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Test Item Influences and Dependencies

Test Item Influences and Dependencies

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Test Item Influences and Dependencies

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  1. Test Item Influences and Dependencies G. Donald Allen Department of Mathematics Texas A&M University Test Item Influences and Dependencies

  2. Given and n item test • We can arrange the items in any order we wish. • Problem. What is the best strategy for arranging problems on a test? • Placing the easy items first followed by the more difficult ones? • Randomly placing items? • Cluster difficult and easy items separately? Test Item Influences and Dependencies

  3. The Situation • Additional assumptions are needed, the foremost being some model of the effect of one question upon succeeding ones. • For example, if the test begins with a very difficult item, one which most students will not solve, will this event affect their state of mind, or confidence, toward solving subsequent problems? Test Item Influences and Dependencies

  4. Goal • What we intend to show is that if we do allow test item dependencies, there can results a substantial variation on test scores depending on the ordering of the test item. Test Item Influences and Dependencies

  5. Toward a model Test Item Influences and Dependencies

  6. This means… Test Item Influences and Dependencies

  7. The grade Test Item Influences and Dependencies

  8. Influence and DependenciesHypotheses Test Item Influences and Dependencies

  9. Parameters of Influence Test Item Influences and Dependencies

  10. The Threshold Test Item Influences and Dependencies

  11. Positive or Negative? Test Item Influences and Dependencies

  12. The factors Test Item Influences and Dependencies

  13. Boost & Fade Test Item Influences and Dependencies

  14. Conditional Probabilities Test Item Influences and Dependencies

  15. Psychological factors • In fact α and β are psychological factors of emotional responses to test questions. • For poor test takers α may be larger than β, and vice-versa for good test takers. • Using different α and β here makes the problem very difficult. Test Item Influences and Dependencies

  16. Rewriting the model Test Item Influences and Dependencies

  17. Conditional probability Test Item Influences and Dependencies

  18. The Two Question Test Test Item Influences and Dependencies

  19. Two Cases Test Item Influences and Dependencies

  20. What to compare? Quantities are not comparable as is, without more information Test Item Influences and Dependencies

  21. More Assumptions Test Item Influences and Dependencies

  22. Easy precedes Difficult Test Item Influences and Dependencies

  23. Many Question Test • Multiple Questions • Multiple difficulties • Constant β’s • Constant γ’s Test Item Influences and Dependencies

  24. Many Question Test • Two possible models • Simplistic. Question i influences Question i+1 only • More realistic. The influence for question i+1 comes from all preceding questions, though perhaps with fading memory. Test Item Influences and Dependencies

  25. Simple Model Grade Test Item Influences and Dependencies

  26. Optimize Test Item Influences and Dependencies

  27. Strategies and Observations Test Item Influences and Dependencies

  28. Expanded version Test Item Influences and Dependencies

  29. An Interesting Connection Traveling Salesman problem Test Item Influences and Dependencies

  30. Traveling Salesman Test Item Influences and Dependencies

  31. The Two Difficulties Test Test Item Influences and Dependencies

  32. Main Result Test Item Influences and Dependencies

  33. Proof (sketch) Test Item Influences and Dependencies

  34. Test Item Influences and Dependencies

  35. Test Item Influences and Dependencies

  36. Step two. Test Item Influences and Dependencies

  37. Test Item Influences and Dependencies

  38. Step Three Test Item Influences and Dependencies

  39. Test Item Influences and Dependencies

  40. Avoiding every single detail, we have… Test Item Influences and Dependencies

  41. Multiple Item Difficulties • Here there are no clear answers. • It seems somewhat dependent on gamma, unless • Essentially, we can demonstrate there is no universal algorithm for a priori arranging the test items. Test Item Influences and Dependencies

  42. Ordering the Other Test Items Test Item Influences and Dependencies

  43. Local Strategy Test Item Influences and Dependencies

  44. A Weaker Local Result Test Item Influences and Dependencies

  45. Case 1 Test Item Influences and Dependencies

  46. Case 2 Test Item Influences and Dependencies

  47. Case 3 Test Item Influences and Dependencies

  48. Comments Test Item Influences and Dependencies

  49. Test Item Influences and Dependencies

  50. Test Item Influences and Dependencies