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kappa.py
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kappa.py
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#!/usr/bin/env python
# -*- coding: utf-8 -*-
import argparse
import math
import sys
from tabulate import tabulate
def calculate_kappa(Npp_param, Npa_param, Nap_param, Naa_param,
kappatest_param):
"""Created march 2003 by G.W.Payne
Kappa calculator as described by Mr Graham McBride in Evaluation of Colilert Procedures
Using Cohen's "Kappa" Statistic As The Measure Of Agreement With A Standard.
"""
#define all the variables used
n = 0 #number pairs
Npp = float(0)
Npa = float(0)
Nap = float(0)
Naa = float(0)
#a,b,c,d are cell frequencies
a = float(0) #Npp/n
b = float(0) #Npa/n
c = float(0) #Nap/n
d = float(0) #Naa/n
#p1,p2 row frequencies, q1,q2 column frequencies
p1 = float(0) #a+b
p2 = float(0) #a+c
q1 = float(0) #c+d
q2 = float(0) #b+d
#po, pe observed and chance-expected agreement frequencies
po = float(0) #a+d
pe = float(0) #p1*p2 + q1*q2
kappatest = float(0) #test value of kappa between 0 and 1
#estmated Kappa value - k is used to shorten expressions later
kappahat = float(0) #(po-pe)/(1.-pe)
k = float(0) #kappahat
kappaplus = float(0) #(a-p1*p2)/(p1-p1*p2)
kappaminus = float(0) #(d-q1*q2)/(q1-q1*g2)
#Standard error for test of zero kappa (Fleiss)
denom = float(0) #(1.-pe)*sqrt(N)
numer = float(0) #sqrt(pe+pe**2-p1*p2*(p1+p2)-q1*q2*(q1+q2)
se0 = float(0) #numer/denom
#Standard error test of non zero kappa (Fleiss, eqs 12.15-13.18)
capA = float(0) #a*(1.-(p1+p2)*(1.-k))**2+d*(1.-(q1+q2)*(1.-k))**2
capB = float(0) #((1.-k)**2) * (b*(p2+q1)**2+c*(p1+q2)**2)
capC = float(0) #(k-pe*(1.-k))**2
sek = float(0) #(sqrt(capA+capB-capC))/denom
#Standard error test of non zero Kappa (Bishop et al 1975 eq 11.4-4,5,6)
#theta3 = float(0) #a*(p1+p2)+d*(q1+q2)
#theta4 = float(0) #a*(p1+p2)**2+b*(p2+q1)**2+c*(p1+q2)**2+d(q1+q2)**2
#E = float(0) #po*(1.-po)
#F = float(0) #2.*(1-po)*2.*po*pe-thetha3)/(1.-pe)
#G = float(0) #((1.-po)**2)*(theta4-4.*pe**2)/(1.-pe)**2
# sekB=float(0) #sqrt((E+F+G))/denom - gives same result as sek, not used
z = float(0) #kappahat/se0
p = float(0) #1.-PROBN(z) kappa=<0
Npp = float(Npp_param)
Npa = float(Npa_param)
Nap = float(Nap_param)
Naa = float(Naa_param)
kappatest = float(kappatest_param)
# all output lines are indicated by #* at beginning
#estimated kappas (k is used later to shorten expressions
n = Npp + Npa + Nap + Naa
a = Npp / float(n)
b = Npa / n
c = Nap / n
d = Naa / n
#p1,p2 row frequencies, q1,q2 column frequencies
p1 = a + b
p2 = a + c
q1 = c + d
q2 = b + d
#po, pe observed and chance-expected agreement frequencies
po = a + d
pe = p1 * p2 + q1 * q2
#check for special cases
#b=c=d=0
if Npa == 0 and Nap == 0 and Naa == 0:
#Write
#*Perfect agreement (all rating pairs are "present")
#*kappahat, kappa+ and kappa- are all undefined.
#*No tests can be performed.
headers = ['Info']
table = []
table.append(['Perfect agreement (all rating pairs are "present")'])
table.append(['kappahat, kappa+ and kappa- are all undefined.'])
table.append(['No tests can be performed.'])
return tabulate(table, headers=headers, tablefmt="grid")
#a=b=c=0
if Npp == 0 and Npa == 0 and Nap == 0:
#Write
#*Perfect agreement (all rating pairs are "absent")
#*kappahat, kappa+ and kappa- are all undefined.
