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Useful
Statistics 



statistical
modelling 

Cstatistic
 This statistic is utilized to test for the statistical significance
of clustered patterns for a large number of clustering routines.
more...



statistical
modelling 

chisquare
 Properties
 A special case of the gamma distribution
 The distribution for the sum of squares of independent standard
normal random variables.
 Requires the use of a statistical table.
 Useful theorems
 The sum of two statistically independent random variables
with chisquare distributions is another randomvariable with
a chisqure distribution whose number of degrees of freedom is
equal to the sum of the degrees of freedom of both variables.
 Useful applications
 Useful in the construction of confidence intervals for the
sample variances of normally distributed independnet random variables.
 Adjusting for the presence of patterns brought about by random
chance. cluster analysis (proximity
measures)



statistical
modelling 

Fstatistic
 Properties
 The ratio of two independent random variables with chisquare
distribution, whose degrees of freedom m (numerator) and
n denominator) are those of the two independent random
variables.
 Requires the use of a statistical table.
 Useful theorems



statistical
modelling 

tstatistic (Student  t)
 Properties
 The ratio of an independent standard normal variable and
the square root of another independent random variable with chisquare
distribution that has been divided by its number of degrees of
freedom.
 The degrees of freedom of the Student  t are the same as
those of the random variable with chisquare distribution.
 Unlike the chisquare distribution the Student t statistic
is distributed symmetrically.
 The Student  t distribution is very similar to that of a
normal distribution, but is flatter with greater probability
associated in both tails.
 Requires the use of a statistical table.
 Useful theorems
 Given n independent normally distributed random variables,
the tstatistics is the ratio of the difference of the sample
and population means divided by the square root of the sample
variance divided by the number of variables.
 Useful applications
 Used in the construction of confidence intervals for normally
distributed independent random variables.
 Used in testing the nullhypothesis for single coefficiencts
of a regression equation.
 Used in measuring the ability of a discriminant function
to predict accurately group membership from a sample population.



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