SAMPLING - PowerPoint PPT Presentation

1 / 21
About This Presentation
Title:

SAMPLING

Description:

Sampling Population: The overall group to which the research findings are intended to apply Sample: Any subset of the population, whether or not randomly drawn – PowerPoint PPT presentation

Number of Views:188
Avg rating:3.0/5.0
Slides: 22
Provided by: Juliu161
Category:

less

Transcript and Presenter's Notes

Title: SAMPLING


1
SAMPLING
2
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
3
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

4
RANDOM (PROBABILITY) SAMPLING
5
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

6
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
7
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
8
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?

9
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)
10
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)
11
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?

12
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?
13
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!
14
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)

15
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?
16
OTHER SAMPLING TECHNIQUES
17
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

18
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?

19
Practical exercise
20
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!
21
(No Transcript)
Write a Comment
User Comments (0)
About PowerShow.com