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Statistics
is the branch of mathematics that analyzes and interprets data.
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Data
are pieces of information, usually organized and expressed as numbers.
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Measurement (Meline, pg. 70)
“the process of systematically assigning numbers to objects, persons or events according to some prescribed rules”
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Steven’s classic levels
– a-d become more rigorous, mathematically sound, ascending order
A. Nominal level of measurement
B. Ordinal level of measurement
C. Interval level of measurement
D. Ratio level of measurement
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Steven’s classic levels
These levels “allow progressively more sophisticated quantitative procedures to be performed”
the statistics used to analyze the data depend on the scale of the data.
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Nominal (“in name only”)
- - Indicates a difference (category)
- - In research, attributes often coded as a number (0, 1) but these are place-holders.
Examples: telephone numbers (has no quantitative value, not poorer if you have a 213 vs a 310 number, there is no quantitative operation)
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Ordinal
- Indicates a difference (category)
- - Indicates direction of difference, meaning,
- - can be put into an order (rank)
- - there is order, a direction of difference
- Differences between ranks not equal units (#1 rank would have more points)
Example: class rank - rating scale - Likert scaling (1-5 ranking)
- ** for both ordinal and nominal need statistics that will tell you
- a difference
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Interval
- - Indicates a difference (category)
- - Indicates direction of difference
- - Indicates amount of difference, in equal intervals
- - (the difference between rank position is equal)
- - No true zero in units of measure
- - (usually an arbitraty number assigned)
Examples: temperature (Fahrenheit)
intelligence (IQ)
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