ProportionDiffSamplingDistribution.simulate() - Code Metrics - Inspection of "Implement the proportion diff and mean diff sampli..." - chen0040/pysie - Measure and Improve Code Quality continuously with Scrutinizer

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Push — master ( 712fe6...f1f19a )

by Xianshun

created 2017-05-31 01:42 UTC

ProportionDiffSamplingDistribution.simulate() A

↳ Parent: ProportionDiffSamplingDistribution

Complexity

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Total Lines

Duplication

Lines	0
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Importance

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Metric	Value
cc	2
dl	0
loc	9
rs	9.6666
c	0
b	0
f	0

import math
import random

from enum import Enum

from scipy.stats import norm, t


class DistributionFamily(Enum):
    normal = 1
    student_t = 2
    fisher = 3
    chi_square = 4
    simulation = 5


class MeanSamplingDistribution(object):
    sample_distribution = None
    point_estimate = None
    distribution_family = None
    df = None
    sample_sd = None
    sample_size = None

    def __init__(self, sample_distribution=None, sample_mean=None, sample_sd=None, sample_size=None):
        if sample_mean is not None:
            self.point_estimate = sample_mean

        if sample_sd is not None:
            self.sample_sd = sample_sd

        if sample_size is not None:
            self.sample_size = sample_size

        if sample_distribution is not None:
            self.sample_distribution = sample_distribution
            self.point_estimate = sample_distribution.mean
            self.sample_sd = sample_distribution.sd
            self.sample_size = sample_distribution.sample_size

        self.standard_error = MeanSamplingDistribution.calculate_standard_error(self.sample_sd, self.sample_size)

        self.df = self.sample_size - 1.0
        if self.sample_size < 30:
            self.distribution_family = DistributionFamily.student_t
        else:
            self.distribution_family = DistributionFamily.normal

    @staticmethod
    def calculate_standard_error(sample_sd, sample_size):
        return sample_sd / math.sqrt(sample_size)

    def confidence_interval(self, confidence_level):
        q = 1 - (1 - confidence_level) / 2
        if self.distribution_family == DistributionFamily.normal:
            z = norm.ppf(q)
            pf = z * self.standard_error
            return self.point_estimate - pf, self.point_estimate + pf
        else:
            t_df = t.ppf(q, self.df)
            pf = t_df * self.standard_error + self.point_estimate
            return self.point_estimate - pf, self.point_estimate + pf


class MeanDiffSamplingDistribution(object):
    grp1_sample_distribution = None
    grp2_sample_distribution = None
    grp1_point_estimate = None
    grp2_point_estimate = None
    grp1_sample_sd = None
    grp2_sample_sd = None
    grp1_sample_size = None
    grp2_sample_size = None
    distribution_family = None
    df = None
    point_estimate = None

    def __init__(self, grp1_sample_distribution=None, grp1_sample_mean=None, grp1_sample_sd=None, grp1_sample_size=None,
                 grp2_sample_distribution=None, grp2_sample_mean=None, grp2_sample_sd=None, grp2_sample_size=None):
        self.build_grp1(grp1_sample_distribution, grp1_sample_mean, grp1_sample_sd, grp1_sample_size)
        self.build_grp2(grp2_sample_distribution, grp2_sample_mean, grp2_sample_sd, grp2_sample_size)

        self.standard_error = self.calculate_standard_error()

        self.df = min(self.grp1_sample_size - 1.0, self.grp2_sample_size - 1.0)
        self.point_estimate = self.grp1_point_estimate - self.grp2_point_estimate

        if self.grp1_sample_size < 30 or self.grp2_sample_size < 30:
            self.distribution_family = DistributionFamily.student_t
        else:
            self.distribution_family = DistributionFamily.normal

    def build_grp1(self, grp1_sample_distribution=None, grp1_sample_mean=None, grp1_sample_sd=None, grp1_sample_size=None):
        if grp1_sample_mean is not None:
            self.grp1_point_estimate = grp1_sample_mean

        if grp1_sample_sd is not None:
            self.grp1_sample_sd = grp1_sample_sd

        if grp1_sample_size is not None:
            self.grp1_sample_size = grp1_sample_size

