andrew_gelman_stats andrew_gelman_stats-2012 andrew_gelman_stats-2012-1352 knowledge-graph by maker-knowledge-mining
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Introduction: 19. A survey is taken of students in a metropolitan area. At the first stage a school is sampled at random. The schools are divided into two strata: 20 private schools and 50 public schools are sampled. At the second stage, 5 classes are sampled within each sampled school. At the third stage, 10 students are sampled within each class. What is the probability that any given student is sampled? Express this in terms of the number of students in the class, number of classes in the school, and number of schools in the area. Define appropriate notation as needed. Solution to question 18 From yesterday : 18. A survey is taken of 100 undergraduates, 100 graduate students, and 100 continuing education students at a university. Assume a simple random sample within each group. Each student is asked to rate his or her satisfaction (on a 1–10 scale) with his or her experiences. Write the estimate and standard error of the average satisfaction of all the students at the university. Introd
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same-blog 1 1.0 1352 andrew gelman stats-2012-05-29-Question 19 of my final exam for Design and Analysis of Sample Surveys
Introduction: 19. A survey is taken of students in a metropolitan area. At the first stage a school is sampled at random. The schools are divided into two strata: 20 private schools and 50 public schools are sampled. At the second stage, 5 classes are sampled within each sampled school. At the third stage, 10 students are sampled within each class. What is the probability that any given student is sampled? Express this in terms of the number of students in the class, number of classes in the school, and number of schools in the area. Define appropriate notation as needed. Solution to question 18 From yesterday : 18. A survey is taken of 100 undergraduates, 100 graduate students, and 100 continuing education students at a university. Assume a simple random sample within each group. Each student is asked to rate his or her satisfaction (on a 1–10 scale) with his or her experiences. Write the estimate and standard error of the average satisfaction of all the students at the university. Introd
2 0.78340089 1353 andrew gelman stats-2012-05-30-Question 20 of my final exam for Design and Analysis of Sample Surveys
Introduction: 20. Explain in two sentences why we expect survey respondents to be honest about vote preferences but possibly dishonest about reporting unhealty behaviors. Solution to question 19 From yesterday : 19. A survey is taken of students in a metropolitan area. At the first stage a school is sampled at random. The schools are divided into two strata: 20 private schools and 50 public schools are sampled. At the second stage, 5 classes are sampled within each sampled school. At the third stage, 10 students are sampled within each class. What is the probability that any given student is sampled? Express this in terms of the number of students in the class, number of classes in the school, and number of schools in the area. Define appropriate notation as needed. Solution: Probability a student is sampled is A*B*C, where A = 20/(# private schools) if the student is at a private school, or 50/(# public schools) if the student is at a public school, B = 5/(# classes in the student
3 0.49121362 1349 andrew gelman stats-2012-05-28-Question 18 of my final exam for Design and Analysis of Sample Surveys
Introduction: 18. A survey is taken of 100 undergraduates, 100 graduate students, and 100 continuing education students at a university. Assume a simple random sample within each group. Each student is asked to rate his or her satisfaction (on a 1–10 scale) with his or her experiences. Write the estimate and standard error of the average satisfaction of all the students at the university. Introduce notation as necessary for all the information needed to solve the problem. Solution to question 17 From yesterday : 17. In a survey of n people, half are asked if they support “the health care law recently passed by Congress” and half are asked if they support “the law known as Obamacare.” The goal is to estimate the effect of the wording on the proportion of Yes responses. How large must n be for the effect to be estimated within a standard error of 5 percentage points? Solution: se is sqrt(.5*.5/(n/2)+.5*.5/(n/2)) = 1/sqrt(n). Solve 1/sqrt(n) = .05, you get n = (1/.05)^2 = 400.
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Introduction: 10. Out of a random sample of 100 Americans, zero report having ever held political office. From this information, give a 95% confidence interval for the proportion of Americans who have ever held political office. Solution to question 9 From yesterday : 9. Out of a population of 100 medical records, 40 are randomly sampled and then audited. 10 out of the 40 audits reveal fraud. From this information, give an estimate, standard error, and 95% confidence interval for the proportion of audits in the population with fraud. Solution: estimate is p.hat=10/40=0.25. Se is sqrt(1-f)*sqrt(p.hat*(1-.hat)/n)=sqrt(1-0.4)*sqrt(0.25*0.75/40)=0.053. 95% interval is [0.25 +/- 2*0.053] = [0.14,0.36].
