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Sample design and sampling error

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Title: Sample design and sampling error


1
Sample design and sampling error
  • Survey Research and Design
  • Spring 2006
  • Class 4

2
Todays objectives
  • Answer questions you have about material covered
    thus far
  • Examine various sampling strategies and
    associated costs
  • Understand standard errors and confidence
    intervals
  • Apply knowledge of sampling to group projects

3
Survey Process
Define Research Objectives
Choose Mode of Collection
Choose Sampling Frame
Construct and Pretest Questionnaire
Design and Select Sample
Recruit and Measure Sample
Code and Edit Data
Make Postsurvey Adjustments
Perform Analysis
4
Quality perspective (Groves, et al., p. 48)
Measurement
Representation
_ Y
Target Population
m1
Construct
Coverage Error
Validity
_ yc
Measurement
Sampling Frame
Yi
Sampling Error
Measurement Error
_ ys
Sample
Response
yi
Nonresponse Error
Processing Error
_ yr
Respondents
Edited Response
Adjustment Error
yip
Postsurvey Adjustments
_ yrw
_ yprw
Survey Statistic
5
Two sampling approaches
  • Probability sample
  • Each element in the sampling frame has a known
    and nonzero probability of being selected
  • Probabilities do not need to be equal
  • E.g., simple random sample, cluster sample
  • Non-probability sample
  • The probability of being selected is unknown

6
Non-probability samples
  • Common terms
  • Convenience
  • Purposeful
  • Snowball
  • Always to be avoided!
  • there is no direct theoretical support for
    using them to describe the characteristics of the
    larger frame population. Groves et al. p. 95

7
Probability samples
  • Simple random
  • Finite population correction
  • Cluster
  • Design effect
  • Stratified random
  • Proportionate allocation
  • Disproportionate allocation
  • What are the strengths and weaknesess of each?

8
Probability samples
  • If you are analyzing survey data from a complex
    probability sample (not SRS), you will need to
    use statistical software that can take into
    account the complexity.

9
Probability samples and standard errors
  • Random selection
  • Human influence is removed from the selection
    process
  • E.g., dice, random number generator
  • Probability samples use random selection to draw
    a subset of the sampling frame
  • Sampling error arises because of this
  • Standard errors allow us to quantify this error

10
Laws of Sampling Theory
  • Whenever a random sample is taken from a
    population there will be sampling error.
  • If sample is truly random, then characteristics
    of sample will be an unbiased estimate of
    population characteristics.
  • As sample size increases, the range (the size) of
    sampling error decreases.

11
Central Limit Theorem
  • The sampling distribution, or the distribution of
    the sampling error for any sample drawn from a
    given population, approximates a normal curve.
  • Standard error - standard deviation of the sample
    estimates of means that would be formed if an
    infinite number of samples.

12
Standard error
  • Relies on the concept of repeated samples from a
    population
  • Due to chance, the means of these samples will
    vary around the population mean
  • We can measure this variance and determine how
    much the typical sample will deviate from the
    population mean (i.e., the standard deviation or
    SD)
  • This SD is the standard error (SE)
  • http//www.ruf.rice.edu/lane/stat_sim/sampling_di
    st/index.html

13
Standard errors
  • Standard error of the mean
  • s is the SD from our sample n is sample size
  • We can see that as n increases, SE decreases
  • Different formulas for different statistics
    (proportions, comparing two means, etc.), but
    they have a similar form

14
Confidence Intervals
  • The range within which the parameter in question
    could be expected to be included a specified
    percentage of the time if procedure were to be
    repeated.
  • C Z statistic associated with the confidence
    level 1.96 corresponds to the .95,
  • 2.33 corresponds to the 98 level,
  • and 2.58 corresponds to the 99 confidence level

15
Standard errors
  • Confidence intervals (CI) use SE and tell us the
    precision of our estimates
  • 95 CI for a mean
  • Very specific definition if we calculated
    similar CIs on 100 similar samples, 95 of them
    would bracket the population parameter
  • Does not mean there is a 95 probability that
    population parameter falls in your CI either it
    does or it doesnt
  • http//www.ruf.rice.edu/lane/stat_sim/conf_interv
    al/

16
Standard errors
  • Margin of error in polls is a confidence
    interval, usually a 95 CI

17
How large a sample?
  • Usually depends on resources
  • Dont forget to take into account nonresponse
  • Once you have a sample size, check table in
    Dillman (p. 207) to get an idea of how precise
    your estimates will be.
  • Sample size calculator (courtesy of Mike Valiga,
    ACT)
  • Countless websites (e.g., http//www.surveysystem.
    com/sscalc.htm)

18
Using Excel to draw a random sample
  • Use the RAND() function
  • Input all the id numbers of your sample in a
    column
  • Type RAND() into the first cell next to the
    first element copy and paste for all elements
  • Select the random number column, copy and Paste
    Special on itself, choosing Values this prevents
    the function from recalculating when the
    worksheet changes

19
Using Excel to draw a random sample
20
Using Excel to draw a random sample
  • Highlight both columns and sort on the random
    number column
  • Start at the top and choose the first n elements,
    where n is the sample size you need.
  • Example

21
Summary
  • Probability samples are the way to go
  • Choosing a sample introduces sampling error SEs
    and CIs allow us to describe the effect of that
    error
  • Complex samples can save resources during data
    collection but make analysis complex
  • Try to get a large a sample as possible, all else
    being equal reduces sampling error

22
Group Projects
  • What is the objective of your survey?
  • What constructs do you plan to measure?
  • What is your target population?
  • What is your sampling frame?
  • What types of coverage issues might you expect?
  • How will you sample?
  • How large will your sample be?

23
Next week
  • Readings for next week
  • Groves, Chapter 5
  • Dillman, Chapter 4
  • Tourangeau et al. (2000). Chapter 10, Mode of
    data collection, in The psychology of survey
    response
  • DUE Application exercise 1
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