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11-15-2012, 08:48 AM
#391
Dalton
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Quote:
 Originally Posted by eva unit zero Your error was not realizing the other definiton of "means". The idea Czech has behind using AS for direct comparison of seasons played by multiple players is predicated on the fact that average scoring fluctuates on a yearly basis. Example: Joe Smith scores 20 goals every year in three consecutive years. Bob Jones scores 25, 25, and 10 in those same years. They have the same overall totals, and we'll assume they had the same GP. Adjusted stats provide us insight into whether it was harder to score goals in a given season, and might highlight one or the other a truly achieving more. In this example, if the third season has a higher league GPG than the first two, there's a good chance Bob Jones ends up with more AG. And before you begin with the "See, I told you it was flawed!" this is no different than taking three random seasons out of Gretzky's career and comparing them to three random seasons out of Jagr's.
This would be fundamental error in thinking. This paragraph addresse that issue.

"As a second illustration of the implications of our results, consider the research domain of utility analysis in preemployment testing and training and development. Utility analysis is built upon the assumption of normality, most notably with regard to the standard deviation of individual performance (SDy), which is a key component of all utility analysis equations. In their seminal article, Schmidt et al. (1979) defined SDy as follows: “If job performance in dollar terms is normally distributed, then the difference between the value to the organization of the products and services produced by the average employee and those produced by an employee at the 85th percentile in performance is equal to SDy” (p. 619). The result was an estimate of \$11,327. What difference would a Paretian distribution of job performance make in the calculation of SDy? Consider the distribution found across all 54 samples in Study 1 and the productivity levels in this group at (a) the median, (b) 84.13th percentile, (c) 97.73rd percentile, and (d) 99.86th percentile. Under a normal distribution, these values correspond to standardized scores (z) of 0, 1, 2, and 3. The difference in productivity between the 84.13th percentile and the median was two, thus a utility analysis assuming normality would use SDy= 2.0. A researcher at the 84th percentile should produce \$11,327 more output than the median researcher (adjusted for inflation). Extending to the second standard deviation, the difference in productivity between the 97.73rd percentile and median researcher should be four, and this additional output is valued at \$22,652. However, the difference between the two points is actually seven. Thus, if SDy is two, then the additional output of these workers is \$39,645 more than the median worker. Even greater disparity is found at the 99.86th percentile. Productivity difference between the 99.86th percentile and median worker should be 6.0 according to the normal distribution; instead the difference is more than quadruple that (i.e., 25.0). With a normality assumption, productivity among these elite workers is estimated at \$33,981 (\$11,327 × 3) above the median, but the productivity of these workers is actually \$141,588 above the median. We chose Study 1 because of its large overall sample size, but these same patterns of productivity are found across all five studies. In light of our results, the value-added created by new preemployment tests and the dollar value of training programs should be reinterpreted from a Paretian point of view that acknowledges that the differences between workers at the tails and workers at the median are considerably wider than previously thought. These are large and meaningful differences suggesting important implications of shifting from a normal to a Paretian distribution. In the future, utility analysis should be conducted using a Paretian point of view that acknowledges that differences between workers at the tails and workers at the median are considerably wider than previously thought."