Mini-course 1 Decision Analysis (Dr. Mariya Sodenkamp) / Class 2 / Paderborn_ITB_L2_ 2015_04_17 Students
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Nominal scale
This scale suppose existence of a finite number of equivalence classes.
Each class is named or labeled. Example: gender {male=0, female=1}.
Measurement: determina@on of the class the object belongs to. Hierarchy of classes is possible; for example, post addresses.
Invariant under one to one correspondence (bijec@ve func@ons) preserve the scale.
Each name is mapped to another name. Permi`ed opera@on – test for coincidence.
§ Male XY, Female XX
§ Berlin B, Bamberg BA, Baden-Baden BAD, …
§ Map each student to the student ID.
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Ordinal (rank) scale
Things are ordered by number but the magnitudes of the numbers only serve to designate order, increasing or decreasing.
Invariant under monotone transforma@ons.
• A transforma@on f is monotone if A>B f(A) > f(B)
Cannot be mul@plied or added even if the numbers belong to the same scale.
For example, scale of rela2onship: mother=father > brother=sister uncle=aunt < sun=daughter
• 1st Position A, 2nd Position B, 3rd Position C
• x ex, x
• “Sehr gut” 1,0; “Gut” 2,0; “Befriedigend” 3,0 …
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Interval scale
The distance between numbers or units on the scale is equal over all levels of the scale.
For example, Celsius scale of temperature.
Invariant under a linear transformation ax + b; a > 0, b ≠0. For example, the linear transformation F = (9/5) C + 32 for converting a Celsius to a Fahrenheit temperature reading.
Two readings on an interval scale cannot be added. Taking average of such readings is valid.
There is no absolute zero point.
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Convert Celcius temperature to Fahrenheit. |
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Transform Julian calender to Gregorian calender. |
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Transform Time in hh:mm:ss DD/MM/YY format into unixtime. |
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Ratio (Cardinal) scale
Consists from the equidistance points and a meaningful zero point. Here “zero” signifies absence. For example, Person’s age, market share, quantities purchased.
It joins attributes of nominal, ordinal and interval scales.
Invariant under positive similarity (scaling) transformation ax, a > 0.
For example, weight in pounds converts to kilograms using
similarity transformation K=2.2P. Weight (Object 1)=8 kg=3.6 lbs; Weight (Object 2)=4 kg=1.8 lbs.
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Convert meters to parsecs |
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Convert kilograms to grams. |
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Convert the speed from m/s to km/h. |
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Decision process
Step 9. Evaluate solutions against problem statement
The alternatives selected by the applied decision making tools have always to be validated against the requirements and goals of the decision problem.
It may happen that the decision making tool was misapplied. In complex problems the selected alternatives may also call the attention of the decision makers and stakeholders that further goals or requirements should be added to the decision model.
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Quan@fying saving e ects of behavioral interven@ons
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Let us inves@gate the e ect the smart water meter has on its users
• Do households that install the given feedback device save energy?
• Do families perform be`er than single households?
• How to design the experiment?
– Dependent and independent variable?
– Control group and/or baseline measurement?
– Data analysis?
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Par@cipa@ng households were assigned into the control group experimental groups
Water |
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consumption in |
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Decision process
Step 10. Feedback
The feedback should provide a proper orientation in a learning process by showing the participants whether they are right or wrong in their understanding.
The richness of a feedback environment should fit the complexity of the task
-> pre-implementation feedback
-> post-implementation feedback
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Summary...
The general objec-ve of decision analysis (DA) is to assist a decision maker (DM) or a group of DMs to choose the best alterna@ve
from a range of alterna@ves in an environment of conflic@ng and compe@ng criteria.
Characteris2cs of all decision methods:
•Deal with complex situa2ons (criteria), consider di erent scales and aspects, social/technical issues and type of data
•Involve more than one decision maker (stakeholder par2cipa2on, actors, communica2on)
•Inform stakeholders in order to increase their knowledge and
change their opinion and behavior (problem structuring, tool for learning, transparency)
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