        if grp1_sample_distribution is not None:
            self.grp1_sample_distribution = grp1_sample_distribution
            self.grp1_point_estimate = grp1_sample_distribution.mean
            self.grp1_sample_sd = grp1_sample_distribution.sd
            self.grp1_sample_size = grp1_sample_distribution.sample_size
            
    def build_grp2(self, grp2_sample_distribution=None, grp2_sample_mean=None, grp2_sample_sd=None, grp2_sample_size=None):
        if grp2_sample_mean is not None:
            self.grp2_point_estimate = grp2_sample_mean

        if grp2_sample_sd is not None:
            self.grp2_sample_sd = grp2_sample_sd

        if grp2_sample_size is not None:
            self.grp2_sample_size = grp2_sample_size

        if grp2_sample_distribution is not None:
            self.grp2_sample_distribution = grp2_sample_distribution
            self.grp2_point_estimate = grp2_sample_distribution.mean
            self.grp2_sample_sd = grp2_sample_distribution.sd
            self.grp2_sample_size = grp2_sample_distribution.sample_size

    def calculate_standard_error(self):
        return math.sqrt(self.grp1_sample_sd * self.grp1_sample_sd / self.grp1_sample_size + 
                         self.grp2_sample_sd * self.grp2_sample_sd / self.grp2_sample_size)

    def confidence_interval(self, confidence_level):
        q = 1 - (1 - confidence_level) / 2
        if self.distribution_family == DistributionFamily.normal:
            z = norm.ppf(q)
            pf = z * self.standard_error
            
            return self.point_estimate - pf, self.point_estimate + pf
        else:
            t_df = t.ppf(q, self.df)
            pf = t_df * self.standard_error + self.point_estimate
            return self.point_estimate - pf, self.point_estimate + pf


class ProportionSamplingDistribution(object):
    sample_distribution = None
    point_estimate = None
    distribution_family = None
    sample_size = None
    categorical_value = None
    standard_error = None
    simulated_proportions = None

    def __init__(self, sample_distribution=None, categorical_value=None, sample_proportion=None, sample_size=None):
        if sample_proportion is not None:
            self.point_estimate = sample_proportion

        if sample_size is not None:
            self.sample_size = sample_size

        if categorical_value is not None:
            self.categorical_value = categorical_value

        if sample_distribution is not None:
            self.build(sample_distribution)

        if self.sample_size * self.point_estimate < 10 or self.sample_size * (1 - self.point_estimate) < 10:
            self.distribution_family = DistributionFamily.simulation
            self.simulate()
        else:
            self.distribution_family = DistributionFamily.normal
            self.standard_error = math.sqrt(self.point_estimate * (1 - self.point_estimate) / self.sample_size)

    def build(self, sample_distribution):
        self.sample_distribution = sample_distribution
        self.point_estimate = sample_distribution.proportion
        self.categorical_value = sample_distribution.categorical_value
        self.sample_size = sample_distribution.sample_size

    def simulate(self):
        self.simulated_proportions = [0] * 1000
        for i in range(1000):
            count = 0
            for trials in range(self.sample_size):
                if random.random() <= self.point_estimate:
                    count += 1
            self.simulated_proportions[i] = float(count) / self.sample_size
        self.simulated_proportions = sorted(self.simulated_proportions)

    def confidence_interval(self, confidence_level):

        q = 1 - (1 - confidence_level) / 2
        if self.distribution_family == DistributionFamily.normal:
            z = norm.ppf(q)
            pf = z * self.standard_error
            return self.point_estimate - pf, self.point_estimate + pf
        else:
            threshold1 = int(1000 * (1 - confidence_level) / 2)
            threshold2 = int(1000 * q)
            return self.simulated_proportions[threshold1], self.simulated_proportions[threshold2]
        
        
class ProportionDiffSamplingDistribution(object):
    grp1_sample_distribution = None
    grp2_sample_distribution = None
    grp1_point_estimate = None
    grp2_point_estimate = None
    distribution_family = None
    grp1_sample_size = None
    grp2_sample_size = None
    categorical_value = None
    standard_error = None
    grp1_simulated_proportions = None
    grp2_simulated_proportions = None
    diff_simulated_proportions = None
    point_estimate = None

    def __init__(self, categorical_value=None,
                 grp1_sample_distribution=None, grp1_sample_proportion=None, grp1_sample_size=None,
                 grp2_sample_distribution=None, grp2_sample_proportion=None, grp2_sample_size=None):
        if categorical_value is not None:
            self.categorical_value = categorical_value
            
