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Fisher IMPS2012c InvitedSymposiumMetaphor


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Presentation on metaphor and measurement given in invited symposium on validity in measurement, International Meetings of the Psychometric Society, July 2012

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Fisher IMPS2012c InvitedSymposiumMetaphor

  1. 1. Metaphor as Measurement and Vice Versa A Study of the Metaphor “Love is a Rose” William P. Fisher, Jr. University of California, Berkeley International Meeting of the Psychometric Society 9-13 July 2012 Lincoln, Nebraska
  2. 2. Two Preliminary Points• On the distinction between the literal and the metaphorical…• Metaphor is necessary in discourse as it is the means by which new things come into language.
  3. 3. Overview• Metaphors as construct models• Models as construct metaphors• A study of “Love is a rose”• Implications• Directions for future research
  4. 4. "What I cannot create, I do not understand." From Richard Feynmans Caltech classroom blackboard at the time of his death. Hawking, S. W. (2001). The universe in a nutshell. New York: Bantam Books, p. 83.
  5. 5. Constructs Recreated from Theory• Irvine, Dunn, Anderson, 1990 – British Army Recruitment Battery R > .70• Embretson, 1998: Abstract Reasoning Test R > .70• Stenner & Smith, 1982: Knox Cube Test R > .90• Fischer, 1973: Elementary calculus test R > .85• Stenner, et al, 1983: Peabody Vocab Test R > .80• Stenner, et al, 1997: Reading tests R > .90• Bejar, et al, 2003: Math tests R > .85• Fisher, 2008: Physical function surveys R > .90
  6. 6. Criteria for Laboratory Synthesis and Demonstrated Understanding• Data fit a model has the form of a multiplicative scientific law.• A linear unit is defined by the invariance of the estimates across subsamples.• A predictive theory explains a significant portion of the variance in the item location estimates.• The metaphor-model informs a distributed metrology system for point-of-use applications.
  7. 7. "Every metaphor is the tip of a submerged model." Black, M. (1962). Models and metaphors. Ithaca, New York: Cornell University Press, p. 30. And so might it also be that every model elaborates an often unnoticed metaphor? Perhaps there would be some value in expanded use of a concept of heuristic fiction, fictional truth, or guiding ideal.
  8. 8. Models as Metaphors “To take a parallel from elementary physics:A ‘mathematical pendulum’ is defined as ‘aheavy point, swinging frictionless on aweightless string in vacuum.’ A contraption likethat was never seen; thus as a model for themotion of a real pendulum it is ‘unrealistic’. “ Rasch (1973/2011, p. 1309)
  9. 9. Models as Metaphors• George Box (1979, p. 202): – “All models are wrong, but some are useful.”• Georg Rasch (1960, pp. 37-38): – “That the model is not true is certainly correct, no models are—not even the Newtonian laws…. Models should not be true, but it is important that they are applicable.”• Also see Rasch (1973/2011): – “All statistical models are wrong!”
  10. 10. “Love is a rose”
  11. 11. Love is a Rose Study• 68 entailments, such as – Love is beautiful. Love is thorny. – Love can be bought in a store. – Love grows in the ground. – Love is given to a special person. – Love fades. Love needs sunlight. – Love has leaves. Love inspires passion.
  12. 12. Construct Hypotheses• Before data were gathered, entailments were divided into three groups • Most likely to be rated TRUE • Rating UNDECIDABLE • Most likely to be rated UNTRUE
  13. 13. Three survey forms• 33-36 items each – 20 items in common – 11-14 items unique to each form• On each form, items were selected to – Span the full expected calibration range – Represent equally the three hypothetical groups
  14. 14. 36 total respondents• Subset of original 44 – Selected for completion & cooperative responses – Locations • 15 in Moline, Illinois • 21 in Chicago, Illinois – Sex • 18 Female • 18 Male – Age • Overall average 39.2 • No significant differences by location or sex
  15. 15. Model-MetaphorMultiplicative Form of Rasch Rating Scale Model Lrqs = Or / Vq / Eswhere• L is the rate at which love is a rose in the interaction of person r with entailment q at the s level of fictional truth, and L is equal to • the love-rose experience O of person r divided by • the love-rose unity V of entailment q and divided by • the level of love-rose fictional truth E of rating s.
  16. 16. PersonsEntailments
  17. 17. 15-20 responses per item. R = .94 R disattenuated = 1.00
  18. 18. 17 or 18 responses per item for each group.
  19. 19. 35 or 36 responses per item.
  20. 20. F = .08, 3 df, p = .97
  21. 21. Romantic entailments of “love is a rose.”
  22. 22. Concrete entailments of “Love is a rose”
  23. 23. Conclusions• The model has the form of a multiplicative scientific law.• A linear unit is defined by the invariance of the estimates across subsamples.• A predictive theory explains about 80% of the variance in the item location estimates.• The metaphor itself embodies a distributed metrology system for point-of-use expressions of a measure of romantic love.
  24. 24. "The greatest thing by faris to be a master of metaphor.” Aristotle