#*No tests can be performed.
headers = ['Info']
table = []
table.append(['Perfect agreement (all rating pairs are "absent")'])
table.append(['kappahat, kappa+ and kappa- are all undefined.'])
table.append(['No tests can be performed.'])
return tabulate(table, headers=headers, tablefmt="grid")
#a=c=d=0
if Npp == 0 and Nap == 0 and Naa == 0:
#Write
#*Perfect disagreement (all rating pairs are "present"/"absent")
#*kappahat = kappa+ = 0 (= minimum value in this case), but kappa- is undefined.
#*No tests performed.
headers = ['Info']
table = []
table.append(
['Perfect disagreement (all rating pairs are "present"/"absent")'])
table.append([
'kappahat = kappa+ = 0 (= minimum value in this case), but kappa- is undefined.'
])
table.append(['No tests performed.'])
return tabulate(table, headers=headers, tablefmt="grid")
#a=b=d=0
if Npp == 0 and Npa == 0 and Naa == 0:
#Write
#*Perfect disagreement (all rating pairs are "absent"/"present")
#*kappahat = kappa- = 0 (= minimum value in this case), but kappa+ is undefined.
#*No tests performed.
headers = ['Info']
table = []
table.append(
['Perfect disagreement (all rating pairs are "present"/"absent")'])
table.append([
'kappahat = kappa- = 0 (= minimum value in this case), but kappa+ is undefined.'
])
table.append(['No tests performed.'])
return tabulate(table, headers=headers, tablefmt="grid")
#b=d=0
if Npp != 0 and Npa == 0 and Nap != 0 and Naa == 0:
#Write
#*Rater B has marked all tests as "present"; rater A has "present" and "absent".
#*In this case kappahat = kappa- = 0 but kappa+ is undefined.
#*No tests are performed.
headers = ['Info']
table = []
table.append([
'Rater B has marked all tests as "present"; rater A has "present" and "absent".'
])
table.append(
['In this case kappahat = kappa- = 0 but kappa+ is undefined.'])
table.append(['No tests are performed.'])
return tabulate(table, headers=headers, tablefmt="grid")
#a=c=0
if Npp == 0 and Npa != 0 and Nap == 0 and Naa != 0:
#write
#*Rater B has marked all tests as "absent"; rater A has "present" and "absent".
#*In this case kappahat = kappa+ = 0 but kappa- is undefined.
#*No tests performed.
headers = ['Info']
table = []
table.append([
'Rater B has marked all tests as "absent"; rater A has "present" and "absent".'
])
table.append(
['In this case kappahat = kappa+ = 0 but kappa- is undefined.'])
table.append(['No tests performed.'])
return tabulate(table, headers=headers, tablefmt="grid")
#c=d=0
if Npp != 0 and Npa != 0 and Nap == 0 and Naa == 0:
#write
#*Rater A has marked all tests as "present"; rater B has "present" and "absent".
#*In this case kappahat = kappa+ = 0 but kappa- is undefined.
#*No tests are performed.
headers = ['Info']
table = []
table.append([
'Rater A has marked all tests as "present"; rater B has "present" and "absent".'
])
table.append(
['In this case kappahat = kappa+ = 0 but kappa- is undefined.'])
table.append(['No tests are performed.'])
return tabulate(table, headers=headers, tablefmt="grid")
#a=b=0
if Npp == 0 and Npa == 0 and Nap != 0 and Naa != 0:
#write
#*Rater A has marked all tests as "absent"; rater B has "present" and "absent".
#*In this case kappahat = kappa- = 0 but kappa+ is undefined.
#*No tests are performed.
headers = ['Info']
table = []
table.append([
'Rater A has marked all tests as "absent"; rater B has "present" and "absent".'
])
table.append(
['In this case kappahat = kappa- = 0 but kappa+ is undefined.'])
table.append(['No tests are performed.'])
return tabulate(table, headers=headers, tablefmt="grid")
#b=c=0
if Npa == 0 and Nap == 0 and Naa != 0 and Npp != 0:
#write
#*Perfect agreement (some rating pairs are "present", all others are "absent").
#*In this case kappahat = kappa+ = kappa- = 1.
#*No tests performed.
headers = ['Info']
table = []
table.append([
'Perfect agreement (some rating pairs are "present", all others are "absent").'
