Information Technology Reference
In-Depth Information
predetermined parameters (a parametric model), be parameter-free
(nonparametric), or be a mixture of the two types (semiparametric).
The definitions in the following section apply to the random
component.
PARAMETRIC, NONPARAMETRIC, AND
SEMIPARAMETRIC STATISTICAL PROCEDURES
Parametric
statistical procedures concern the parameters of distributions of
a known form. One may want to estimate the variance of a normal distrib-
ution or the number of degrees of freedom of a chisquare distribution.
Student
t
, the
F
ratio, and maximum likelihood are typical parametric
procedures.
Nonparametric
procedures concern distributions whose form is unspeci-
fied. One might use a nonparametric procedure like the bootstrap to
obtain an interval estimate for a mean or a median or to test that the dis-
tributions of observations drawn from two different populations are the
same. Nonparametric procedures are often referred to as distribution-
free, though not all distribution-free procedures are nonparametric in
nature.
Semiparametric
statistical procedures concern the parameters of distribu-
tions whose form is not specified. Permutation methods and
U
statistics
are typically employed in a semiparametric context.
SIGNIFICANCE LEVEL AND
p
VALUE
The
significance level
is the probability of making a Type I error. It is a
characteristic of a statistical procedure.
The
p value
is a random variable that depends both upon the sample
and the statistical procedure that is used to analyze the sample.
If one repeatedly applies a statistical procedure at a specific significance
level to distinct samples taken from the same population when the hypoth-
esis is true and all assumptions are satisfied, then the
p
value will be less
than or equal to the significance level with the frequency given by the
significance level.
TYPE I AND TYPE II ERROR
A Type I error is the probability of rejecting the hypothesis when it is
true. A Type II error is the probability of accepting the hypothesis when
an alternative hypothesis is true. Thus, a Type II error depends on the
alternative.
