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shorter than 1.6m. But if we ask, ?hat is the
probability that a principal in the line is 1.7m? that tail weights, exponential?evel
Then the probability could be 0.2 (i.e. 10% or 2
persons). Hence this explains the finite
variance ??which is dependent upon the
sample size. Normal distributions assume
few values far from the mean and
therefore, the mean is representative of the
population. Even the largest deviations, which
are exceptionally rare, are still only about a
factor of two from the mean in either
direction and are well characterized by
(Clauset, Shalizi and Newman, 2009). This
property of normal curve, in particular the
notion that extreme ends of both variance are
less likely to occur, has significant implication 87) states that ?onsiderable evidence
as will be discussed.
Is the normal distribution the standard to
determine acceptable findings in educational
research? One possible answer is a study done
by Micceri (1989). His investigation involved
obtaining secondary data from 46 different
test sources and 89 different populations that
have done psychometric and
achievement / ability measures.
He managed to obtain
analyzed data from
440 researchers.
He submitted these
secondary data to
analysis and found
that they were
significantly
non?ormal at
significance
level.
19
In fact, his findings found
asymmetry, severe digit preferences,
multimodalities, and modes external to
the mean/median interval were evident.
His conclusion was that the underlying
tenets of normality?ssuming statistics
appear fallacious for the psychometric
measures. Micceri (1989, p. 16) added
that ?ne must conclude that the
robustness literature is at best
indicative.??quoting a simple standard deviation
In another well cited article in the Review
of Educational Research, Walberg,
Strykowski, Rovai and Hung (1984 p.
shows that positive?kew distributions
characterize many objects and
fundamental processes in biology, crime,
economics, demography, geography,
industry, information and library
sciences, linguistics, psychology,
sociology, and the production and
utilization of knowledge.??Perhaps the
most pointed statement made by
Walberg et al., that ?ommonly reported
univariate statistics such as means,
standard deviations, and
ranges ??as well as bivariate and
multivariate statistics ??and
regression weights are
generally useless in
revealing skewness??the alpha .01 is worthy to note.