])
table.append(['In this case kappahat = kappa+ = kappa- = 1.'])
table.append(['No tests performed.'])
return tabulate(table, headers=headers, tablefmt="grid")
#test print
#print 'n = ',n
#print 'Npp = ',Npp
#rint 'Npa = ',Npa
#print 'Nap = ',Nap
#print 'Naa = ',Naa
#print 'a = ',a
#print 'b = ',b
#print 'c = ',c
#print 'd = ',d
#print 'p1 = ',p1
#print 'p2 = ',p2
#print 'q1 = ',q1
#print 'q2 = ',q2
#print 'po = ',po
#print 'pe = ',pe
#estmated Kappa value - k is used to shorten expressions later
kappahat = (po - pe) / (1. - pe)
k = kappahat
kappaplus = (a - p1 * p2) / (p1 - p1 * p2)
kappaminus = (d - q1 * q2) / (q1 - q1 * q2)
#a=d=0
if Npp == 0 and Naa == 0 and Nap != 0 and Npa != 0:
#write
#*Perfect disagreement (some rating pairs are "present/absent", all others are "absent/present").
#*If there are equal numbers of both then kappahat = kappa+ =kappa- = -1, otherwise
#*kappahat is between 0 and -1 and is straddled by kappa+ and kappa-.
#*No tests performed. For the record kappahat = {kappahat}, kappa+ = {kappaplus}, kappa- = {kappaminus}
headers = ['Info']
table = []
table.append([
'Perfect disagreement (some rating pairs are "present/absent", all others are "absent/present").'
])
table.append([
'If there are equal numbers of both then kappahat = kappa+ = kappa- = -1, otherwise'
])
table.append([
'kappahat is between 0 and -1 and is straddled by kappa+ and kappa-.'
])
table.append([
'No tests performed. For the record kappahat = ' +
str(kappahat)[:6] + ', kappa+ = ' + str(kappaplus)[:6] +
', kappa- = ' + str(kappaminus)[:6]
])
return tabulate(table, headers=headers, tablefmt="grid")
#test kappa value make sure between 0 and 1
if kappatest < 0 or kappatest >= 1:
#Write
#*Kappatest must be greater than or equal to zero and less than 1.
#*Use the back button to go back to the input page to correct.
headers = ['Info']
table = []
table.append([
'Kappatest must be greater than or equal to zero and less than 1.'
])
table.append(['Try to correct the input and try again'])
return tabulate(table, headers=headers, tablefmt="grid")
#Standard error for test of zero kappa (Fleiss)
denom = (1. - pe) * math.sqrt(n)
numer = math.sqrt(pe + pe**2 - p1 * p2 * (p1 + p2) - q1 * q2 * (q1 + q2))
se0 = numer / denom
#Standard error test of non zero kappa (Fleiss, eqs 12.15-13.18)
capA = a * (1. - (p1 + p2) * (1. - k))**2 + d * (1. - (q1 + q2) *
(1. - k))**2
capB = ((1. - k)**2) * (b * (p2 + q1)**2 + c * (p1 + q2)**2)
capC = (k - pe * (1. - k))**2
sek = (math.sqrt(capA + capB - capC)) / denom
#Standard error test of non zero Kappa (Bishop et al 1975 eq 11.4-4,5,6)
#theta3 = a * (p1 + p2) + d * (q1 + q2)
#theta4 = a * (p1 + p2)**2 + b * (p2 + q1)**2 + c * (p1 + q2)**2 + d * (
# q1 + q2)**2
#E = po * (1. - po)
#F = 2. * (1 - po) * (2. * po * pe - theta3) / (1. - pe)
#G = ((1. - po)**2) * (theta4 - 4. * pe**2) / (1. - pe)**2
# sekB gives same result as sek, not used
# sekB=math.sqrt((E+F+G))/denom
#print 'n = ',n
#print 'Npp = ',Npp
#print 'Npa = ',Npa
#print 'Nap = ',Nap
#print 'Naa = ',Naa
#print 'Kappahat = ',kappahat
#print 'Kappaplus = ',kappaplus
#print 'Kappaminus = ',kappaminus
#print 'se0 = ',sezero
#print 'sek = ',sek
#print 'z = ',z
#print 'p1 = ',p
#write out results - write out all lines below that start with #*, items in {} are variables to be written
#*RESULTS FOR 2x2 INTERRATER TABLE
#*
#*Rater A | Rater B |
#* | present absent |
#*--------|--------------------|
#*present | {Npp} {Npa} |
#*absent | {Nap} {Naa} |
