-
Notifications
You must be signed in to change notification settings - Fork 0
/
nonParametric.py
244 lines (163 loc) · 6.11 KB
/
nonParametric.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
import numpy as npy
import pandas as pd
import scipy.stats as spy
import statsmodels.stats as sm
from matplotlib import pyplot as plt
# SIGN TEST IN PYTHON ( 1 sample)
data = npy.array([0.78,0.51,3.79,0.23,0.77,0.98,0.96,0.89])
null = 1.0
#shapiro wilk test in python
print(spy.shapiro(data))
# tests for normality
# TEST STATISTIC = # of measurements less or greater (depending the right or left tailed)
# ^^^^^^ for two-tailed, it's whichever has more measurements on left or right , the biggest of the 2
print(spy.binomtest(k=8-7,n=8, alternative='less')) # k = # of measurements that dont fit the alternative
# k = # of successes (opposite of the alternative)
# n = sample size
#gives test statistic n p value
# FTR
#---------------------
'''
INDEPENDENT SAMPLES WILCOXON TEST
D = probability distribution
HYPOTHESES:
D1= D2 (D1 is identical to D2)
D1 ><!= D2 (D1 is shifted left/right/from D2)
TEST STATISTIC
w = sum of ranks - mean of the rank
'''
aug18, aug19= npy.array([87,88,91,92,92,93,93,95]), npy.array([88,89,90,92,93,94,95,96,97])
print(spy.shapiro(aug18))
print(spy.shapiro(aug19))
print(spy.ranksums(aug18, aug19, alternative='two-sided'))
S13,S17 = npy.array([38,34,25,38,62,19,39,23,17,52]), npy.array([61,38,51,63,31,73,31,45,49,37])
print(spy.shapiro(S13), spy.shapiro(S17), sep='\n')
print(spy.ranksums(S13,S17,alternative='less'))
'''
-------------------
PAIRED WILCOXON TEST
hypotheses:
H0: D1-D2 or D1 is identical to D2
Ha: D1<>!=D2 is shifted to the left/right/from D2
test statistic : sum of the ranks or n(n+1)/2
TS for 2 tail : sum of ranks - mean of rank
'''
# ex 1, gives small sample size warning
chimps=npy.array([[23,22,21,23,19,19,19],[21,22,23,21,18,16,19]])
print(spy.shapiro(chimps[0]), spy.shapiro(chimps[1]), sep='\n')
#print(spy.wilcoxon(chimps[0]-chimps[1], alternative='greater', zero_method='????'))
'''
wtf ??
additive = npy.array([[36.4,36.4,36.6,36.6,36.8,36.9,37 ,37.1,37.2,37.2,36.7,37.5,37.6,37.8,37.9,37.9,38.1,38.4,40.2,40.5,40.9,35 ,32.7,33.6,34.2,35.1,35.2,35.3,35.5,35.9,36 ,36.1,37.2],[36.7,36.9,37 ,37.5,38 ,38.1,38.4,38.7,38.8,38.9,36.3,38.9,39 ,39.1,39.4,39.4,39.5,39.8,40 ,40 ,40.1,36.3,32.8,34.2,34.7,34.9,34.9,35.3,35.9,36.4,36.6,36.6,38.3]])
print(spy.shapiro(additive[0]), spy.shapiro(additive[1]), sep='\n')
print(spy.wilcoxon(additive[0]-additive[1], alternative='greater'))
'''
associate = npy.array([[21 ,22 ,21 ,19 ,18 ,25 ,16 ,18 ,21 ,24 ,21],[14, 21, 24, 16, 18 ,20 ,15 ,20, 17, 16, 18]])
print(spy.wilcoxon(associate[0]-associate[1], alternative = 'greater'))
'''
--------------------------------------
NONPARAMETRIC ANOVA TEST
COMPLETELY RANDOMIZED DESIGN
aka krustal wallis h -test
H0: the k probabiltiy distributions are identical.
