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Psych 5500/6500
Measurement
Fall, 2008
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Measurement: Turning the World
into Numbers
The problem with only having a hammer as a tool,
is that you tend to treat everything like a nail.
(Quote attributed to Abraham Maslow).
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Measurement Scales
• Nominal
• Ordinal
– Rank
• Cardinal
– Interval
– Ratio
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Nominal Scale
Using numbers in place of labels.
– The numbers represent qualitative or categorical
differences.
– The numbers do not represent quantity.
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Ordinal Scale
Numbers reflect an increase or decrease in
quantity, however the size of the steps between
values is not necessarily equal (e.g. the
difference between a ‘1’ and a ‘2’ might not be
the same size as the difference between a ‘2’ and
a ‘3’).
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Rank Scale
A subcategory of ordinal scale, we will talk about it
separately because it has its own set of statistical
procedures.
Step 1: organize the entities you are measuring
into a list that represents an increase or decrease
in some value.
Step 2: assign each entity a number based upon its
location in the list.
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Rank or Ordinal?
Rank scale: the entity’s score depends upon how it
compares to the other scores in the group. Except
for ties, everyone will have a different score.
Non-rank ordinal scale: score does not depend
upon a comparison with others in the group,
everyone could have the same score.
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Cardinal Scales
Cardinal: From Latin for important; primary, central, fundamental.
A change in value represents a change in quantity,
the size of the steps between values is equal (e.g.
the difference between a ‘1’ and a ‘2’ is the same
size as the difference between a ‘2’ and a ‘3’).
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Cardinal Scales
Interval and Ratio scales
Interval does not have a true zero point.
Ratio does have a true zero point.
True Zero Point: a score of zero, whether it is possible or
not, would reflect a completely lack of quantity.
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Translation Between Scales
You can move from cardinal towards nominal
(losing information at each level) but you can’t
move the other direction (as there is not enough
information).
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Discrete vs. Continuous
Discrete: does not have fractional values (e.g.
number of children, military rank).
Continuous: does have fractional values, even if
the measuring process does not (e.g. height
rounded off to the nearest inch).
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Operational vs Abstract Definition of
a Variable
Operational Definition of a variable: the specific
steps (i.e. ‘operations’) you use to measure the
variable.
Abstract or Theoretical Definition of a variable:
what we mean by the term (conceptual).
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Operational Definitions
Strict view of operational definitions, how you
measure is what you measure.
Contemporary view of operational definitions,
different operational definitions may measure
the same abstract variable.
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Measurement Validity
Measurement Validity: the question of whether
you really are measuring what you claim to be
measuring (i.e. how well your operational
definition of the variable fits the abstract
definition of the variable).
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Statistical Procedures and Measurement Validity
There are many ways of establishing measurement
validity, some involve the use of statistics, for
example:
1. Predictive validity
2. Concurrent validity
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Statistical Procedures and Measurement Validity
But...bottom line: If you don’t have
measurement validity then statistical
analysis is useless.
Garbage In -> Garbage Out
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Measurement Reliability
Measurement Reliability: the question of whether
your measuring procedure is consistent. This is
usually established by measuring the same
thing twice (under conditions in which the
score is expected not to change) and then
determining if you get the same (or at least
similar) scores each time.
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Measurement Reliability
Measurement Reliability: the question of whether your
measuring procedure is consistent. This is usually
established by measuring the same thing twice (under
conditions in which the score is expected not to change)
and then determining if you get the same (or at least
similar) scores each time.
Options:
1. Look for agreements.
2. Look for correlation
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Validity and Reliability
Your measuring process can be reliable but not valid.
Your measuring process can not be valid unless it is also reliable.
Lack of reliability means that you also lack validity, thus if you
don’t have a reliable way of measuring then statistical procedures
won’t lead to valid decisions, and we are back to:
Garbage In -> Garbage Out
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