Fall, 2008
Measurement
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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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• Nominal
• Ordinal
– Rank
• Cardinal
– Interval
– Ratio
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Using numbers in place of labels.
– The numbers represent qualitative or categorical differences.
– The numbers do not represent quantity.
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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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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 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 : 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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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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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 : 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 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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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 : 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 : 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 : 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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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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