Introduction INTRODUCTION TO SURVEY SAMPLING. General information. Why sample instead of taking a census? Probability vs. non-probability.

Transcription

1 Introduction Census: Gathering information about every individual in a population Sample: Selection of a small subset of a population Census INTRODUCTION TO SURVEY SAMPLING Sample February 14, 2018 Linda Owens 4 General information Please hold questions until the end of the presentation Slides available at Please raise your hand so that I can see that you can hear me Why sample instead of taking a census? Less expensive Less time-consuming More accurate Samples can lead to statistical inference about the entire population 2 5 Outline Introduction Target Populations Sample Frames Sample Designs Determining Sample Sizes Modes of Data Collection Questions Probability vs. non-probability Probability Sample Generalize to the entire population Unbiased results Known, non-zero probability of selection Non-probability Sample Exploratory research Convenience Probability of selection is unknown 3 6

2 Probability vs Non-Probability Sample Sampling frame Before you can ask people to answer your questions, you have to make contact with them How will you do that? Sampling frame is the mechanism that makes that possible Information on sampling frame has bearing on mode of data collection p=n/n=10/30=.3333 p=n/?=?=? Steve Mays, YouTube video on sampling: Rahul Patwari, YouTube video on non-probability sampling: Target population Definition: The population to which we want to generalize our findings Unit of analysis: Individual/Household/City Geography: State of Illinois/Champaign County/City of Urbana Age/Gender Other variables Sampling frame A complete list of all units, at the first stage of sampling, from which a sample is drawn For example, lists of... addresses landline phone numbers in specific area codes blocks or census tracts in specified geographic areas members of professional organization schools cell phone numbers 8 11 Examples of target populations Population of adults in Champaign County Faculty, staff, or students at the University of Illinois Youth age 5 to 18 in Champaign County Registered Voters Target populations, sample frames, and coverage Example 1: Population: Adults in Champaign County, IL Frames: List of landline numbers, list of census blocks, list of addresses Example 2: Population: Youth age 5 to 18 in Cook County Frame: List of schools Example 3: Population: Adults age in United States Frame:?? Coverage: How well does the sample frame represent the target population? 9 12

3 Coverage Error Simple Random (6 out of 30) Target Population Sample Frame Sample designs for probability samples Simple random samples Systematic samples Stratified samples Cluster Multi-stage Combination (e.g. stratified cluster sample) 14 Systematic sampling Definition: Every element has the same probability of selection, but not every combination can be selected. Use when drawing SRS is difficult List of elements is long & not computerized Procedure Determine population size N and sample size n Calculate sampling interval (N/n) Pick random start between 1 & sampling interval Take every ith case Problem of periodicity 17 Simple random sampling (SRS) Systematic Sample (every 5 th ) Definition: Every element has the same probability of selection and every combination of elements has the same probability of selection. Probability of selection: n/n, where n = sample size; N = population size Use Random Number tables, software packages to generate random numbers Most precision estimates assume SRS 15 18

4 Stratified sampling: Proportionate To ensure sample resembles some aspect of population Disproportionate Stratified Sample (n=12--4 from each stratum, overall p=.24) p=4/25=.16 p=4/10=.40 p=4/15=.267 Population is divided into subgroups (strata) Students by year in school Faculty by gender Simple Random Sample (with same probability of selection) taken from each stratum. Sampling fraction is the same for all strata, regardless of population in each stratum. Larger strata will have larger sample Proportionate Stratified Sample (sampling fraction=1/5) N=25 (n=5) N=10 (n=2) N=15 (n=3) Cluster/Multistage sampling Typically used in face-to-face surveys Population divided into clusters Schools (earlier example) Blocks Draw a sample of clusters Include every member of cluster (=cluster sample) Select random sample of cluster members (=multistage sample) Reasons for cluster sampling Reduction in cost No satisfactory sampling frame available Stratified sampling: Disproportionate Cluster Sample Major use is comparison of subgroups Population is divided into subgroups (strata) Compare girls & boys who play Little League Compare seniors & freshmen who live in dorms Probability of selection needs to be higher for smaller stratum (girls & seniors) to be able to compare subgroups. Requires weighting to adjust for different probabilities of selection 21 24

5 Complex Sample Designs Combination of sample strategies Example: multistage, stratified sample of adults in Chicago 1. Stratify census blocks into groups based on predominant racial/ethnic group 2. Draw a sample of census blocks from each stratum 3. Draw a sample of housing units from each sampled census block 4. Sample one respondent from all eligible adults in the household 5. Each sampling stage has its own probability of selection 6. Final probability of selection of eligible adult is product of all stages 25 Modes of data collection Face to face Phone Web Mail 28 Determining sample size: SRS Target population/frame/mode correspondence Need to consider Precision Variation in subject of interest Formula Sample size n o = CI 2 * (pq) Precision For example: n o = * (.5 *.5).05 2 Sample size not dependent on population size (except finite population correction) Mode needs to be consistent with information in sample frame Mode needs to be consistent with target population Sample size: Other issues Finite Population Correction (FPC) Use when sample >5% of pop = /(1+ ) Design effects Analysis of subgroups Increase size to accommodate nonresponse Cost Cell phone and landline frames Increasing proportion of US households are cell phone only (52.5% in 2017, 5.9% landline only) pdf (Blumberg & Luke) Cell phone only households tend to be Unrelated adults Hispanic adults Younger Lower SES But Landline sample frames can will lead to bias 27 30

6 Cell phone and landline frames, cont. Address-based sampling: disadvantages Cell phone frames harder to target geographically than landline frames Survey researchers are combining landline and cell phone frames Incomplete in rural areas (although improving with address conversion) Difficulties with multidrop addresses Best used with mail or face to face surveys. Can be used for web surveys with some additional effort/cost Address-based sampling Thank you! Sampling addresses from a near universal listing of residential mail delivery locations Post Office Delivery Sequence Files (DSF) Future noontime webinars Introduction to Questionnaire Design, Wednesday, February 21 Survey Response Rates: Uses and Misuses, Wednesday, February Address-based sampling: advantages Coverage of households is very high Can be matched to name and listed telephone numbers Evaluation Includes non-telephone households More efficient than traditional block-listing 33 36

7 Questions 37 Resources Books on Sampling: the Classics Leslie Kish, Survey Sampling, 1965 William Cochrane, Sampling Techniques, 3 rd Ed Seymour Sudman, Applied Sampling, 1976 Sharon Lohr, Sampling: Design and Analysis, Rahul Patwari, YouTube video on non-probability sampling: Steve Mays, YouTube video on sampling: 38