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ERIC Number: ED068579
Record Type: RIE
Publication Date: 1972
Pages: 8
Abstractor: N/A
Reference Count: 0
An Incorrect Index of Skewness.
Pettibone, Timothy J.; Diamond, James J.
Checking of parametric assumptions is an often ignored step in the inferential process. A misconception regarding symmetry (one aspect of "robustness") is prevalent: that in nonsymmetric distributions the mean and median are always non-coincidental. It is to this fallacious point that the discussion is directed. A generally accepted index of skewness, as identified in mathematical statistics texts, is the third moment of a random variable around its mean, but this index, sometimes denoted as Beta , is really the average cubed linear z score for a distribution. Thus if the distribution is symmetric, Beta will be zero. By considering two nonsymmetric distributions, further discussion of the point is given. In conclusion, when there is concern about symmetry (for either pedagogical or technical reasons), the data should be plotted and the distribution examined. This inspection technique along with Beta computation will result in a more valid conclusion regarding symmetry. (LH)
Publication Type: N/A
Education Level: N/A
Audience: N/A
Language: N/A
Sponsor: N/A
Authoring Institution: N/A