effect_sizes.py

import math
import scipy.stats as st

# assumes bivariate normal, dichotomised groups
def dichotomy_r_to_d(r) :
    d = 2*r / (math.sqrt(1 - r**2))
    return d

# Equation 9
# https://sci-hub.tw/10.1037/1082-989X.11.4.386
def r_to_d(r, n1, n2) :
    N = n1 + n2
    p1 = n1 / N
    p2 = n2 / N
    d = r / math.sqrt( (1 - r**2) * p1*p2  )
    return d
	
# r.Lakens = CohenDs / sqrt(CohenDs^2 + (N^2 - 2*N)/(n1*n2)
	
def cohens_d(experimentalMean, controlMean, \
            experimentalSd, controlSd, \
            experimentalN, controlN, \
            correctForBias=True) :
    sd = pooled_sd(experimentalSd, controlSd)
    d = (experimentalMean - controlMean) / sd
    
    if correctForBias :
        N = experimentalN + controlN
        correction = ( (N - 3)/(N - 2.25) ) \
                        * math.sqrt( (N-2)/N )
        d = d * correction
    
    return d


def pooled_sd(sd1, sd2) :
    sumSquaredSigma = sd1**2 + sd2**2
    
    return math.sqrt(sumSquaredSigma/2)


# assuming normality as usual
def approx_ci_to_z(lo_ci, hi_ci, alpha=0.05) :
     z = st.norm.ppf(1 - alpha/2)
     # midpoint
     estimate = (lo_ci + hi_ci)/2
     stderr = (hi_ci - lo_ci) / (2 * z)
     
     return estimate / stderr 

# Correction from Lakens
# https://www.frontiersin.org/articles/10.3389/fpsyg.2013.00863/full
def hedges_g(experimentalMean, controlMean, \
            experimentalSd, controlSd, \
            experimentalN, controlN) :
    dof = experimentalN + controlN 
    approxCorrection = 1 - ( 3 / (4*dof - 9) )
    d = cohens_d(experimentalMean, controlMean, \
    	        experimentalSd, controlSd, \
		correctForBias=True)
    
    return d * approxCorrection

# https://www.meta-analysis.com/downloads/Meta-analysis%20Converting%20among%20effect%20sizes.pdf
def odds_ratio_to_d(or_):
    correction = 0.551328895421756
    return math.log(or_) * correction
    

# Elderly priming
doyen = { "primed_mean" : 6.27, \
         "primed_sd" : 2.15,\
         "primed_n" : 60,\
         "control_mean" : 6.39,\
         "control_sd" : 1.11,\
         "control_n" : 60,
}


cohens_d(doyen["primed_mean"], doyen["control_mean"], \
	doyen["primed_sd"], doyen["control_sd"], \
	 doyen["primed_n"], doyen["control_n"]