prop.test

test.r

# hand calculation での注意：二項分布の同等性検定は2×2の分割表によるχ^2検定に等しいのでそちらの計算方法を採用。
# Q1.はサンプル数が少ないのでイェツの補正を行っている。

######################################
# Q1.
#     Head   Tail     S
# A      4      6    10
# B      6      4    10
# S     10     10    20
#
# hand calculation
# T = (20* (|4*4-6*6| - 20/2)^2 ) / (10*10*10*10) = 0.2 < χ^2(1, 0.05) = 3.84 
# ∴ 「差があるとは言えない」

> prop.test(c(4,6),c(10,10))

	2-sample test for equality of proportions with continuity correction

data:  c(4, 6) out of c(10, 10) 
X-squared = 0.2, df = 1, p-value = 0.6547
alternative hypothesis: two.sided 
95 percent confidence interval:
 -0.7294066  0.3294066 
sample estimates:
prop 1 prop 2 
   0.4    0.6 

######################################
# Q2.
#      Head   Tail      S
# A      16     24     40
# B      24     16     40
# S      40     40     80
# 
# hand calculation
# T = (80*(16*16-24*24)^2 ) / (40*40*40*40) =  3.2 < χ^2(1, 0.05) = 3.84
# ∴ 「差があるとは言えない」

> prop.test(c(16,24),c(40,40))

	2-sample test for equality of proportions with continuity correction

data:  c(16, 24) out of c(40, 40) 
X-squared = 2.45, df = 1, p-value = 0.1175
alternative hypothesis: two.sided 
95 percent confidence interval:
 -0.4397033  0.0397033 
sample estimates:
prop 1 prop 2 
   0.4    0.6 

######################################
# Q3.
#     Head  Tail     S
# A     40    60   100
# B     60    40   100
# S    100   100   200
#
# hand calculation
# T = (200*(40*40-60*60)^2 ) / (100*100*100*100) = 8 > χ^2(1, 0.05) = 3.84
# ∴ 「有意な差があると言える」

> prop.test(c(40,60),c(100,100))

	2-sample test for equality of proportions with continuity correction

data:  c(40, 60) out of c(100, 100) 
X-squared = 7.22, df = 1, p-value = 0.00721
alternative hypothesis: two.sided 
95 percent confidence interval:
 -0.34579029 -0.05420971 
sample estimates:
prop 1 prop 2 
   0.4    0.6 

######################################
# Q4.
#    Head   Tail       S
# A   400     600   1000
# B   600     400   1000
# S  1000    1000   2000
#
# hand calculation
# T = (2000*(400*400-600*600)^2 ) / (1000*1000*1000*1000) = 80 > χ^2(1, 0.05) = 3.84
# ∴ 「有意な差があると言える」

> prop.test(c(400,600),c(1000,1000))

	2-sample test for equality of proportions with continuity correction

data:  c(400, 600) out of c(1000, 1000) 
X-squared = 79.202, df = 1, p-value < 2.2e-16
alternative hypothesis: two.sided 
95 percent confidence interval:
 -0.2439407 -0.1560593 
sample estimates:
prop 1 prop 2 
   0.4    0.6 

######################################
# Q5.
#     Head   Tail      S
# A    480    520   1000
# B    520    480   1000
# S   1000   1000   2000
# 
# hand calculation
# T = (2000*(480*480-520*520)^2 ) / (1000*1000*1000*1000) = 3.2 < χ^2(1, 0.05) = 3.84
# ∴ 「差があるとは言えない」

> prop.test(c(480,520),c(1000,1000))

	2-sample test for equality of proportions with continuity correction

data:  c(480, 520) out of c(1000, 1000) 
X-squared = 3.042, df = 1, p-value = 0.08114
alternative hypothesis: two.sided 
95 percent confidence interval:
 -0.084791052  0.004791052 
sample estimates:
prop 1 prop 2 
  0.48   0.52 

######################################
# Q6.
#     Head   Tail      S
# A    470    530   1000
# B    570    430   1000
# S   1000   1000   2000
# 
# hand calculation
# T = (2000*(470*470-530*530)^2 ) / (1000*1000*1000*1000) = 7.2 > χ^2(1, 0.05) = 3.84
# ∴ 「有意な差があると言える」

> prop.test(c(470,530),c(1000,1000))

	2-sample test for equality of proportions with continuity correction

data:  c(470, 530) out of c(1000, 1000) 
X-squared = 6.962, df = 1, p-value = 0.008326
alternative hypothesis: two.sided 
95 percent confidence interval:
 -0.10474717 -0.01525283 
sample estimates:
prop 1 prop 2 
  0.47   0.53 

######################################
# Q7.
#   Head   Tail     S
# A    8     12    20
# B   48     32    80
# S   56     44   100
#
# hand calculation
# T = (100*(8*32-12*48)^2 ) / (20*80*56*44) = 2.60 < χ^2(1, 0.05) = 3.84
# ∴ 「差があるとは言えない」

> prop.test(c(8,48),c(20,80))

	2-sample test for equality of proportions with continuity correction

data:  c(8, 48) out of c(20, 80) 
X-squared = 1.8491, df = 1, p-value = 0.1739
alternative hypothesis: two.sided 
95 percent confidence interval:
 -0.47129558  0.07129558 
sample estimates:
prop 1 prop 2 
   0.4    0.6 

######################################
# Q8.
#             job non-job        S
# last     95,100   4,900  100,000
# this     95,000   5,000  100,000
#    S    190,100   9,900  200,000
#
# hand calculation
# T = (200000*(95100*5000-95000*4900)^2 ) / (100000*100000*191000*9900) = 1.06 < χ^2(1, 0.05) = 3.84
# ∴ 「差があるとは言えない」

> prop.test(c(4900,5000),c(100000,100000))

	2-sample test for equality of proportions with continuity correction

data:  c(4900, 5000) out of c(1e+05, 1e+05) 
X-squared = 1.0416, df = 1, p-value = 0.3075
alternative hypothesis: two.sided 
95 percent confidence interval:
 -0.002911256  0.000911256 
sample estimates:
prop 1 prop 2 
 0.049  0.050 

######################################
# Q9. 
# (say = "自分ではっきり言う")
#      say   not     S
#  5M   53   247   300
# 20M   48   152   200
#   S  101   399   500
#
# hand calculation
# T = (500*(53*152-48*247)^2 ) / (300*200*101*399) = 2.99 < χ^2(1, 0.05) = 3.84
# ∴ 「差があるとは言えない」

> prop.test(c(53,48),c(300,200))

	2-sample test for equality of proportions with continuity correction

data:  c(53, 48) out of c(300, 200) 
X-squared = 2.606, df = 1, p-value = 0.1065
alternative hypothesis: two.sided 
95 percent confidence interval:
 -0.14075264  0.01408597 
sample estimates:
   prop 1    prop 2 
0.1766667 0.2400000