project index  
 
 English or languish - Probing the ramifications
of Hong Kong's language policy
   
 
Useful Statistics    
 
statistical modelling

C-statistic

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

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)
 
statistical modelling  

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
 
statistical modelling  

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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