        self.build_grp1(grp1_sample_distribution, grp1_sample_proportion, grp1_sample_size)
        self.build_grp2(grp2_sample_distribution, grp2_sample_proportion, grp2_sample_size)

        if not self.is_clt_held():
            self.distribution_family = DistributionFamily.simulation
            self.simulate()
        else:
            self.distribution_family = DistributionFamily.normal
            self.standard_error = self.calculate_standard_error()

        self.point_estimate = self.grp1_point_estimate - self.grp2_point_estimate
            
    def calculate_standard_error(self):
        return math.sqrt(self.grp1_point_estimate * (1 - self.grp1_point_estimate) / self.grp2_sample_size +
                         self.grp2_point_estimate * (1 - self.grp2_point_estimate) / self.grp2_sample_size)

    def is_clt_held(self):
        if self.grp1_sample_size * self.grp1_point_estimate < 10:
            return False
        if self.grp1_sample_size * (1 - self.grp1_point_estimate) < 10:
            return False
        if self.grp2_sample_size * self.grp2_point_estimate < 10:
            return False
        if self.grp2_sample_size * (1 - self.grp2_point_estimate) < 10:
            return False
        return True

    def build_grp1(self, grp1_sample_distribution=None, grp1_sample_proportion=None, grp1_sample_size=None):
        if grp1_sample_proportion is not None:
            self.grp1_point_estimate = grp1_sample_proportion

        if grp1_sample_size is not None:
            self.grp1_sample_size = grp1_sample_size

        if grp1_sample_distribution is not None:
            self.grp1_sample_distribution = grp1_sample_distribution
            self.grp1_point_estimate = grp1_sample_distribution.proportion
            self.categorical_value = grp1_sample_distribution.categorical_value
            self.grp1_sample_size = grp1_sample_distribution.sample_size

    def build_grp2(self, grp2_sample_distribution=None, grp2_sample_proportion=None, grp2_sample_size=None):
        if grp2_sample_proportion is not None:
            self.grp2_point_estimate = grp2_sample_proportion

        if grp2_sample_size is not None:
            self.grp2_sample_size = grp2_sample_size

        if grp2_sample_distribution is not None:
            self.grp2_sample_distribution = grp2_sample_distribution
            self.grp2_point_estimate = grp2_sample_distribution.proportion
            self.categorical_value = grp2_sample_distribution.categorical_value
            self.grp2_sample_size = grp2_sample_distribution.sample_size
            
    def simulate(self):
        self.grp1_simulated_proportions = ProportionDiffSamplingDistribution.simulate_grp(self.grp1_point_estimate,
                                                                                          self.grp1_sample_size)
        self.grp2_simulated_proportions = ProportionDiffSamplingDistribution.simulate_grp(self.grp2_point_estimate,
                                                                                          self.grp2_sample_size)

        self.diff_simulated_proportions = [0] * 1000;
        for i in range(1000):
            self.diff_simulated_proportions[i] = self.grp1_simulated_proportions[i] - self.grp2_simulated_proportions[i]
        
    @staticmethod
    def simulate_grp(proportion, sample_size):
        simulated_proportions = [0] * 1000
        for iter in range(1000):
            count = 0
            for trials in range(sample_size):
                if random.random() <= proportion:
                    count += 1
            simulated_proportions[iter] = float(count) / sample_size

        return sorted(simulated_proportions)
    
    def confidence_interval(self, confidence_level):

        q = 1 - (1 - confidence_level) / 2
        if self.distribution_family == DistributionFamily.normal:
            z = norm.ppf(q)
            pf = z * self.standard_error
            return self.point_estimate - pf, self.point_estimate + pf
        else:
            threshold1 = int(1000 * (1 - confidence_level) / 2)
            threshold2 = int(1000 * q)
            return self.diff_simulated_proportions[threshold1], self.diff_simulated_proportions[threshold2]





