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Multivariate Statistics
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  1. Multivariate Statistics Philosophical Considerations

  2. Psychological Constructs • Important psychological constructs are complex and difficult to measure. • Can’t use a single number to adequately represent such concepts as: • Personality • Parenting style • Management style • Adjustment • Even IQ is not really adequately represented by a single number

  3. Operational Definitions • We operationally define these constructs to permit scientific study. • Operational Definition: The meaning of a variable is specified in terms of the operations necessary to measure it in any concrete situation, or in terms of the experimental methods involved in its determination

  4. Examples of Operational Definitions • For research purposes we can define parenting style by using a parenting styles questionnaire. The persons parenting style is given by their scores on the scales or subscales. • We can define management style by using a management styles inventory.

  5. Problems • There may be several different questionnaires available to assess a psychological construct. • Different measures give different results • Use different subscales and different dimensions • Which is right? • Frequently, when two research studies disagree on the results, it is because they have used different definitions. Source of disagreement in science.

  6. Questions • Which operational definition is right? • Which operational definition is best? • Is the operational definition the problem or is our idea of the concept wrong? • Can we do better?

  7. Metaphysics • It is impossible get a perfect measure of important and meaningful psychological constructs. • Due to complexity • Due to limitations in • Human intelligence and cognitive capacity • Technology

  8. The Parable of the Blind Men and the Elephant • Three blind men come across an elephant. They decide to feel the elephant to determine what sort of creature it is. One blind man feels the back leg of the elephant. He says, "An elephant is like a tree." The second blind man feels the trunk. He says, "An elephant is like a snake." The third blind man feels the tail. He says, "An elephant is like a rope." The three blind men argue a long time about what an elephant is and based on their own personal experience each is right.

  9. Metaphysically • Psychology is a unique discipline from a philosophical point of view. • Here we have a creature trying to understand itself. • In many ways it is like the blind men and the elephant

  10. Bracketing • One of the best approaches to understanding complex concepts is to use bracketing • Bracketing involves setting boundaries on a construct. • We may not know for sure what it is but we are pretty sure it is between these two limits.

  11. Bracketing • This provides greater accuracy than using a single best guess to represent the construct. • We try to refine our estimates by making our brackets narrower and narrower. • We try to trap the construct between our limits. • Science is like building a fence around the construct and then moving the fence in until we can get close enough to it to understand and control it.

  12. Bracket Example • Evaluating two individuals ability to use positive discipline (to make a hiring decision). • Report says: • Person A is in the good to very good range • Person B is in the average to good range • Hire A

  13. Multiple Convergent Measures • For the blind men and the elephant, the report of all three provided a better and more complete understanding of the elephant than any one report alone. Even though their reports appeared contradictory and impossible to reconcile. • If the blind men continue to examine different aspects of the elephant and combine their knowledge they may well come up with a pretty good understanding of what an elephant is like.

  14. Multiple Convergent Measures • Similarly, the best understanding of complex psychological constructs and processes will develop from approaches that use multiple measurement, assessment, and evaluation techniques to look at the same construct. • Multiple convergent measures

  15. Approach • The approach is to use multiple convergent measures to bracket complex psychological constructs and processes.

  16. Multivariate Statistical Methods • Multivariate statistical methods permit us to use multiple convergent measures to bracket complex constructs.