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Introduction: Phil Harris and Bruce Smith write: We have only recently chanced upon your blog while we were looking for responses to the “decline effect” in medical and scientific studies. We were especially taken by your comment that there is something wrong with the scientific method “if this method is defined as running experiments and doing data analysis in a patternless way and then reporting, as true, results that pass a statistical significance threshold.” To us, that seems to be standard operating procedure in much of social science, including our own field of education. Indeed quasi-experimental designs are the stock in trade of those who attempt to use “science” — we dare not say haruspicy, but you can if you like — to influence the course of public policy. Now, a new entrant into the cherry pickers sweepstakes seems to have emerged. It is on Charter School Performance in Indiana Schools . We are by no means professional statisticians or data analysts, but we have some background in
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Introduction: 19. A survey is taken of students in a metropolitan area. At the first stage a school is sampled at random. The schools are divided into two strata: 20 private schools and 50 public schools are sampled. At the second stage, 5 classes are sampled within each sampled school. At the third stage, 10 students are sampled within each class. What is the probability that any given student is sampled? Express this in terms of the number of students in the class, number of classes in the school, and number of schools in the area. Define appropriate notation as needed. Solution to question 18 From yesterday : 18. A survey is taken of 100 undergraduates, 100 graduate students, and 100 continuing education students at a university. Assume a simple random sample within each group. Each student is asked to rate his or her satisfaction (on a 1–10 scale) with his or her experiences. Write the estimate and standard error of the average satisfaction of all the students at the university. Introd
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Introduction: 20. Explain in two sentences why we expect survey respondents to be honest about vote preferences but possibly dishonest about reporting unhealty behaviors. Solution to question 19 From yesterday : 19. A survey is taken of students in a metropolitan area. At the first stage a school is sampled at random. The schools are divided into two strata: 20 private schools and 50 public schools are sampled. At the second stage, 5 classes are sampled within each sampled school. At the third stage, 10 students are sampled within each class. What is the probability that any given student is sampled? Express this in terms of the number of students in the class, number of classes in the school, and number of schools in the area. Define appropriate notation as needed. Solution: Probability a student is sampled is A*B*C, where A = 20/(# private schools) if the student is at a private school, or 50/(# public schools) if the student is at a public school, B = 5/(# classes in the student
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Introduction: 18. A survey is taken of 100 undergraduates, 100 graduate students, and 100 continuing education students at a university. Assume a simple random sample within each group. Each student is asked to rate his or her satisfaction (on a 1–10 scale) with his or her experiences. Write the estimate and standard error of the average satisfaction of all the students at the university. Introduce notation as necessary for all the information needed to solve the problem. Solution to question 17 From yesterday : 17. In a survey of n people, half are asked if they support “the health care law recently passed by Congress” and half are asked if they support “the law known as Obamacare.” The goal is to estimate the effect of the wording on the proportion of Yes responses. How large must n be for the effect to be estimated within a standard error of 5 percentage points? Solution: se is sqrt(.5*.5/(n/2)+.5*.5/(n/2)) = 1/sqrt(n). Solve 1/sqrt(n) = .05, you get n = (1/.05)^2 = 400.
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Introduction: 23. Suppose you are conducting a survey in which people are asked about their health behaviors (how often they wash their hands, how often they go to the doctor, etc.). There is a concern that different interviewers will get different sorts of responses—that is, there may be important interviewer effects. Describe (in two sentences) how you could estimate the interviewer effects within your survey. Can the interviewer effects create problems of reliability of the survey responses? Explain (in one sentence). Can the interviewer effects create problems of validity of the survey responses? Explain (in one sentence). Solution to question 22 From yesterday : 22. A supermarket chain has 100 equally-sized stores. It is desired to estimate the proportion of vegetables that spoil before being sold. Three stores are selected at random and are checked: the percent of spoiled vegetables are 3%, 5%, and 10% in the three stores. Give an estimate and standard error for the percentage of spo
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