1		import math
2		import random
3
4		from enum import Enum
5
6		from scipy.stats import norm, t
7
8
9		class DistributionFamily(Enum):
10		normal = 1
11		student_t = 2
12		fisher = 3
13		chi_square = 4
14		simulation = 5
15
16
17		class MeanSamplingDistribution(object):
18		sample_distribution = None
19		point_estimate = None
20		distribution_family = None
21		df = None
22		sample_sd = None
23		sample_size = None
24
25		def __init__(self, sample_distribution=None, sample_mean=None, sample_sd=None, sample_size=None):
26		if sample_mean is not None:
27		self.point_estimate = sample_mean
28
29		if sample_sd is not None:
30		self.sample_sd = sample_sd
31
32		if sample_size is not None:
33		self.sample_size = sample_size
34
35		if sample_distribution is not None:
36		self.sample_distribution = sample_distribution
37		self.point_estimate = sample_distribution.mean
38		self.sample_sd = sample_distribution.sd
39		self.sample_size = sample_distribution.sample_size
40
41		self.standard_error = MeanSamplingDistribution.calculate_standard_error(self.sample_sd, self.sample_size)
42
43		self.df = self.sample_size - 1.0
44		if self.sample_size < 30:
45		self.distribution_family = DistributionFamily.student_t
46		else:
47		self.distribution_family = DistributionFamily.normal
48
49		@staticmethod
50		def calculate_standard_error(sample_sd, sample_size):
51		return sample_sd / math.sqrt(sample_size)
52
53		def confidence_interval(self, confidence_level):
54		q = 1 - (1 - confidence_level) / 2
55		if self.distribution_family == DistributionFamily.normal:
56		z = norm.ppf(q)
57		pf = z * self.standard_error
58		return self.point_estimate - pf, self.point_estimate + pf
59		else:
60		t_df = t.ppf(q, self.df)
61		pf = t_df * self.standard_error + self.point_estimate
62		return self.point_estimate - pf, self.point_estimate + pf
63
64
65		class MeanDiffSamplingDistribution(object):
66		grp1_sample_distribution = None
67		grp2_sample_distribution = None
68		grp1_point_estimate = None
69		grp2_point_estimate = None
70		grp1_sample_sd = None
71		grp2_sample_sd = None
72		grp1_sample_size = None
73		grp2_sample_size = None
74		distribution_family = None
75		df = None
76		point_estimate = None
77
78		def __init__(self, grp1_sample_distribution=None, grp1_sample_mean=None, grp1_sample_sd=None, grp1_sample_size=None,
79		grp2_sample_distribution=None, grp2_sample_mean=None, grp2_sample_sd=None, grp2_sample_size=None):
80		self.build_grp1(grp1_sample_distribution, grp1_sample_mean, grp1_sample_sd, grp1_sample_size)
81		self.build_grp2(grp2_sample_distribution, grp2_sample_mean, grp2_sample_sd, grp2_sample_size)
82
83		self.standard_error = self.calculate_standard_error()
84
85		self.df = min(self.grp1_sample_size - 1.0, self.grp2_sample_size - 1.0)
86		self.point_estimate = self.grp1_point_estimate - self.grp2_point_estimate
87
88		if self.grp1_sample_size < 30 or self.grp2_sample_size < 30:
89		self.distribution_family = DistributionFamily.student_t
90		else:
91		self.distribution_family = DistributionFamily.normal
92
93		def build_grp1(self, grp1_sample_distribution=None, grp1_sample_mean=None, grp1_sample_sd=None, grp1_sample_size=None):
94		if grp1_sample_mean is not None:
95		self.grp1_point_estimate = grp1_sample_mean
96
97		if grp1_sample_sd is not None:
98		self.grp1_sample_sd = grp1_sample_sd
99
100		if grp1_sample_size is not None:
101		self.grp1_sample_size = grp1_sample_size
102
103		if grp1_sample_distribution is not None:
104		self.grp1_sample_distribution = grp1_sample_distribution
105		self.grp1_point_estimate = grp1_sample_distribution.mean
106		self.grp1_sample_sd = grp1_sample_distribution.sd
107		self.grp1_sample_size = grp1_sample_distribution.sample_size
108
109		def build_grp2(self, grp2_sample_distribution=None, grp2_sample_mean=None, grp2_sample_sd=None, grp2_sample_size=None):
110		if grp2_sample_mean is not None:
111		self.grp2_point_estimate = grp2_sample_mean
112
113		if grp2_sample_sd is not None:
114		self.grp2_sample_sd = grp2_sample_sd
115
116		if grp2_sample_size is not None:
117		self.grp2_sample_size = grp2_sample_size
118
