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English
or languish - Probing the ramifications
of Hong Kong's language policy |
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| Useful
Statistics |
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| statistical
modelling |
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C-statistic
- This statistic is utilized to test for the statistical significance
of clustered patterns for a large number of clustering routines.
more...
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| statistical
modelling |
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chi-square
- 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 chi-square distributions is another randomvariable with
a chi-squre 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)
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| statistical
modelling |
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F-statistic
- Properties
- The ratio of two independent random variables with chi-square
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
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| statistical
modelling |
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t-statistic (Student - t)
- Properties
- The ratio of an independent standard normal variable and
the square root of another independent random variable with chi-square
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 chi-square distribution.
- Unlike the chi-square 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 t-statistics 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 null-hypothesis 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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