SP 225 Lecture 2 Writing with Statistics Sampling Methods

Agenda  Survey Sampling Sampling basics United States Census  Census Issue Essay

Designing Studies  Selection Method  Questionnaire Design  United States Census

Population vs. Sample  Population: All subjects in a study population  Sample: Subset of subjects included in the study

Parameter vs. Statistic Population: All People Parameter: 5 of 15 or 33% wear glasses Sample: 3 Randomly Selected People Statistic: 0 of 3 or 0% wear glasses

Random Sampling  Random sample: each individual member of a population has an equal chance of being selected  EPSEM  Important Questions: Is every member of a population equally likely to be chosen? Is every combination of members equally likely to be chosen?

Convenience Sampling uses results that are easy to get

Systematic Sampling Select some starting point and then select every k th element in the population

Stratified Sampling subdivide the population into at least two different subgroups that share the same characteristics, then draw a sample from each subgroup (or stratum)

Cluster Sampling divide the population into sections (or clusters); randomly select some of those clusters; choose all members from selected clusters

Sampling Error  Sample Error: Difference between sample result and true population result  Non-Sample Error: Difference caused by data that has been incorrectly collected, recorded or analyzed

Common Study Problems  Loaded questions Would you vote for Mr. President if you knew he had gone to prison? (push-polling)  Order of questions Would you say traffic contributes more to air pollution than industry? (45% traffic, 27% ind.) Would you say industry contributes more to pollution than traffic? (24% traffic, 57% ind.)

The United States Census  Every 10 Years the Census Bureau attempts to count and survey all citizens of the United States  Number of US Representatives in each state are determined by the census  The amount of Federal funds each state receives depends on the Census (over $185 billion each year)  Approximately 310 million residents  Requires 860,000 employees to conduct the census  All households receive a short-form questionnaire and 1 in 6 receive a long-form questionnaire that takes about 40 minutes to complete

Census Methodology  The census is used to calculate population parameters  Is the census successful?

Differential Undercount  Some groups counted at different rates  The General Accounting Office estimates some states were entitled to and additional $208 million while some states were overpaid $368 million  In 1980 a House district was taken from Indiana and given to Florida after count correction  Legal challenges against imputation and to require the use of sampling to correct counts

Census Correction   Count Question Resolution petition for local governments

Statistical Methods for Correction  1850 counts for California counties lost at sea  1940 sampling was used to determine personal characteristics so less households were required to use the long form  Imputation used alone or with sampling  1970 used to correct count when the post office had only partial updated address listings Sampling estimates number missed Imputation determines characteristics  1980 Census tries synthetic estimation  1990 sampling used for those on probation with help of probation officers

Sampling in the 2000 Census  Sampling for non response Sample non responders in each census tract (1700 households) to test rate of vacancy  Capture-recapture for large geographic areas  Multiplicity estimation for homeless combines count with usage

Census Discussion  What groups of people are more likely to be missed by the census?What does the term differential undercount mean?  How are census results confirmed?  How has sampling historically been used in the census?  What arguments are there in favor of sampling in the census?  What arguments are there against sampling in the census?

Census Essay  Write a position paper arguing either the Democratic or Republican position on the use of sampling methods considered during the 2000 Census to arrive at an adjusted count in the 2010 Census  In your essay: Clearly state and justify the position Explain usage, operation and scope of sampling methods under consideration Enumerate the consequences of your position Address the counter position

Reading  Chapter 1 of Essentials of Social Research