Merge branch 'master' of github.com:MicrosoftResearch/Azimuth

azimuth/corrstats.py

@@ -0,0 +1,120 @@
+"""
+Functions for calculating the statistical significant differences between two dependent or independent correlation
+coefficients.
+The Fisher and Steiger method is adopted from the R package http://personality-project.org/r/html/paired.r.html
+and is described in detail in the book 'Statistical Methods for Psychology'
+The Zou method is adopted from http://seriousstats.wordpress.com/2012/02/05/comparing-correlations/
+Credit goes to the authors of above mentioned packages!
+Author: Philipp Singer (www.philippsinger.info)
+
+------------------------------------------------------------
+README.md:
+CorrelationStats
+This Python script enables you to compute statistical significance tests on both dependent and independent correlation coefficients. For each case two methods to choose from are available.
+
+For details, please refer to: http://www.philippsinger.info/?p=347
+#copied from on 4/24/2015 from https://github.com/psinger/CorrelationStats/blob/master/corrstats.py
+"""
+
+
+from __future__ import division
+
+__author__ = 'psinger'
+
+import numpy as np
+from scipy.stats import t, norm
+from math import atanh, pow
+from numpy import tanh
+
+def rz_ci(r, n, conf_level = 0.95):
+    zr_se = pow(1/(n - 3), .5)
+    moe = norm.ppf(1 - (1 - conf_level)/float(2)) * zr_se
+    zu = atanh(r) + moe
+    zl = atanh(r) - moe
+    return tanh((zl, zu))
+
+def rho_rxy_rxz(rxy, rxz, ryz):
+    num = (ryz-1/2.*rxy*rxz)*(1-pow(rxy,2)-pow(rxz,2)-pow(ryz,2))+pow(ryz,3)
+    den = (1 - pow(rxy,2)) * (1 - pow(rxz,2))
+    return num/float(den)
+
+def dependent_corr(xy, xz, yz, n, twotailed=True, conf_level=0.95, method='steiger'):
+    """
+    Calculates the statistic significance between two dependent correlation coefficients
+    @param xy: correlation coefficient between x and y
+    @param xz: correlation coefficient between x and z
+    @param yz: correlation coefficient between y and z
+    @param n: number of elements in x, y and z
+    @param twotailed: whether to calculate a one or two tailed test, only works for 'steiger' method
+    @param conf_level: confidence level, only works for 'zou' method
+    @param method: defines the method uses, 'steiger' or 'zou'
+    @return: t and p-val
+    """
+    if method == 'steiger':
+        d = xy - xz
+        determin = 1 - xy * xy - xz * xz - yz * yz + 2 * xy * xz * yz
+        av = (xy + xz)/2
+        cube = (1 - yz) * (1 - yz) * (1 - yz)
+
+        t2 = d * np.sqrt((n - 1) * (1 + yz)/(((2 * (n - 1)/(n - 3)) * determin + av * av * cube)))
+        p = 1 - t.cdf(abs(t2), n - 2)
+
+        if twotailed:
+            p *= 2
+
+        return t2, p
+    elif method == 'zou':
+        L1 = rz_ci(xy, n, conf_level=conf_level)[0]
+        U1 = rz_ci(xy, n, conf_level=conf_level)[1]
+        L2 = rz_ci(xz, n, conf_level=conf_level)[0]
+        U2 = rz_ci(xz, n, conf_level=conf_level)[1]
+        rho_r12_r13 = rho_rxy_rxz(xy, xz, yz)
+        lower = xy - xz - pow((pow((xy - L1), 2) + pow((U2 - xz), 2) - 2 * rho_r12_r13 * (xy - L1) * (U2 - xz)), 0.5)
+        upper = xy - xz + pow((pow((U1 - xy), 2) + pow((xz - L2), 2) - 2 * rho_r12_r13 * (U1 - xy) * (xz - L2)), 0.5)
+        return lower, upper
+    else:
+        raise Exception('Wrong method!')
+
+def independent_corr(xy, ab, n, n2 = None, twotailed=True, conf_level=0.95, method='fisher'):
+    """
+    Calculates the statistic significance between two independent correlation coefficients
+    @param xy: correlation coefficient between x and y
+    @param xz: correlation coefficient between a and b
+    @param n: number of elements in xy
+    @param n2: number of elements in ab (if distinct from n)
+    @param twotailed: whether to calculate a one or two tailed test, only works for 'fisher' method
+    @param conf_level: confidence level, only works for 'zou' method
+    @param method: defines the method uses, 'fisher' or 'zou'
+    @return: z and p-val
+    """
+
+    if method == 'fisher':
+        xy_z = 0.5 * np.log((1 + xy)/(1 - xy))
+        xz_z = 0.5 * np.log((1 + ab)/(1 - ab))
+        if n2 is None:
+            n2 = n
+
+        se_diff_r = np.sqrt(1/(n - 3) + 1/(n2 - 3))
+        diff = xy_z - xz_z
+        z = abs(diff / se_diff_r)
+        p = (1 - norm.cdf(z))
+        if twotailed:
+            p *= 2
+
+        return z, p
+    elif method == 'zou':
+        L1 = rz_ci(xy, n, conf_level=conf_level)[0]
+        U1 = rz_ci(xy, n, conf_level=conf_level)[1]
+        L2 = rz_ci(ab, n2, conf_level=conf_level)[0]
+        U2 = rz_ci(ab, n2, conf_level=conf_level)[1]
+        lower = xy - ab - pow((pow((xy - L1), 2) + pow((U2 - ab), 2)), 0.5)
+        upper = xy - ab + pow((pow((U1 - xy), 2) + pow((ab - L2), 2)), 0.5)
+        return lower, upper
+    else:
+        raise Exception('Wrong method!')
+
+#print dependent_corr(.396, .179, .088, 200, method='steiger')
+#print independent_corr(.560, .588, 100, 353, method='fisher')
+
+#print dependent_corr(.396, .179, .088, 200, method='zou')
+#print independent_corr(.560, .588, 100, 353, method='zou')