A MEASURE OF SKEWNESS FOR TESTING DEPARTURES FROM NORMALITY

Testing for a deficit in single-case studies: effects of departures from normality.

In neuropsychological single-case research inferences concerning a patient's cognitive status are often based on referring the patient's test score to those obtained from a modestly sized control sample. Two methods of testing for a deficit (z and a method proposed by Crawford and Howell [Crawford, J. R. & Howell, D. C. (1998). Comparing an individual's test score against norms derived from sma...

A general measure of skewness

An Improved Skewness Measure

Skewness is an important property of a population. Although many measures have been proposed there is no consensus on what should be used in practice. We propose a new measure which is appropriate when the direction of the skewness is known a priori. It is simple to interpret and easy to estimate.

Testing for normality.

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Skewness and kurtosis as locally best invariant tests of normality

Consider testing normality against a one-parameter family of univariate distributions containing the normal distribution as the boundary, e.g., the family of t-distributions or an infinitely divisible family with finite variance. We prove that under mild regularity conditions, the sample skewness is the locally best invariant (LBI) test of normality against a wide class of asymmetric families a...