This document discusses sampling techniques for research including representative sampling, sample size, variation, and risk. It defines key terms like population, sample, variation, and risk. It also explains different sampling methods like simple random sampling, systematic sampling, stratified sampling, and matched pairs design. An example of a randomized control trial is provided to illustrate how experimental groups can be compared.

1. Quantitative
Methods
for
Lawyers
Research Design - Part III
Class #3
@ computational
computationallegalstudies.com
professor daniel martin katz danielmartinkatz.com
lexpredict.com slideshare.net/DanielKatz

2. Sampling

3. Sampling
Representative Sampling
A sample is representative when it is an accurate
proportional representation of the population under
study
Representativeness is a
contingent concept that
must considered relative
to the overall population
under study

4. Sample size is dependent
upon variation and risk.

5. Variation

6. Variation refers to the
amount of differences
expected among the
cases in the sample

7. Lets work through an example
to better understand variation

8. Imagine We Had a Bag Full
of Puzzle Pieces

9. Our Goal is to Make an
Inference Regarding the
Color(s) and/or Image(s)
in the Overall Puzzle

10. As we draw them from the
bag, each puzzle piece
provides some information
about color / images

11. How many pieces would you
need to observe in order to
feel confident regarding the
color / images in the puzzle?

12. For example, imagine you
drew these five puzzle pieces

13. Now make an inference
regarding the “population”

14. In other words, what does
the puzzle look like?

15. Like this?

16. Or Like this?

17. In general, the greater the
variance in the population the
larger sample you will need

18. Also, the fewer the number of
significant variables, the
smaller a sample can be.

19. Why?

20. Because we need to
ensure representativeness
on all relevant variables

21. For example, a study which only
examines a gender distinction will
probably be successful with a smaller
sample size than a study with a large
number of variables, such as age,
income, race, education, etc.

22. Risk

23. Risk involves amount
of acceptable
toleration for error.

24. Normally, a social science
researcher tolerates up to a
5% chance of random error.

25. If the study involves medicine where
life and health is at issue, there is
little toleration for error. The study
would then require a large sample.

26. All else equal, greater accuracy is
obtained with larger sample sizes
and a lower levels of accuracy are
obtained with a smaller sample sizes.

27. Question: The researcher randomly selects 100 murder
trials prosecuted in this state over the last six years.
The researcher seeks to evaluate whether court
appointed legal representation disproportionately
enhances the likelihood of a death penalty outcome.
The analysis suggests lower death penalty outcomes
when attorneys are privately hired. A prosecutor seeks
to challenge this study claiming the sample as invalid.
Name some potential arguments can the prosecutor
assert against the sampling approach?

28. The researcher studied 100 murder
trials over a 6 year period. It is
important for the trial lawyer to establish
if the sample was sufficiently large and
sufficiently reflective of the greater
population. The attorney can raise many
questions about the sample.

29.
What percentages of the sample involved court appointed attorneys and
privately funded attorneys?
How do those percentages compare to the full population of murder trials
within that state?
Did the sample of 100 trials represent a particularly small or particularly
large size when compared to the full population of murder trials from that
state?
For instance, is there any category in the data which measures a
disproportional death penalty impact solely because the murder was
particularly gruesome and hideous?
Here are just a few:

30.
Did the sample consider the strength and experience of the attorneys
regardless if they were court appointed or privately funded?
Did the sample consider whether some trials were high profile?
Did the sample consider race and income of the defendants?
And a few more:

31. Sampling Techniques

32. Concept: In most instances, it is
impractical and overly expensive to
study every member of the population.
The researcher must seek to obtain a
representative sample of that greater
population. It is a two part process.

33. First, Define the Relevant Population

34.
Example: Should a researcher
elect to study death penalty
data, the researcher must define
the limits of that population.

35.
Is the population limited to those
actually sentenced to death or is the
population broader to include those
who were eligible under the law to be
sentenced to death?
Or, is the researcher using the
population of those who could have
been sentenced to death but were not?

36. Second, Select a Sampling Technique

37. Here are the Most Common Approaches
1. Simple random
2. Systematic
3. Stratified random
4. Matched Pairs

38. Each individual (or object) is chosen randomly and entirely by
chance, such that each individual has the same probability of being
chosen at any stage during the sampling process
Simple Random
See Also
Replacement vs. Non-Replacement ?

39.
Quick Word on
Randomness ...
We have patterns in
our behavior even
when we think we are
acting randomly
Try this Applet
Rock
Paper
Scissors
Randomness
http://www.nytimes.com/interactive/science/rock-paper-scissors.html

40. Systematic Sampling

41. Systematic sampling
normally draws a sample
from every Nth case

42. The starting point or order is
normally selected randomly, but the
researcher pre-selects the interval
of the remaining selections.

43. Watch out for some unknown
component that generates bias.

44. For example, every select you
select every 7th case and the
data is organized by date

45. Stratified Sampling

46.
A stratified sampling technique is used to
insure that targeted members of the selected
population are included in the sample.

47.
The researcher divides the entire
target population into different
subgroups called strata.

48.
The researcher then randomly selects
from all of the different strata.

49.
For example, to obtain a stratified sample of
university students, the researcher might first
organize the population by college class and
then randomly select from each strata (i.e. an
appropriate number of freshmen, sophomores,
juniors, and seniors).

50. Matched Pairs Design

51. Concept: Matched pairs is an example of a “related design.”
It is used commonly with experiments or to mimic the properties
of an experiment.
Participants are matched on variables considered very relevant
For example, pairs might be matched on scores from a health
test or personality tests.
Matched pairs is a sampling technique commonly used with
experimental designs.

52. Example: The prosecution’s expert at a DUI sentencing. The
expert’s testimony concerns a research experiment on that
topic.
In that experiment, the effect of drinking and driving is
demonstrated by two groups of people driving around a
pre-selected course with specified amounts of alcohol in
their bodies.
The control group has no alcohol and the experimental
group drives the same course after consuming a specified
amount of alcohol.
As the lawyer objecting to this testimony, what serious
research problem will you assert about these two groups?

53. The participants from the two groups may significantly vary
in personality, age, sex, cognitive ability, attention span,
etc. IF the researcher did not match those groups to
establish similarity between the groups on variables deemed
important to the experiment.
For example, If one group consists of elderly drivers while
the other group is younger drivers, is the experiment
measuring the manipulated alcohol variable or is the
experiment measuring the impact from age differences?
Matched Pairs

54. The Randomized
Control Trial

55. Imagine a Study
Involving Thirty Patients

56. We Would Like to Randomly
Assign These Individuals to
Two Groups
Control Treatment

57. Then We Will Give the
Treatment to the
Treatment Group
Treatment

58. Give Either Placebo or
Baseline Treatment to the
Control Group
Control

59. Then, Compare Results
that the Follow
Control Treatment

60. Are These Differences
Statistically Significant?
Control Treatment

61. Randomized Control Trial
Control Group
Treatment Group
Follow Up Evaluation
Follow Up Evaluation

62. RCT’s Are Often Considered the
Gold Standard in Science

63. Because if properly executed
there is a fairly clean relationship
between cause and effect

64. Daniel Martin Katz
@ computational
computationallegalstudies.com
lexpredict.com
danielmartinkatz.com
illinois tech - chicago kent college of law@