Files
copycat/copycat/statistics.py

129 lines
4.0 KiB
Python

from collections import defaultdict
from pprint import pprint
from math import log
# comparison values for n degrees freedom
# These values are useable for both the chi^2 and G tests
_ptable = {
1:3.841,
2:5.991,
3:7.815,
4:9.488,
5:11.071,
6:12.592,
7:14.067,
8:15.507,
9:16.919,
10:18.307,
11:19.7,
12:21,
13:22.4,
14:23.7,
15:25,
16:26.3
}
_get_count = lambda k, d : d[k]['count'] if k in d else 0
def g_value(actual, expected):
# G = 2 * sum(Oi * ln(Oi/Ei))
answerKeys = set(list(actual.keys()) + list(expected.keys()))
degreesFreedom = len(answerKeys)
G = 0
for k in answerKeys:
E = _get_count(k, expected)
O = _get_count(k, actual)
if E == 0:
print(' Warning! Expected 0 counts of {}, but got {}'.format(k, O))
elif O == 0:
print(' Warning! O = {}'.format(O))
else:
G += O * log(O/E)
G *= 2
return degreesFreedom, G
def chi_value(actual, expected):
answerKeys = set(list(actual.keys()) + list(expected.keys()))
degreesFreedom = len(answerKeys)
chiSquared = 0
for k in answerKeys:
E = _get_count(k, expected)
O = _get_count(k, actual)
if E == 0:
print(' Warning! Expected 0 counts of {}, but got {}'.format(k, O))
else:
chiSquared += (O - E) ** 2 / E
return degreesFreedom, chiSquared
def probability_difference(actual, expected):
actualC = 0
expectedC = 0
for k in set(list(actual.keys()) + list(expected.keys())):
expectedC += _get_count(k, expected)
actualC += _get_count(k, actual)
p = 0
Et = 0
Ot = 0
for k in set(list(actual.keys()) + list(expected.keys())):
E = _get_count(k, expected)
O = _get_count(k, actual)
Ep = E / expectedC
Op = O / actualC
p += abs(Ep - Op)
p /= 2 # P is between 0 and 2 -> P is between 0 and 1
return p
def dist_test(actual, expected, calculation):
df, p = calculation(actual, expected)
if df not in _ptable:
raise Exception('{} degrees of freedom does not have a corresponding chi squared value.' + \
' Please look up the value and add it to the table in copycat/statistics.py'.format(df))
return (p < _ptable[df])
def cross_formula_table(actualDict, expectedDict, calculation, probs=False):
data = dict()
for ka, actual in actualDict.items():
for ke, expected in expectedDict.items():
if probs:
data[(ka, ke)] = probability_difference(actual, expected)
else:
data[(ka, ke)] = dist_test(actual, expected, calculation)
return data
def cross_table(problemSets, calculation=g_value, probs=False):
table = defaultdict(dict)
for i, (a, problemSetA) in enumerate(problemSets):
for b, problemSetB in problemSets[i + 1:]:
for problemA in problemSetA:
for problemB in problemSetB:
if (problemA.initial == problemB.initial and
problemA.modified == problemB.modified and
problemA.target == problemB.target):
answersA = problemA.distributions
answersB = problemB.distributions
table[(problemA.initial,
problemA.modified,
problemA.target)][(a, b)] = (
cross_formula_table(
answersA, answersB, calculation, probs))
return table
def iso_chi_squared(actualDict, expectedDict):
for key in expectedDict.keys():
assert key in actualDict, 'The key {} was not tested'.format(key)
actual = actualDict[key]
expected = expectedDict[key]
if not dist_test(actual, expected, g_value):
raise Exception('Value of G higher than expected')