119		if grp2_sample_distribution is not None:
120		self.grp2_sample_distribution = grp2_sample_distribution
121		self.grp2_point_estimate = grp2_sample_distribution.mean
122		self.grp2_sample_sd = grp2_sample_distribution.sd
123		self.grp2_sample_size = grp2_sample_distribution.sample_size
124
125		def calculate_standard_error(self):
126		return math.sqrt(self.grp1_sample_sd * self.grp1_sample_sd / self.grp1_sample_size +
127		self.grp2_sample_sd * self.grp2_sample_sd / self.grp2_sample_size)
128
129		def confidence_interval(self, confidence_level):
130		q = 1 - (1 - confidence_level) / 2
131		if self.distribution_family == DistributionFamily.normal:
132		z = norm.ppf(q)
133		pf = z * self.standard_error
134
135		return self.point_estimate - pf, self.point_estimate + pf
136		else:
137		t_df = t.ppf(q, self.df)
138		pf = t_df * self.standard_error + self.point_estimate
139		return self.point_estimate - pf, self.point_estimate + pf
140
141
142		class ProportionSamplingDistribution(object):
143		sample_distribution = None
144		point_estimate = None
145		distribution_family = None
146		sample_size = None
147		categorical_value = None
148		standard_error = None
149		simulated_proportions = None
150
151		def __init__(self, sample_distribution=None, categorical_value=None, sample_proportion=None, sample_size=None):
152		if sample_proportion is not None:
153		self.point_estimate = sample_proportion
154
155		if sample_size is not None:
156		self.sample_size = sample_size
157
158		if categorical_value is not None:
159		self.categorical_value = categorical_value
160
161		if sample_distribution is not None:
162		self.build(sample_distribution)
163
164		if self.sample_size * self.point_estimate < 10 or self.sample_size * (1 - self.point_estimate) < 10:
165		self.distribution_family = DistributionFamily.simulation
166		self.simulate()
167		else:
168		self.distribution_family = DistributionFamily.normal
169		self.standard_error = math.sqrt(self.point_estimate * (1 - self.point_estimate) / self.sample_size)
170
171		def build(self, sample_distribution):
172		self.sample_distribution = sample_distribution
173		self.point_estimate = sample_distribution.proportion
174		self.categorical_value = sample_distribution.categorical_value
175		self.sample_size = sample_distribution.sample_size
176
177		def simulate(self):
178		self.simulated_proportions = [0] * 1000
179		for i in range(1000):
180		count = 0
181		for trials in range(self.sample_size):
182		if random.random() <= self.point_estimate:
183		count += 1
184		self.simulated_proportions[i] = float(count) / self.sample_size
185		self.simulated_proportions = sorted(self.simulated_proportions)
186
187	View Code Duplication	def confidence_interval(self, confidence_level):
		0 ignored issues – show Duplication introduced 2017-05-31 01:43 UTC by Report Bug Copy Issue Report This code seems to be duplicated in your project. Loading history...
188		q = 1 - (1 - confidence_level) / 2
189		if self.distribution_family == DistributionFamily.normal:
190		z = norm.ppf(q)
191		pf = z * self.standard_error
192		return self.point_estimate - pf, self.point_estimate + pf
193		else:
194		threshold1 = int(1000 * (1 - confidence_level) / 2)
195		threshold2 = int(1000 * q)
196		return self.simulated_proportions[threshold1], self.simulated_proportions[threshold2]
197
198
199		class ProportionDiffSamplingDistribution(object):
200		grp1_sample_distribution = None
201		grp2_sample_distribution = None
202		grp1_point_estimate = None
203		grp2_point_estimate = None
204		distribution_family = None
205		grp1_sample_size = None
206		grp2_sample_size = None
207		categorical_value = None
208		standard_error = None
209		grp1_simulated_proportions = None
210		grp2_simulated_proportions = None
211		diff_simulated_proportions = None
212		point_estimate = None
213
214		def __init__(self, categorical_value=None,
215		grp1_sample_distribution=None, grp1_sample_proportion=None, grp1_sample_size=None,
216		grp2_sample_distribution=None, grp2_sample_proportion=None, grp2_sample_size=None):
217		if categorical_value is not None:
218		self.categorical_value = categorical_value
