Correlation
======================================

`Correlation` is capable of performing pearson, spearman, kendalltau, or pointbiserial 
correlations between multiple variables. Printing the object will output coefficients, 
and non-familywise error corrected 2-tail p-values. Larzelere and Mulaik step down 
Significance testing is also performed. 

Example using `DataFrame` object
--------------------------------

.. sourcecode:: python

    df=DataFrame()
    
    df['A']=[24,61,59,46,43,44,52,43,58,67,62,57,71,49,54,43,53,57,49,56,33]
    
    df['B']=[42.93472681237495,  78.87307334936268,  75.37292628918023, 
             65.49076317291956,  55.55965179772366,  56.777730638998236, 
             62.19451880792437,  54.73710611356715,  72.10021832823149, 
             85.94377749485642,  78.2087578930983,   72.01681829338037, 
             84.27889316830063,  60.20516982367225,  65.6276497088971, 
             62.36549856901088,  69.18772114281175,  67.00548667483324, 
             59.042687027269466, 71.99214593063917,  45.00831155783992]
             
    df['C']=[-53.05540625388731, -96.33996451998567,  -92.32465861908086, 
             -70.90536432779966, -55.953777697739255, -74.12814626217357, 
             -75.89188834814621, -64.24093256012688,  -89.62208010083313, 
             -87.41075066046812, -80.40932820298143,  -77.99906284144805, 
             -95.31607277596169, -61.672429800914486, -85.26088499198657, 
             -63.4402296673869,  -74.84950736563589,  -85.00433219746624, 
             -71.5901436929124,  -76.43243666219388,  -48.01082320924727]
            
    cor=df.correlation(['A','B','C'],coefficient='spearman')
    print(cor)

::

    Bivariate Correlations

                             A           B           C     
    ======================================================
    A   spearman                 1       0.958      -0.924 
        Sig (2-tailed)           .   9.699e-12   2.259e-09 
        N                       21          21          21 
    ------------------------------------------------------
    B   spearman             0.958           1      -0.890 
        Sig (2-tailed)   9.699e-12           .       0.000 
        N                       21          21          21 
    ------------------------------------------------------
    C   spearman            -0.924      -0.890           1 
        Sig (2-tailed)   2.259e-09       0.000           . 
        N                       21          21          21 

    Larzelere and Mulaik Significance Testing

     Pair     i   Correlation       P       alpha/(k-i+1)   Sig. 
    ============================================================
    A vs. B   1         0.958   9.699e-12           0.017   **   
    A vs. C   2         0.924   2.259e-09           0.025   **   
    B vs. C   3         0.890   6.850e-08           0.050   **