Class 3.1: How do we observe

Methodology of Scientific Research

Psychologist Stanley Smith Stevens proposed a taxonomy of Levels of Measurement

Stevens, S.S. (1946). On the Theory of Scales of Measurement. Science, 103 2684, 677-80.

Semi qualitative, Rank
- Example: ‘completely agree’, ‘mostly agree’, ‘indifferent’, ‘mostly disagree’, ‘completely disagree’
There is order, but intervals can be different
- Real differences between adjacent ranks may not be equal
Mathematical operations: less-than, sort
Central tendency: median
And all the properties of Nominal

degree of difference between items, but not the ratio between them
Examples
- Temperature in the Celsius scale
- date when measured from an arbitrary epoch (such as AD)
- location in Cartesian coordinates
- direction measured in degrees from north
Mathematical operations: Plus, Minus, ratio of differences
Central tendency: arithmetic mean, standard deviation

Has a meaningful (unique and non-arbitrary) zero value
Most measurements in physical sciences and engineering
- mass, length, duration, plane angle, energy, and electric charge
- values have units of measurement
Mathematical operations: multiplication, division
Central tendency: geometric mean, harmonic mean, coefficient of variation

Names
Grades (ordered labels like beginner, intermediate, advanced)
Ranks (orders with 1 being the smallest or largest, 2 the next smallest or largest, and so on)
Counted fractions (bound by 0 and 1)
Counts (non-negative integers)
Amounts (non-negative real numbers)
Balances (any real number)

Incremental progress	Measure property	Mathematical operators	Advanced operations	Central tendency
Nominal	Classification, membership	=, ≠	Grouping	Mode
Ordinal	Comparison, level	>, <	Sorting	Median
Interval	Difference, affinity	+, −	Yardstick	Mean, Deviation
Ratio	Magnitude, amount	×, /	Ratio	Geometric mean, Coefficient of variation

Wikipedia: Levels of Measurement

These categories are used for teaching and education research

Knowledge “involves the recall of specifics and universals, the recall of methods and processes, or the recall of a pattern, structure, or setting.”
Comprehension “refers to a type of understanding or apprehension such that the individual knows what is being communicated and can make use of the material or idea being communicated without necessarily relating it to other material or seeing its fullest implications.”

Application refers to the “use of abstractions in particular and concrete situations.”
Analysis represents the “breakdown of a communication into its constituent elements or parts such that the relative hierarchy of ideas is made clear and/or the relations between ideas expressed are made explicit.”

Synthesis involves the “putting together of elements and parts so as to form a whole.”
Evaluation engenders “judgments about the value of material and methods for given purposes.”