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Understanding Different Levels of Ordering in Modeling

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This course explores the fundamental concepts of ordering in modeling, focusing on four key levels: nominal, ordinal (ranking), interval, and ratio scales. Each level represents different ways of distinguishing and ranking concepts, essential for data analysis in various fields, including physics, social sciences, and finance. Students will engage with interactive quizzes to reinforce their understanding and apply their knowledge to practical examples. By the end of the course, learners will comprehend how numbers and scales impact ordering and measurement in modeling frameworks.

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Understanding Different Levels of Ordering in Modeling

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  1. A core Course on Modeling Introductionto Modeling 0LAB0 0LBB0 0LCB0 0LDB0 c.w.a.m.v.overveld@tue.nl v.a.j.borghuis@tue.nl S.8

  2. Properties: serve todistinguish andsometimes toorder concepts

  3. ordering level 1: nominal onlytodistinguishindividuals http://commons.wikimedia.org/wiki/File:Stamp_collection.jpg • numbersmaybenominal: • telephonenumbers • lotterynumbers • social security numbers • ...

  4. ordering level 1: nominal onlytodistinguishindividuals QUIZ Numberscanoccur as nominallabels. Typically, numbers are usedfor ordering. Givean example of orderingwithoutnumbersinvolved. http://commons.wikimedia.org/wiki/File:Stamp_collection.jpg • numbersmaybenominal: • telephonenumbers • lotterynumbers • social security numbers • ...

  5. ordering level 2: ranking imposean order onto pairs of individuals http://commons.wikimedia.org/wiki/File:Commissioned_Officer_Rank_Structure_of_the_Bulgarian_Navy_-_sleeve_insignia.png partial order: order betweensome pairs total order: order betweenall pairs

  6. ordering level 2: ranking imposean order onto pairs of individuals QUIZ Numbers are totallyordered: foranytwo non-equalnumbers, one of the two is bigger. Whataboutintervals ([p,q])? Whataboutfractions (p/q, p and q are both integers)? Whatabout complex numbers? http://commons.wikimedia.org/wiki/File:Commissioned_Officer_Rank_Structure_of_the_Bulgarian_Navy_-_sleeve_insignia.png partial order: order betweensome pairs total order: order betweenall pairs

  7. ordering level 2: ranking imposean order onto pairs of individuals http://commons.wikimedia.org/wiki/File:Commissioned_Officer_Rank_Structure_of_the_Bulgarian_Navy_-_sleeve_insignia.png • physics: • Mohsscale (hardness of minerals) • socialsciences: • preferences

  8. ordering level 3: difference (or:Interval) scale differencebetweenvalues has meaning http://commons.wikimedia.org/wiki/File:Keyboard_of_grand_piano_-_Steinway_%26_Sons_(Hamburg_factory).jpg • physics: • heat transfer  temperaturedifference • potential energy • centigradescale (0C) • water height (river) • finance: •  growth • credit / debt

  9. ordering level 4: ratio scale ratio betweenvalues has meaning length: 1 : ½ : 1/3 frequency: 1 : 2 : 3 http://commons.wikimedia.org/wiki/File:Vibration_corde_fondamentale_trois_longueurs_petit.gif • physics: • heat transfer  temperaturedifference • potential energy • centigradescale (0C) • water height (river) • finance: •  growth • credit / debt • physics: • heat contents  absolute temperature (K) • kinetic energy • Kelvin scale (K) • water flow (m3/s) • finance: • % growth • assets

  10. operationrestrictions per ordering level:

  11. operationrestrictions per ordering level:

  12. operationrestrictions per ordering level:

  13. operationrestrictions per ordering level:

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