TwoSampleTests            package:fBasics            R Documentation

_T_w_o _S_a_m_p_l_e _T_e_s_t_s

_D_e_s_c_r_i_p_t_i_o_n:

     A collection and description of functions for  two sample
     statistical tests. The functions allow  an easy use to test two
     financial return series for  distributional equivalence, for
     difference in  location, variance and scale, and for correlations
     and association. 

     Distributional Equivalence:

       'ks2Test'  Two sample Kolmogorov-Smirnov test.

     Test Difference in Locations:

       'locationTest'  The location test suite,
       'method="t"'    the t test,
       'method="kw"'   the Kruskal-Wallis test.

     Test Difference in Variance:

       'varianceTest'       The variance test suite,
       'method="varf"'      the variance F test,
       'method="bartlett"'  the Bartlett test,
       'method="fligner"'   the Fligner-Killeen test.

     Test Difference in Scale:

       'scaleTest'      The scale test suite,
       'method=ansari'  the Ansari-Bradley test,
       'method=mood'    the Mood test.

     Test for Correlations:

       'correlationTest'  The correlation test suite,
       'method=pearson'   Pearson's coefficient,
       'method=kendall'   Kendall's tau,
       'method=spearman'  Spearman's rho.

_U_s_a_g_e:

     ks2Test(x, y, title = NULL, description = NULL)

     locationTest(x, y, method = c("t", "kw2"), 
         title = NULL, description = NULL) 
     varianceTest(x, y, method = c("varf", "bartlett", "fligner"), 
         title = NULL, description = NULL)
     scaleTest(x, y, method = c("ansari", "mood"), 
         title = NULL, description = NULL)
         
     correlationTest(x, y, method = c("pearson", "kendall", "spearman"), 
         title = NULL, description = NULL)

_A_r_g_u_m_e_n_t_s:

description: optional description string, or a vector of character
          strings. 

  method: a character string naming which test should be applied. 

   title: an optional title string, if not specified the inputs data 
          name is deparsed. 

    x, y: numeric vectors of data values. 

_D_e_t_a_i_l_s:

     The tests may be of interest for many financial  and economic
     applications, especially for the  comparison of two time series.
     The tests are grouped  according to their functionalities. 

     *Distributional Equivalence:* 

        The test 'ks2Test' performs a Kolmogorov-Smirnov two sample
     test  that the two data samples 'x' and 'y' come from the same 
     distribution, not necessarily a normal distribution. That means
     that  it is not specified what that common distribution is.  

     *Differences in Location:* 

        The 'tTest' can be used to determine if the two sample  means
     are equal for unpaired data sets. Two variants are used, assuming
     equal or unequal variances. 

     The 'kw2Test' performs a Kruskal-Wallis rank sum  test of the null
     hypothesis that the central tendencies or medians of  two samples
     are the same. The alternative is that they differ.  Note, that it
     is not assumed that the two samples are drawn from the  same
     distribution. It is also worth to know that the test assumes  that
     the variables under consideration have underlying continuous 
     distributions. 

     *Differences in Variances:* 

          The 'varfTest' can be used to compare variances of two 
     normal samples performing an F test. The null hypothesis is that 
     the ratio of the variances of the populations from which they were
      drawn is equal to one. 

     The 'bartlett2Test' performs the Bartlett's test of the  null
     hypothesis that the variances in each of the samples are the 
     same. This fact of equal variances across samples is also called 
     _homogeneity of variances_. Note, that Bartlett's test is 
     sensitive to departures from normality. That is, if the samples 
     come from non-normal distributions, then Bartlett's test may
     simply  be testing for non-normality. The Levene test (not yet
     implemented) is an alternative to the Bartlett test that is less
     sensitive to  departures from normality. 

     The 'fligner2Test' performs the Fligner-Killeen test of  the null
     that the variances in each of the two samples are the same.  

     *Differences in Scale:* 

        The 'ansariTest' performs the Ansari-Bradley two-sample  test
     for a difference in scale parameters. The test returns for  any
     sizes of the series 'x' and 'y' the exact p value  together with
     its asymptotic limit.  

     The code{moodTest}, is another test which performs a  two-sample
     test for a difference in scale parameters. The underlying  model
     is that the two samples are drawn from _f(x-l)_ and 
     _f((x-l)/s)/s_, respectively, where _l_ is a common  location
     parameter and _s_ is a scale parameter. The null  hypothesis is
     _s=1_.  

     *Correlations:* 

        The 'correlationTest' for association between paired samples, 
     allows to compute Pearson's product moment correlation
     coefficient,  Kendall's tau, or Spearman's rho.

_V_a_l_u_e:

     In contrast to R's output report from S3 objects of class
     '"htest"' a different output report is produced. The classical
     tests presented here return an S4 object of class '"fHTEST"'. The
     object contains the following slots:

   @call: the function call.   

   @data: the data as specified by the input argument(s). 

   @test: a list whose elements contail the results from the
          statistical test. The information provided is similar to a
          list object of class{"htest"}. 

  @title: a character string with the name of the test. This can be 
          overwritten specifying a user defined input argument. 

@description: a character string with an optional user defined
          description.  By default just the current date when the test
          was applied will be returned. 

statistic: the value(s) of the test statistic. 

 p.value: the p-value(s) of the test. 

parameters: a numeric value or vector of parameters. 

estimate: a numeric value or vector of sample estimates. 

conf.int: a numeric two row vector or matrix of 95 

  method: a character string indicating what type of test was
          performed. 

data.name: a character string giving the name(s) of the data. 

_N_o_t_e:

     Some of the test implementations are selected from R's 'ctest' 
     package.

_A_u_t_h_o_r(_s):

     R-core team for the tests from R's ctest package,
      Diethelm Wuertz for the Rmetrics R-port.

_R_e_f_e_r_e_n_c_e_s:

     Conover, W. J. (1971); _Practical nonparametric statistics_, New
     York: John Wiley & Sons.

     Durbin J. (1961);  _Some Methods of Constructing Exact Tests_,
     Biometrika 48, 41-55. 

     Durbin,J. (1973); _Distribution Theory Based on the Sample
     Distribution Function_, SIAM, Philadelphia.

     Lehmann E.L. (1986);  _Testing Statistical Hypotheses_,  John
     Wiley and Sons, New York.

     Moore, D.S. (1986); _Tests of the chi-squared type_,  In:
     D'Agostino, R.B. and Stephens, M.A., eds.,  Goodness-of-Fit
     Techniques, Marcel Dekker, New York.

_E_x_a_m_p_l_e_s:

     ## x, y -
        x = rnorm(50)
        y = rnorm(50)
       
     ## ks2Test - 
        ks2Test(x, y)
        
     ## locationTest | .tTest | .kw2Test - 
        locationTest(x, y)
        
     ## varianceTest | .varfTest, .bartlett2Test | .fligner2Test -
        varianceTest(x, y)

     ## scaleTest | .ansariTest | .moodTest -
        scaleTest(x, y)
        
     ## correlationTest | .pearsonTest | .kendallTest | .spearmanTest -
        correlationTest(x, y)

