SAMPLING

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SAMPLING
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Basic concepts

• Why not measure everything?
• Practical reason Measuring every member of a
  population is too expensive or impractical
• Mathematical reason Random sampling allows us to
  test hypotheses using inferential (probability)
  statistics
• Population
• Largest group to which we intend to project the
  findings of a study (e.g., every inmate in Jays
  prison)
• Parameter A statistic of the population e.g.,
  mean sentence length
• Sample
• Any subgroup of the population, however selected
• Samples intended to represent a population must
  be selected in a way to make them
  representative (will come up later)
• Unit of analysis
• Persons, places, things or events under study
• The container for the variables
• Member or element of the population
• What we call a case once its been drawn into a
  sample
• Sampling frame
• A listing of all elements or members of the
  population
• Probability sampling
• Gold standard - every element (case) in the
  population has the same chance of being included
  in the sample
• Random sampling is the most common probability
  technique

Jays correctional institution
Population
Sample
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Sampling accuracy and error

• Representativeness Samples should accurately
  reflect, or represent, the population from which
  they are drawn
• If a sample is representative, then we can
  accurately make inferences (apply our findings)
  to the population
• We can simply describe the population
• Or we can test hypotheses and extend our findings
  to the population
• Warning we cannot generalize to other
  populations only the population from which the
  sample was drawn
• Sampling error Unintended differences between a
  population parameter and the equivalent statistic
  from an unbiased sample
• Inevitable result of sampling
• Try it out in class! Calculate the parameter,
  mean age. Then take a random sample (more about
  that later) and compare it to the sample
  statistic.
• Any difference between the two is sampling
  error. It should decrease as sample size
  increases
• Rule of thumb To minimize sampling error sample
  size should be at least 30 for populations up to
  about 500 for larger populations sample size
  should be greater

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RANDOM (PROBABILITY) SAMPLING
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Sampling process

• Sample with or without replacement?
• With replacement Return each case to the
  population before drawing the next
• Keeps the probability of being drawn the same
• Makes it possible to redraw the same case
• Without replacement Drawn cases are not returned
  to the population
• Probability of undrawn cases being selected
  increases as cases are drawn
• In social science research sampling without
  replacement is by far the most common
• Most sampling frames are sufficiently large so
  that as elements are drawn changes in the
  probability of being drawn are small
• Sample simple or stratified? (examples on next
  two slides)
• In simple random sampling we randomly draw from
  the entire population
• In stratified random sampling we divide the
  population into subgroups according to a
  characteristic of interest
• For example, male and female officers and
  supervisors violent offenders and property
  offenders
• Can designate strata before or after sampling
• Proportionate Draw a sample from the population
  without regard to strata, then stratify
• Disproportionate (most common) Stratify first,
  then draw samples of equal size from each
  stratum

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Exercise - using simple random samplingto
describe a population
Population 200 inmatesMean sentence 2.94 years
Assignment Draw a random sample of 10 and
compare its mean to the population parameter.
Then do the same with a random sample of 30. How
much error is there? Does it change with sample
size?
Frequency ( prisoners)
Sentence length in years
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Exercise - using stratified random samplingto
describe a population
Population 200 inmates mean sentence 2.94 years
Assignment Draw a random sample of 30 from each
stratum and compare its mean to the corresponding
population parameters. How much error is there?
Violent crimes 50 Mean sentence 3.12
Property crimes 150 Mean sentence 2.88
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Exercise - using random samplingto test a
hypothesis

• Hypothesis A pre-existing personal relationship
  between criminal and victim is more likely in
  violent crimes than in crimes against property
• You have full access to crime data for Sin City.
  These statistics show that in 2014 there were 200
  crimes, of which 75 percent were property crimes
  and 25 percent were violent crimes. For each
  crime, you know whether the victim and the
  suspect were acquainted (yes/no).  
• Applying what we learned from the preceding two
  slides
• 1. Identify the population. 
• 2. How would you sample? 
• A. Would you stratify before or after?
• B. Which is better? Why?

