7. Which of the following statements accurately summarize claims made by Page and Shapiro in The Rational Public and their associated research articles? (Indicate all that apply.)
(a) Americans’ attitudes on policy alternatives are highly unstable over time, reflecting a rational response to unstable political conditions.
(b) When studying public opinion, question-wording is less important than scholars have traditionally thought.
(c) Attitudes about foreign policy change more abruptly than attitudes on domestic issues.
(d) The contents of the mass media account for a high proportion of opinion changes on foreign policy.
(e) Using the assumption of rationality, Page and Shapiro fit a hedonic regression to estimate the underlying utility function of survey respondents.
(f) Page and Shapiro use the term “rational” ironically; their fundamental claim is that Americans are easily distracted and that rational-public models are seriously flawed.
Solution to question 6
From yesterday:
6. A survey of New York City residents is performed using cluster sampling. The design effect is 3.0. From the survey, the estimated proportion who prefer the Mets to the Yankees is 0.42 with a standard error of 0.05. How many people were in the sample?
Solution: The standard error is sqrt(d.eff)*0.5/sqrt(n) = 0.05. Thus sqrt(n) = sqrt(d.eff)*(0.5/0.05), so n = 3*(0.5/0.05)^2 = 300.
Andrew, for educational purposes, could you explain this:
“standard error is sqrt(d.eff)*0.5/sqrt(n)”?
I always thought that SE=SD/sqrt(n). If that’s true, the above means that
SD = sqrt(d.eff )/2, meaning that design effect is simply 4 times the variance. Also, your formula implies that “design effect” is not unitless.
I can’t reconcile either with the definition of “design effect” given, e.g., in http://www.princeton.edu/~mjs3/salganik06.pdf :
“the ratio of the variance of the estimate under a specified sampling plan to the variance under simple random sampling (deff)”.
or in http://nces.ed.gov/statprog/2002/glossary.asp :
“The design effect (DEFF) is the ratio of the true variance of a statistic (taking the complex sample design into account) to the variance of the statistic for a simple random sample with the same number of cases”.
Thanks!
DK:
In a simple random sample, sd = sigma/sqrt(n). For a 0-1 outcome, sigma = sqrt(p*(1-p)) = 0.5 if p is near 1/2.
If it’s not a simple random sample, you have to multiply the variance by the design effect, i.e. multiply the se by the square root of the design effect.
Hence, in this case, se = sqrt(d.eff)*0.5/sqrt(n).
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