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 - 3)
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!')
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