219
220		self.build_grp1(grp1_sample_distribution, grp1_sample_proportion, grp1_sample_size)
221		self.build_grp2(grp2_sample_distribution, grp2_sample_proportion, grp2_sample_size)
222
223		if not self.is_clt_held():
224		self.distribution_family = DistributionFamily.simulation
225		self.simulate()
226		else:
227		self.distribution_family = DistributionFamily.normal
228		self.standard_error = self.calculate_standard_error()
229
230		self.point_estimate = self.grp1_point_estimate - self.grp2_point_estimate
231
232		def calculate_standard_error(self):
233		return math.sqrt(self.grp1_point_estimate * (1 - self.grp1_point_estimate) / self.grp2_sample_size +
234		self.grp2_point_estimate * (1 - self.grp2_point_estimate) / self.grp2_sample_size)
235
236		def is_clt_held(self):
237		if self.grp1_sample_size * self.grp1_point_estimate < 10:
238		return False
239		if self.grp1_sample_size * (1 - self.grp1_point_estimate) < 10:
240		return False
241		if self.grp2_sample_size * self.grp2_point_estimate < 10:
242		return False
243		if self.grp2_sample_size * (1 - self.grp2_point_estimate) < 10:
244		return False
245		return True
246
247		def build_grp1(self, grp1_sample_distribution=None, grp1_sample_proportion=None, grp1_sample_size=None):
248		if grp1_sample_proportion is not None:
249		self.grp1_point_estimate = grp1_sample_proportion
250
251		if grp1_sample_size is not None:
252		self.grp1_sample_size = grp1_sample_size
253
254		if grp1_sample_distribution is not None:
255		self.grp1_sample_distribution = grp1_sample_distribution
256		self.grp1_point_estimate = grp1_sample_distribution.proportion
257		self.categorical_value = grp1_sample_distribution.categorical_value
258		self.grp1_sample_size = grp1_sample_distribution.sample_size
259
260		def build_grp2(self, grp2_sample_distribution=None, grp2_sample_proportion=None, grp2_sample_size=None):
261		if grp2_sample_proportion is not None:
262		self.grp2_point_estimate = grp2_sample_proportion
263
264		if grp2_sample_size is not None:
265		self.grp2_sample_size = grp2_sample_size
266
267		if grp2_sample_distribution is not None:
268		self.grp2_sample_distribution = grp2_sample_distribution
269		self.grp2_point_estimate = grp2_sample_distribution.proportion
270		self.categorical_value = grp2_sample_distribution.categorical_value
271		self.grp2_sample_size = grp2_sample_distribution.sample_size
272
273		def simulate(self):
274		self.grp1_simulated_proportions = ProportionDiffSamplingDistribution.simulate_grp(self.grp1_point_estimate,
275		self.grp1_sample_size)
276		self.grp2_simulated_proportions = ProportionDiffSamplingDistribution.simulate_grp(self.grp2_point_estimate,
277		self.grp2_sample_size)
278
279		self.diff_simulated_proportions = [0] * 1000;
280		for i in range(1000):
281		self.diff_simulated_proportions[i] = self.grp1_simulated_proportions[i] - self.grp2_simulated_proportions[i]
282
283		@staticmethod
284		def simulate_grp(proportion, sample_size):
285		simulated_proportions = [0] * 1000
286		for iter in range(1000):
287		count = 0
288		for trials in range(sample_size):
289		if random.random() <= proportion:
290		count += 1
291		simulated_proportions[iter] = float(count) / sample_size
292
293		return sorted(simulated_proportions)
294
295	View Code Duplication	def confidence_interval(self, confidence_level):
		0 ignored issues – show Duplication introduced 2017-05-31 01:43 UTC by Report Bug Copy Issue Report This code seems to be duplicated in your project. Loading history...
296		q = 1 - (1 - confidence_level) / 2
297		if self.distribution_family == DistributionFamily.normal:
298		z = norm.ppf(q)
299		pf = z * self.standard_error
300		return self.point_estimate - pf, self.point_estimate + pf
301		else:
302		threshold1 = int(1000 * (1 - confidence_level) / 2)
303		threshold2 = int(1000 * q)
304		return self.diff_simulated_proportions[threshold1], self.diff_simulated_proportions[threshold2]
305
306
307
308

chen0040 / pysie

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ProportionDiffSamplingDistribution.simulate() A

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