STT 350: SURVEY SAMPLING Dr. Cuixian Chen Chapter 2: Elements of the Sampling Problem Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow 1 Chapter 2

Survey sampling Chapter 2Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow 2

Be careful what you believe  “4 out of 5 doctors recommend…”  “22% of Americans doubt that the Holocaust ever occurred…” (Does it seem possible or does is seem impossible to you that the Nazi extermination of the Jews never happened?)  “Alcohol is more harmful than heroin” ( /Alcohol-is--more-harmful-than-heroin_-Really--Sample- before-you-speak.html) /Alcohol-is--more-harmful-than-heroin_-Really--Sample- before-you-speak.html  HOWEVER, there are good sources of information (that attempt to sample appropriately!!), Census Bureau, Bureau of Labor Statistics, Gallup Poll. Chapter 2Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow 3

Chapter 2: Elements of the Sampling Problem Technical terms  Element – an element is an object on which a measurement is taken.  E.g.: An element is a registered voter in the community.  Measurement taken on an element is the voter’s preference on the bond issue.  Because measurements are usually considered to be numbers, the experimenter can obtain numerical data by recording a 1 for a voter in favor of the bond issue and a 0 for a voter not in favor. Chapter 2Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow 4

Chapter 2: Elements of the Sampling Problem Technical terms  Element – an element is an object on which a measurement is taken  Population – a population is a collection of elements about which we wish to make an inference  Sampling units – sampling units are nonoverlapping collections of elements from the population that cover the entire population.  E.g.: The population in our example is the collection of voters in the community, and a sampling unit may be a registered voter in the community. Chapter 2Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow 5

Definitions continued  Frame – a frame is a list of sampling units  Sample – a sample is a collection of sampling units drawn from a single frame or from multiple frames.  Census – when sample is the entire population.  E.g.: If we take the household as the sampling unit, then a telephone directory, a city directory, or a list of household heads obtained from census data can serve as a frame. Chapter 2Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow 6

2.3 How to select the sample  Objective of sampling is to estimate population parameters, such as mean, total or proportion, from information contained in a sample.  Error of estimation=  Bound is usually selected as 2  (theta-hat)  Probability: Chapter 2Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow 7

2.3 How to select the sample  Probability sampling versus Quota Sampling  simple random sampling (SRS)  Stratified random sample (eg: gender)  Cluster sample (eg: city blocks)  Systematic sample (eg: draw the sample by selecting one name near the beginning of the list and every 10th or 15th name thereafter. If the sampling is conducted in this manner) Chapter 2Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow 8

2.4: Sources of Errors in Surveys  Non-observation (sampled elements make up only part of the target population; examples include sampling, coverage, non-response)  Sampling error – variation in sample response because not from population (can be estimated for probability samples)..can be reduced by survey design and sample size  Coverage…frames do not include everyone in target population (unlisted numbers in telephone directories)  Non-response (inability to contact sampled elements, inability of person to answer questions correctly, refusal to answer) Chapter 2Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow 9

Errors of Observation  Observation (recorded data deviate from the truth; examples include interviewer or data collector, instrument, sampling method)  Interviewer can bias how questions are asked  Respondent errors (recall bias, prestige bias, not understanding question)  Measurement error (measurements should be clearly defined…for example, education) Chapter 2Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow 10

Reducing Errors in Surveys  Callbacks  Rewards and incentives  Trained interviewers  Data checks  Questionnaire construction Chapter 2Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow 11

2.5 Designing a Questionnaire  Question ordering – the ordering of questions can change perspectives Example: A. Do you think the US should let Communist newspaper reporters from other countries come in here and send back to their papers the news as they see it? B. Do you think a Communist country like Russia should let American newspaper reporters come in and send back to America the news as they see it? Ordering (A, B): 54.7% answered yes to A, and 63.7% answered yes to B; Ordering (B, A): 74.6% answered yes to A, and 81.9% answered yes to B. Chapter 2Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow 12

Open versus Closed, Response Options and Wording of Questions  Open is good for qualitative information (and to help design options for closed questions).  Closed is good for quantitative information (however, options should be appropriately chosen).  Response Options – Should there be a “Don’t know” or “Not enough information to say” option.  Wording of questions…should try to ensure it is not biased: For example: for Yes-No question: a) Do you favor the use of capital punishment? Should be asked in a more balanced form, such as: b) Do you favor or oppose the use of capital punishment? Chapter 2Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow 13

2.6 Planning a Survey 1. Statement of Objectives 2. Target population 3. The frame 4. Sample design 5. Method of measurement (usually personal interviews, telephone interviews, mailed questionnaire, or direct observation) 6. Measurement instrument (if questionnaire, carefully create questions) 7. Train fieldworkers (if necessary) 8. The pretest 9. Organization of fieldwork (if necessary) 10. Organization of data management 11. Data analysis Chapter 2Elementary Survey Sampling, 7E, Scheaffer, Mendenhall, Ott and Gerow 14

STT315: Chapter 5: Bivariate and multivariate probability distributions 15

STT315: Sec 5.2 Bivariate and multivariate probability distributions 16 Review: Example 5.1, page 226 Ex 5.1y1 y /92/91/9 12/9 0 21/900 Eg5.1.1: The following is the joint distribution function of Y1 and Y2.

Sec 5.3 marginal and conditional probability distribution 17 Eg5.1.1: Find the marginal probability function of Y1 and Y2. Ex 5.1y1 y /92/91/9 12/9 0 21/900

Copyright © 2013, 2009, and 2007, Pearson Education, Inc. Chapter 3 Association: Contingency, Correlation, and Regression Section 3.1 The Association Between Two Categorical Variables

Copyright © 2013, 2009, and 2007, Pearson Education, Inc. 19 Contingency Tables: Calculate Proportions and Conditional Proportions Questions: 1.What proportion of organic foods contain pesticides? 2. What proportion of conventionally grown foods contain pesticides? 3. What proportion of all sampled items contain pesticides?

Copyright © 2013, 2009, and 2007, Pearson Education, Inc. 20 For questions 1, 2 and 3, these proportions are called conditional proportions because their formation is conditional on (in this example) food type. Calculate Proportions and Conditional Proportions Table 3.2 Conditional Proportions on Pesticide Status, for Two Food Types. These conditional proportions (using two decimal places) treat pesticide status as the response variable. The sample size n in a row shows the total on which the conditional proportions in that row were based. Pr(Pest|Organic) Pr(Pest|Convent) Pr(Pest|All)