency • Can balance tests profitably inform the analyses of results? • What should one do if a balance test fails?

17. Three proposed “remedies” for failed balance tests • Inclusion of covariates • Post-stratification • Re-randomization

18. 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?

19. Inclusion of covariates 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.

20. 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.

21. 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

22. 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…

23. 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

24. 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

25. 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.”

26. 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.”

27. EXAMPLE 2: Five dummies for 6 conditions Regressions run amok with survey-experimental findings!

28. 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.

29. Four Issues in Analyses • Randomization checks/Balance tests • Statistical models for analysis • Weighting data to population parameters • Use and misuse of covariates

30. 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

31. Possible Weighting Options • 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 .

32. 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.

33. Calculating the Loss • 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.

34. Within-Condition Weights • Calculate via same formula for within-subject • Compare loss of power in within versus whole sample weighting

35. 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.

36. Four Issues in Analyses • Randomization checks/Balance tests • Statistical models for analysis • Weighting data to population parameters • Use and misuse of covariates

37. 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

38. 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 • Not a cure for an unlucky randomization (which isn’t necessary in any case) • But what’s the harm? Biased results

39. EXAMPLE 3: Treatment effects and their interactions with other variables

40. Treatment effects and their interactions with other variables But then what are these? “Control variables”

41. 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.

42. 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.