v0.2.20

docs/statlab_corr_spearman_rho.rst

@@ -61,15 +61,15 @@ Let :math:`(Y_{i1}, Y_{i2})` be a pair of random variables corresponding to the
 Let :math:`(R_{i1}, R_{i2})` be the rank of :math:`Y_{i1}` and the rank of :math:`Y_{i2}`.
 In the case of ties, one method is to assign the tied group with the average of unique ranks corresponding the tied group.
 For the :math:`i` th sample, let 
-:math:`s_1` be the number of observed values less than :math:`Y_{i1}`,
-:math:`s_2` be the number of observed values equal to :math:`Y_{i1}`,
-and :math:`s_3` be the number of observed values greater to :math:`Y_{i1}`.
+:math:`S_1` be the number of observed values less than :math:`Y_{i1}`,
+:math:`S_2` be the number of observed values equal to :math:`Y_{i1}`,
+and :math:`S_3` be the number of observed values greater to :math:`Y_{i1}`.
 We can calculate the rank of a single sample as 
 
 .. math::
   :label: eq_rank
 
-  R_{i^*1} = s_1 + \frac{s_2+1}{2} = n - s3 - \frac{s_2-1}{2}.
+  R_{i^*1} = S_1 + \frac{S_2+1}{2} = n - S_3 - \frac{S_2-1}{2}.
 
 For a vector, ``pandas.DataFrame`` has the ``rank`` function with ``method='average'`` option to calculate rank as defined in :eq:`eq_rank`. 
 In ``R``, that can be calculated using the ``rank`` function with ``ties.method='average'`` option.
@@ -80,10 +80,10 @@ The Spearman's :math:`\rho` can be calculated as:
 .. math::
   :label: eq_rho
 
-  \rho = \frac{\frac{1}{n}\sum_i R_{i1}R_{i2} - \frac{1}{4}(n+1)^2}{t_1 t_2},
+  \rho = \frac{\frac{1}{n}\sum_i R_{i1}R_{i2} - \frac{1}{4}(n+1)^2}{s_1 s_2},
 
-where :math:`t_1 = \sum_i Y_{i1}^2 - \frac{1}{4}(n+1)^2`,
-and :math:`t_2 = \sum_i Y_{i2}^2 - \frac{1}{4}(n+1)^2`.
+where :math:`s_1 = \sum_i Y_{i1}^2 - \frac{1}{4}(n+1)^2`,
+and :math:`s_2 = \sum_i Y_{i2}^2 - \frac{1}{4}(n+1)^2`.
 
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 Example - Group-1