Basic Sampling Issues Chapter 11. What is sampling Sampling: a way of studying a subset of the population but still ensuring “generalizability” (vs. census.

Basic Sampling Issues

Chapter 11

What is samplingSampling: a way of studying a subset

of the population but still ensuring “generalizability”

(vs. census – study of entire population) – does the study have external validity?

Definitions of Important TermsPopulation or Universe – entire set of

elements to be studiedCensus – all elements that completely

make up the population.Sample – a subset

Unit of Analysis

Level of social life beingstudied – individuals orgroups of individuals

Child Neighborhood

Elements Individual members of thepopulation

Charlie, Lucy, Linus, Patty,Violet, etc.

Midtown, Natomas, Land Park,

Sampling Frame

List of all elements orother units containing theelements; used fordrawing sample

Public school rollsPhone listingsMarketing list ofhouseholds with children

List of neighborhoodsList of cities in Sacramentoregion

Steps in Developing a Sample Plan

Step 1: Define thePopulation of

Interest

Step 2: Choose aData collection Method

Step 3: Choosing a Sampling Frame

Step 5: Sample Size

Step 4: Selecting a Sampling Method

BoundariesOperationalImplementability

Sampling MethodProbability samples: Samples in which

every element of the population has a known, nonzero probability of selection.GeneralizableSampling error Expensive; More time and effort needed

Non-probability samples: Samples that include elements from the population selected in a nonrandom manner.Hidden agendasBiased towards well known members of the population;

Biased against unusual population members

Sampling and Nonsampling ErrorsParameter vs. Statistic (Estimate)Sample statistic: statistic (e.g. mean)

computed from sample data- Population parameter: true value for

statistic (e.g. mean) for population (we don’t know this)

- Sampling error: population parameter – sample statistic (we don’t know this)

- Confidence interval: interval in which we can be confident that true value lies, based on sample statistic and its standard error

Advantages Of Probability Samples

1. Information from a representative cross-section

2. Sampling error can be computed

3. Results are projectable to the total population. Disadvantages Of Probability

Samples

1. More expansive than nonprobabiity samples

2. Take more time to design and execute.

Disadvantages of Nonprobability Samples

1. Sampling error cannot be computed

2. Representativeness of the sample is not known

3. Results cannot be projected to the population. Advantages of Nonprobability Samples

1. Cost less than probability

2. Can be conducted more quickly

3. Produces samples that are reasonably representative

Classification of Sampling Methods

SamplingMethods

ProbabilitySamples

SimpleRandom

Systematic Stratified

Non-probability

Judgment

Convenience Snowball

Cluster

Quota

Sampling ErrorThe error that results when the same sample is not perfectly representative of the population.

Remember?Sampling And Nonsampling Errors

+- sns

+-X =

X = sample mean

= true population mean

s = sampling error

ns = nonsampling error

Sampling ErrorThe error that results when the same sample is not perfectly representative of the population.

• Administrative error: problems in the execution of the sample (can be reduced)

• Random error: due to chance and cannot be avoided; but can be contolled by random sampling and…..estimated!

Measurement or Nonsampling Error

Includes everything other than sampling error that can cause inaccuracy and bias (data entry, biased q’s, bad analysis etc).

Sampling And Nonsampling Errors

Probability Sampling Methods

Simple Random SamplingA probability sample is a sample in which every element

of the population has a known and equal probability of being selected into the sample- EPSEM.

Probability of Selection = Sample Size

Population Size

Probability Sampling Methods

Systematic SamplingProbability sampling in which the entire population is

numbered, and elements are drawn using a skip interval.

Skip Interval = Population Size

Sample Size

Probability Sampling Methods

Stratified SamplesProbability samples that select elements from relevant

population subsets to be more representative.

Cluster SamplesProbability sample of geographic areas

Three steps: In implementing a properly stratified sample:

1. Identify salient demographic or classification factors correlated with the behavior of interest.

2. Determine what proportions of the population fall into various sub subgroups under each stratum.

• proportional allocation

• disproportional or optimal allocation

3. Select separate simple random samples from each stratum

Stratified SamplesProbability samples that select elements from relevant population subsets to be more representative.

Cluster SamplesSampling units are selected in groups.

1. The population of interest is divided into mutually exclusive and exhaustive subsets.

2. A random sample of the subsets is selected.• One-stage cluster—all elements in subset selected• Two-stage cluster—elements selected in some

probabilistic manner from the selected subsets

StratifiedExample

Reasonfor use

StrataDivide city into districts2. Draw random sample ofhouseholds from each district.

To ensure desired number of households in each district.

Cluster1.Divide city into districts (clusters).2.Draw random sample of districts.3.Draw random sample ofhouseholds from each district.

To make it easier to do door-to-doorsurveys.

Handout 1 – Baseball Example1. Ramon Aviles 0.2772. Larry Bowa 0.2673. Pete Rose 0.2824. Mike Schmidt 0.2865. Manny Trillo 0.2926. John Yukovich0.161 Mean = 1.565 / 6 = 0.261

SRS of sample size = 2 Mean Error Aviles, Bowa 0.272 +0.011Aviles, Rose 0.280 +0.019Aviles, Schmidt 0.282 +0.021Aviles, Trillo 0.285 +0.024Aviles, Yukovich 0.219 -

0.042Bowa, Rose 0.275

+0.014Bowa, Schmidt 0.277 +0.016

SRS of sample size = 2Bowa, Trillo 0.280 +0.019Bowa, Yukovich 0.214 -0.047Rose, Schmidt 0.284 +0.023Rose, Trillo 0.287 +0.026Rose, Yukovich 0.222 -0.039Schmidt, Trillo 0.289 +0.028Schmidt, Yukovich 0.224 -0.037Trillo, Yukovich0.227 -0.034

StratificationLet’s divide the sample into two strataOne with Yukovich and another with all

othersStratum 1: YukovichStratum 2: Aviles, Bowa, Rose, Trillo,

Schmidt

Stratified Sampling1. Yukovich, Aviles2. Yukovich, Bowa3. Yukovich, Rose4. Yukovich, Schmidt5. Yukovich, TrilloWeight the sample. Why? For anyone from Stratum 2, multiply

their value by 5

Example – Mean computationYukovich, SchmidtYukovich = 0.161Schmidt = 0.286Therefore, Schmidt’s value is (0.286 * 5)

which is 1.43Yukovich + Schmidt = 0.161 + 1.43 = Mean (Yukovich + Schmidt) = 1.591 / 6 =

0.265

Stratified Sampling1. Yukovich Aviles 0.258 -

0.0032. Yukovich, Bowa 0.249 -0.0123. Yukovich, Rose 0.262

+0.0014. Yukovich, Schmidt 0.265

+0.0045. Yukovich, Trillo 0.270

+0.009What’s happening to errors of estimate?

Nonprobability Sampling Methods

Convenience SamplesNonprobability samples used primarily because they are

easy to collect ; Theory testingJudgment Samples

Nonprobability samples in which the selection criteria are based on personal judgment that the element is representative of the population under study

Nonprobability Sampling Methods

Snowball SamplesNonprobability samples in which selection of additional

respondents is based on referrals from the initial respondents.

Quota SamplesNonprobability samples in which a population subgroup

is classified on the basis of researcher judgment Different from Stratified