Ha: at least 2 of the k probability distributions differ in location
assumptions:
- k samples are random and independent
- n>= 5 for each sample
- continuous data (can be broken sometimes)
'''
#ex
pties=npy.array([[149,139,139,49,59.0],[98,35,35,37,29.0],[104.0,99,99,29.97,142]])
print(spy.kruskal(*pties))
stay = [[1,3,4,6,7,7,7,9,9,13],[1,4,4,5,5,5,6,7,8,10],[1,1,5,5,5,7,8,8],[2,3,3,4,5,5,6,6,6]]
print(spy.kruskal(*stay, nan_policy='omit'))
#MAY NOT GIVE THE EXACT P VALUE, BE CAREFUL
'''
NONPARAMETRIC ANOVA TEST
RANDOMIZED BLOCK DESIGN
FRIEDSMAN SQUARE TEST
reduces variability as compared to completely randomized
df = k+1
^^^^^ df is +1 instead of -1
CONDITIONS:
treatments randomly assigned to experimental units within the blocks
measurements ranked within blocks
continuous data (to prevent ties)
HYPOTHESES:
H0: probability distributions for the treatments are identical.
Ha: At least 2 of the probability distributions differ in location.
CHI SQUARE DISTRIBUTION X^2
if Fr (test statistic) > X^2 reject null
'''
#INPUT THE TREATMENTS ONLY
rats = pd.DataFrame({1:[6,9,6,5,7,5,6,6],2:[5,8,9,8,8,7,7,5],3:[3,4,3,6,9,6,5,7]})
#treatments
print(spy.friedmanchisquare(list(rats[1]),list(rats[2]),list(rats[3])))
print(spy.levene(rats[1], rats[1],rats[2]))
month = npy.array([[12,16,18,8],[15,17,16,12],[18,15,22,10],[20,12,19,16]])
print(spy.friedmanchisquare(*month))
heartRate= npy.array([[124,100,103,94,125,103,98,119],[124,98,98,91,123,98,82,87],[109,98,100,98,106,100,99,106],[107,99,106,95,110,103,105,111]])
print(spy.friedmanchisquare(*heartRate))
#sample boxplots (for dataframes)
#rats.boxplot()
#plt.show()
'''
BOOTSTRAPPING:
takes small sample of data and simulate the sampling distribution
that should be gotten from the entire population
for loops !!!!!!!!!!!!!
a lot of samples
( usually 8 to 10000 )
repeat sample means a few thousand times
find a mean of all the sample means
final standard error = sd of all means
^^^ DO MORE RESEARCH ON THIS
'''
'''
---------------------------------------------------
CHAPTER 13 NONPARAMETRIC CATEGORICAL TESTING
'''
'''
---------------
MULTINOMIAL EXPERIMENT
properties:
n identical trials
k possible outcomes to each trial (usually classes, categories, or cells)
probabilities always equal 1
trials are independent
basically binomial distribution but has mor ethan 2 categories
'''
#EX LEVEL OF EDUCATION BY EACH CANADIAN ACTORS
#categories: some hs, completed hs, some college, undergrad degree, and grad degree
# ^ 5 categories
# 1 qualitative variable (# of actors)
obs = [30,25,20,5,6,4]
#print(spy.chisquare(obs))
#-------------------
'''
CHI SQUARE CONTINGENCY TABLE
conditions:
1: samples are randomly sampled
2: n>= 5 for every sample
hypotheses:
H0: 2 classifications are independent
Ha: 2 classifications are dependent
2 qualitative variables
'''
data = npy.array([[39,25],[54,70]])
def sum(array2d):
try:
return sum([sum(x) for x in zip(*array2d)])
except:
return "not 2d array"
print("SUM OF A 2D ARRAY IS:",sum(data), sep='\n')
print(spy.chi2_contingency(data))
print(spy.fisher_exact(data))
extraci = npy.array([[9,17,7],[30,25,12]])
# GOES BY ROW COLUMN
print(spy.chi2_contingency(extraci))
#is there an association between categorical var a and b?
id = npy.array([[95,41],[50,114]])
#print(spy.chi2_contingency(id, correction = True))
#SIMULATED P VALUE
print("fijsiofjhiodjhiudfhgufiughduk")