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atest1

PURPOSE ^

ATEST calculates some basic statistics and

SYNOPSIS ^

function [R,z0,z2,z4] = atest(X,Y,alpha,DIM);

DESCRIPTION ^

 ATEST calculates some basic statistics and 
    checks whether two datasets differ significantly
    Currently, the MEAN and the COVARIANCE are implemented. 
    Other statistics can be tested, too. 

 The idea is based on the following assumptions:
  - the sample mean of a statistic is an estimate for the expectation value of this statistic 
  - the standard error of the mean is sqrt(var{x}/N)
  - the sample variance var{x}=sum((x-�)*(x-�))/(N-1) with �=sum(x)/N;
  - the standard error of the mean estimate is independent of the probability distribution [1]
  - not only the mean, but also other statistics can be obtained by averaging.
  - the standard error can be calculated for other estimates, too.
  - hence, we can calculate the standard error for any estimate 
  - these arguments holds for the mean as well as any other statistic 

 R = ATEST(X)
    if X is a numeric array, the basic statistics are calculated
        it includes the sample SUM, the number of samples,
        and the sum of sample squares 
    if X is a struct generated by ATEST (e.g. X=ATEST(x) ),
        derived statistics are calculated
        including the MEAN and STANDARD ERROR OF THE MEAN                

 R = ATEST(X, Y [, z [,DIM]])
    checks whether the MEAN of X and Y differ significantly.
    z determines the significance level [default = 3 (*sd)].
    in case z<0, z is the alpha-level for the significance test. 
    R contains the basic statistics of X and Y combined. 
    DIM denotes the DIMENSION

 see also: SUMSKIPNAN, COVM, SUMSQ, SEM,

CROSS-REFERENCE INFORMATION ^

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