H James M. Clark Professor of Psychology 204-786-9757 204-774-4134 Fax [email protected] >>> "Mike Palij" [email protected]> 20-Jun-11 4:42 PM >> ( mailto:[email protected]> ) (4) Somebody should mention that what John Kulig and Jim Clark allude to below relates to the "central limit theorem". The Wikipedia entry on the normal distribution also coverts this topic; see: http://en.wikipedia.org/wiki/Normal_distribution#Central_limit_theorem and there is a separate entry on it (yadda-yadda) as well: http://en.wikipedia.org/wiki/Central_limit_theorem JC: The central limit theorem, which concerns sampling distribution of means based on n observations, is one specific application of the fact that sums (means if divided by n) of scores increasingly approximate a normal distribution, but as John pointed out any score that is dependent on multiple independent contributing factors will increasingly approximate a normal distribution. Hence, if IQs depend on multiple discrete observations the IQs of individuals (not means of individual IQs) will be normally distributed. The same holds for any variable (score) with multiple contributing factors. In the simulation, for example, the central limit theorem would strictly apply if individuals had dichotomous scores (e.g., dying or not, passing or not, ...) and the distribution represented the sampling distribution of the dichotomous observations for n individuals, either as sums as in the simulation or as means (equivalently proportions for dichotomous -0 1 scores) if divided by n. If, however, the dichotomous 0 1 numbers represent some underlying contributing factor to the individual scores represented by the sums (or means), then the results represent individual scores, which if averaged together for samples would have a sampling distribution of the means of the scores for n individuals. Perhaps just a subtle and esoteric distinction, but isn't that what academics specialize in? Take care Jim
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