#*--------|--------------------|
#*
#*kappahat = {kappa}, (kappa+ = {kappaplus}. kappa- = {kappaminus}
#*s.e.(0) = {se0}, s.e.(kappahat) = {sek}
#*
#*HYPOTHESIS TEST p-VALUES
#*One-sided test, H0 is kappa =<0
output = "Results for 2x2 Interrater table\n"
headers = ['Rater A', 'Rater B', None]
table = []
table.append([None, 'present', 'absent'])
table.append(['present', str(int(Npp)), str(int(Npa))])
table.append(['absent', str(int(Nap)), str(int(Naa))])
output += tabulate(table, headers=headers, tablefmt="grid")
output += "\n"
table = []
table.append([
'kappahat = ' + str(kappahat)[:6] + ', (kappa+ = ' +
str(kappaplus)[:6] + '. kappa- = ' + str(kappaminus)[:6] + ')'
])
table.append(
['s.e.(0) = ' + str(se0)[:6] + ', s.e.(kappahat) = ' + str(sek)[:6]])
table.append([''])
table.append(['Hypothesis test p-values'])
table.append(['One-sided test, H0 is kappa =<0'])
z = kappahat / se0
p = 1. - probn(z)
if p < 0.0001:
table.append(['p = Prob[>kappahat, given that kappa=0] < 0.0001'])
elif p > 0.9999:
table.append(['p = Prob[>kappahat, given that kappa=0] > 0.9999'])
else:
table.append(
['p = Prob[>kappahat, given that kappa=0] = ' + str(p)[:6]])
#*
#*One-sided test, H0 is kappa =< {kappatest}
table.append([''])
table.append(['One-sided test, H0 is kappa =< ' + str(kappatest)[:4]])
z = (kappahat - kappatest) / sek
p = 1 - probn(z)
if p < 0.0001:
table.append([
'p = Prob[>kappahat, given that kappa= ' + str(kappatest)[:6] +
'] < 0.0001'
])
elif p > 0.9999:
table.append([
'p = Prob[>kappahat, given that kappa= ' + str(kappatest)[:6] +
'] > 0.9999'
])
else:
table.append([
'p = Prob[>kappahat, given that kappa= ' + str(kappatest)[:6] +
'] = ' + str(p)[:6]
])
#*
#*Two-sided test, H0 is kappa={kappatest}
table.append([''])
table.append(['Two-sided test, H0 is kappa= ' + str(kappatest)[:6]])
z = abs(kappahat - kappatest) / sek
p = 2. * (1. - probn(z))
if p < 0.0001:
table.append([
'p = Prob[>|kappahat-kappa|, given that kappa= ' +
str(kappatest)[:6] + '] < 0.0001'
])
elif p > 0.9999:
table.append([
'p = Prob[>|kappahat-kappa|, given that kappa= ' +
str(kappatest)[:6] + '] > 0.9999'
])
else:
table.append([
'p = Prob[>|kappahat-kappa|, given that kappa= ' +
str(kappatest)[:6] + '] = ' + str(p)[:6]
])
output += tabulate(table, tablefmt="grid")
return output
def probn(z):
w = abs(z) / math.sqrt(2.)
y = 1. / (1. + 0.5 * w)
erfcc = y * math.exp(-w * w - 1.26551223 + y * (1.00002368 + y * (
0.37409196 + y * (0.09678418 + y *
(-0.18628806 + y *
(0.27886807 + y *
(-1.13520398 + y *
(1.48851587 + y *
(-0.82215223 + y * 0.17087277)))))))))
if z < 0.0:
erfcc = 2. - erfcc
probn = 1.0 - 0.5 * erfcc
return probn
def main(args): # pragma: no cover
parser = argparse.ArgumentParser()
parser.add_argument(
"--npp",
help="number of present/present ratings",
type=float,
required=True,
metavar=0.0)
parser.add_argument(
"--npa",
help="number of present/absent ratings",
type=float,
required=True,
metavar=0.0)
parser.add_argument(
"--nap",
help="number of absent/present ratings",
type=float,
required=True,
metavar=0.0)
parser.add_argument(
"--naa",
help="number of absent/absent ratings",
type=float,
required=True,
metavar=0.0)
parser.add_argument(
"--kappatest",
help="test value of kappa (must be >= 0 and < 1",
type=float,
required=True,
metavar=0.0)
args = parser.parse_args()
kappa = calculate_kappa(args.npp, args.npa, args.nap, args.naa,
args.kappatest)
print(kappa)
if __name__ == '__main__': # pragma: no cover
main(sys.argv[1:])