SP 225Lecture 2

Writing with StatisticsSampling 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 PeopleParameter: 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 Samplingdivide 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

http://www.gao.gov/new.items/d09832t.pdf http://www.census.gov/srd/papers/pdf/rrs2005-01.pdf

Census Correction

http://2010.census.gov/2010census/ 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