Sampling and levels of
measurement
Data collection
Sampling terms
Population: all subjects one is
interested in. Very large or very small
 Element
 Sample: portion of population
 Sampling frame: list of people
(elements) in the population
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Sampling
Representative sample: if the overall
characteristics of the sample
approximate the important
characteristics of the population
 Biased sample: not representative
 Why sample? time and money
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Terms
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Parameters and statistics
Parameters: population
Statistics: samples
Sampling in the U.S.
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Literary Digest polls. Accurate until 1936,
when Landon was predicted as winner of the
presidential election
Reasons: (1) low return rates (2 million out
of 10 million) and (2) sampling frame
(telephone directories and lists of auto
owners)
Poor sampling frames result in bias
Sampling in the U.S.
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1948 Gallup poll predicted Dewey would win.
Problems: (1) stopped polling in Oct.; (2)
quota sampling
Two types of sampling: probability and nonprobability sampling
Probability sampling uses the laws of
probability, whereas non-probability does not
Probability
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p = number of times an event could occur /
total number of outcomes.
Can be expressed as a fraction, a %, as
chances out of 100, or as a decimal.
P can range from 0 (no probability to 1
(certainty)
Sampling
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A sample will be more likely to be
representative of a population from which it is
selected if all members of the population
have an equal chance of being selected in
the sample
Sampling
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Sampling error: error due to the fact that the
sample is not representative
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Necessity of a complete sampling frame
Probability sampling
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Simple random sampling: (out of a hat,
random numbers)
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Systematic random sampling: every nth
element is cnosen, select first element at
random (random start)
Probability sampling
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Stratified random sampling
1. Divide sample into subgroups based on
important population characteristics
2. Randomly sample from those subgroups
in proportion to their percentage in the
population
Probability sampling
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Choice of stratification variables will often
depend on what variables are available, and
how much is known about the population
This technique most likely to be
representative
Non-probability sampling
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Probability sampling only works if there is a
sampling frame of the population.
Sometimes that is not possible (i.e.,
criminals, drug addicts, etc.)
Nonprobability sampling methods, while
running the risk being unrepresentative
might be the only option
Non-probability sampling
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Convenience: the captive audience
College students and prisoners
Purposive: researcher uses judgment
For example, the mentally ill. Works best if
the criteria for inclusion are clear
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Quota: like stratified random. Groups are
selected on the basis of known variables
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In quota sampling, subjects are not selected
randomly--subjects with the desired
characteristics are selected until a quota is
filled for each subgroup
Non-probability sampling
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Snowball: each subject is asked to suggest
other subjects
Tips about sampling
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Sample size: unusually the number of
subjects needs to be at least 30. If several
groups within the sample are to be
compared, there needs to be at least 10 per
group.
The larger the number of subjects (N), the
less likely sampling error
Tips about sampling
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There will always be “mortality”
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Samples should be larger to take this into
account
Tips about sampling
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The greater the heterogeneity of the sample,
the larger the sample must be. The less
population diversity, the smaller N might be.
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N is often determined by time and money
factors
Levels of measurement
Nominal
And
 Ordinal (nonparametric)
 Interval
 And
 Ratio (parametric)
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Nominal
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Nominal: lowest level, simply classifying
observations into categories
Categories should be mutually exclusive and
exhaustive
Examples: gender, major, religion, state
Nominal (continued)
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Numbers assigned to the categories have no
numerical meaning. Assign individuals, and
report the % falling into each category.
Fewer statistical techniques can be used
Ordinal measurement
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Ordinal measurement: one observation
represents more of a given variable than
another observation
Rankings
Newly developed tests
Ordinal (continued)
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Ranks tell whether one observation
represents more or less than another, but not
how much more or less--nothing is known
about the exact difference between any two
ranks
Rankings of crime seriousness
Interval
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Interval: like an ordinal scale, but has equal
intervals between the units of measurement.
Not only an ordering, but also the same
distance or degree of difference between
observations
For example, 81 is 1 point away from 80, etc.
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Well-developed tests are interval level
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With interval measurement, can do addition,
subtraction, multiplication and division, more
statistical tests
Ratio measurement
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Ratio measurement: like interval, with the
additional property of a true zero.
An individual could have two or three time as
much of a trait as another with ratio
measurement
Ratio
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Height or weight. A 200 lb person weighs
twice as much as a 100 pound person
Not true for interval. For example, no such
thing as an IQ of 0, and a person with an IQ
of 100 is not twice as smart as someone with
an IQ of 50
Determining statistical test
1 sample
Nominal
Ordinal
Interval
2 samples
>2 samples
Chi square
MannKruskalWhitney
Wallis
independent
samples;
Wilcoxin
(related
samples)
T-tests
ANOVA