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Stratified proportionate random sampling
Hypothesis A pre-existing personal relationship
between criminal and victim is more likely in
violent crimes than in crimes against property
Sin City200 crimes in 2014
50 violent (25 )
150 property (75 )
randomly select 30 cases (15 of the population)
(expect 7.5 violent 25)
(expect 22.5 property 75)
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Stratified disproportionate random sampling
Hypothesis A pre-existing personal relationship
between criminal and victim is more likely in
violent crimes than in crimes against property
Sin City200 crimes in 2014
50 violent (25 )
150 property (75 )
randomly select 30 cases from each category
30 property
30 violent
Compare proportions within each where suspect and
victim were acquainted (Note cannot combine
results)
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Exercise Using random sampling to test hypotheses
Hypothesis1 Gender affects cynicism
(two-tailed) Hypothesis2 Male cops are more
cynical than female cops (one-tailed)

• Sin City Police Department has 200 officers 150
  are male and 50 are female. We wish to test the
  above hypotheses.
• 1. Identify the population. 
• How would you sample?
• Would you stratify? In advance or later?
• Which is better? Why?

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Stratified proportionate random sampling
Hypothesis Gender affects cynicism
(two-tailed) Male cops are more cynical than
female cops (one-tailed)
50 female(25 )
Sin City200 officers
150 male(75 )
randomly select 30 officers
expect 7.5 females
expect 22.5 males
Compare average cynicism scores
Is there a problem? Hint how many females in
the sample?
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Stratified disproportionate random sampling
Hypothesis Gender affects cynicism
(two-tailed) Male cops are more cynical than
female cops (one-tailed)
Sin City200 officers
150 male (75 )
50 female (25 )
randomly select 30 officers fromeach stratum
30 males
30 females
Compare average cynicism scores Note dont
recombine these into a single sample!
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Sampling in experiments

• Making cops kinder and gentler
• The Anywhere Police Department has 200 patrol
  officers, of which 150 are males and 50 are
  females. Chief Jay wants to test a program thats
  supposed to reduce officer cynicism.
• Hypothesis Officers who complete the training
  program will be less cynical
• Dependent variable Score on cynicism scale (1-5,
  low to high)
• Independent variable Cynicism reduction program
  (yes/no)

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Stratified disproportionate random sampling
Hypothesis officers who complete the training
program will be less cynical
population 200 patrol officers
150 males (75)
50 females (25)
For each group, pre-measure dependent variable
officer cynicism
Apply the intervention (apply the value of the
independent variable the program.)
NO YES
YES NO
For each group, post-measure dependent variable
officer cynicism
Also compare within-group changes what do they
tell us?
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OTHER SAMPLING TECHNIQUES
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Quasi-probability sampling

• Systematic sampling
• Randomly select first element, then choose every
  5th, 10th, etc. depending on the size of the
  sampling frame (number of cases or elements in
  the population)
• If done with care can give results equivalent to
  fully random sampling
• Caution if elements in the sampling frame are
  ordered in a particular way a non-representative
  sample might be drawn
• Cluster sampling
• Method
• Divide population into equal-sized groups
  (clusters) chosen on the basis of a neutral
  characteristic
• Draw a random sample of clusters. The study
  sample contains every element of the chosen
  clusters.
• Often done to study public opinion (city divided
  into blocks)
• Rule of equally-sized clusters usually violated
• The neutral characteristic may not be so and
  affect outcomes!
• Since not everyone in the population has an equal
  chance of being selected, there may be
  considerable sampling error

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Non-probability sampling

• Accidental sample
• Subjects who happen to be encountered by
  researchers
• Example observer ride-alongs in police cars
• Quota sample
• Elements are included in proportion to their
  known representation in the population
• Purposive/convenience sample
• Researcher uses best judgment to select elements
  that typify the population
• Example Interview all burglars arrested during
  the past month
• Issues
• Can findings be generalized or projected to a
  larger population?
• Are findings valid only for the cases actually
  included in the samples?

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Practical exercise
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Class assignment - non-experimental designs

• Hypothesis Higher income persons drive more
  expensive cars - Income ? Car Value
• Independent variable income
• Categorical, nominal studentor faculty/staff
• Dependent variable car value
• Categorical, ordinal 1 (cheapest),2, 3, 4 or 5
  (most expensive)
• Assignment
• Visit one faculty and one student lot.
• Select ten vehicles in each lot using systematic
  sampling
• Use the operationalized car values to code each
  cars value
• Give each team member a filled-in copy and turn
  one in per team next week
• We will complete the tables in class
• This assignment is worth five points

PLEASE BRING THESEFORMS TO EVERY CLASS SESSION!
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