richard — Mar 12, 2014, 10:48 AM
dataf <- read.csv("http://www.math.leidenuniv.nl/~gill/fred3.csv")
attach(dataf)
names(dataf)
[1] "Run" "A1" "A2" "B1" "B2" "Sa" "Tb"
head(dataf)
Run A1 A2 B1 B2 Sa Tb
1 1 -1 1 -1 -1 2 2
2 2 1 -1 1 -1 1 1
3 3 -1 1 1 -1 2 2
4 4 -1 -1 1 -1 2 1
5 5 -1 -1 -1 1 2 2
6 6 1 1 1 -1 2 1
tail(dataf)
Run A1 A2 B1 B2 Sa Tb
95 95 -1 -1 -1 -1 1 1
96 96 1 -1 -1 1 1 2
97 97 1 -1 -1 1 1 2
98 98 -1 -1 1 -1 1 2
99 99 -1 1 -1 -1 2 2
100 100 1 -1 1 -1 1 1
nrow(dataf)
[1] 100
corr11 <- mean((A1*B1)[Sa == 1 & Tb == 1])
corr12 <- mean((A1*B2)[Sa == 1 & Tb == 2])
corr21 <- mean((A2*B1)[Sa == 2 & Tb == 1])
corr22 <- mean((A2*B2)[Sa == 2 & Tb == 2])
corr11
[1] 0.7143
corr12
[1] 0.7576
corr21
[1] 0.6471
corr22
[1] -0.7273
corr11 + corr12 + corr21 - corr22
[1] 2.846
set.seed(123456)
for (i in 1 : 100) {
cat(paste("\nExperiment ", i, "\n"))
Snew <- sample(c(1, 2), 100, replace = TRUE)
Tnew <- sample(c(1, 2), 100, replace = TRUE)
corr11 <- mean((A1*B1)[Snew == 1 & Tnew == 1])
corr12 <- mean((A1*B2)[Snew == 1 & Tnew == 2])
corr21 <- mean((A2*B1)[Snew == 2 & Tnew == 1])
corr22 <- mean((A2*B2)[Snew == 2 & Tnew == 2])
cat(paste("corr11 = ", round(corr11, 4), "\n"))
cat(paste("corr12 = ", round(corr12, 4), "\n"))
cat(paste("corr21 = ", round(corr21, 4), "\n"))
cat(paste("corr22 = ", round(corr22, 4), "\n"))
cat(paste("CHSH is ", round(corr11 + corr12 + corr21 - corr22, 4), "\n"))
}
Experiment 1
corr11 = 0.0435
corr12 = 0.2593
corr21 = 0.28
corr22 = 0.2
CHSH is 0.3827
Experiment 2
corr11 = 0.1429
corr12 = 0.2174
corr21 = 0.0769
corr22 = -0.2174
CHSH is 0.6546
Experiment 3
corr11 = 0.4167
corr12 = 0.4815
corr21 = 0.1111
corr22 = 0.0323
CHSH is 0.977
Experiment 4
corr11 = 0.1818
corr12 = 0.2857
corr21 = 0.1852
corr22 = -0.1304
CHSH is 0.7832
Experiment 5
corr11 = 0.2857
corr12 = 0.3636
corr21 = 0
corr22 = -0.1429
CHSH is 0.7922
Experiment 6
corr11 = 0.44
corr12 = 0.4444
corr21 = 0.0833
corr22 = -0.1515
CHSH is 1.1193
Experiment 7
corr11 = 0.2
corr12 = 0.1111
corr21 = 0
corr22 = -0.0625
CHSH is 0.3736
Experiment 8
corr11 = 0.2174
corr12 = 0.5
corr21 = 0.0345
corr22 = -0.2143
CHSH is 0.9662
Experiment 9
corr11 = 0.3103
corr12 = 0.25
corr21 = 0.0435
corr22 = -0.25
CHSH is 0.8538
Experiment 10
corr11 = 0
corr12 = 0.4194
corr21 = 0.04
corr22 = -0.0909
CHSH is 0.5503
Experiment 11
corr11 = 0.1765
corr12 = 0.2
corr21 = 0.1818
corr22 = -0.0345
CHSH is 0.5928
Experiment 12
corr11 = 0.2632
corr12 = 0.3333
corr21 = 0.3
corr22 = -0.1429
CHSH is 1.0393
Experiment 13
corr11 = 0.1111
corr12 = 0.2857
corr21 = 0.1429
corr22 = -0.2941
CHSH is 0.8338
Experiment 14
corr11 = 0.4783
corr12 = 0.68
corr21 = 0.1538
corr22 = -0.1538
CHSH is 1.466
Experiment 15
corr11 = 0.037
corr12 = 0.1429
corr21 = 0.0714
corr22 = -0.0588
CHSH is 0.3101
Experiment 16
corr11 = 0.4545
corr12 = 0.2143
corr21 = -0.0476
corr22 = -0.2414
CHSH is 0.8626
Experiment 17
corr11 = 0.2667
corr12 = 0.5455
corr21 = 0.44
corr22 = 0.0435
CHSH is 1.2086
Experiment 18
corr11 = 0.3333
corr12 = 0.3913
corr21 = 0
corr22 = -0.037
CHSH is 0.7617
Experiment 19
corr11 = 0.3333
corr12 = 0.36
corr21 = 0.0476
corr22 = -0.0833
CHSH is 0.8243
Experiment 20
corr11 = 0.1538
corr12 = 0.2593
corr21 = -0.1
corr22 = -0.2593
CHSH is 0.5724
Experiment 21
corr11 = 0.2
corr12 = 0.25
corr21 = 0.12
corr22 = -0.2258
CHSH is 0.7958
Experiment 22
corr11 = 0.4
corr12 = 0.2727
corr21 = 0.0714
corr22 = 0.3
CHSH is 0.4442
Experiment 23
corr11 = 0.0968
corr12 = 0.75
corr21 = 0.0625
corr22 = -0.0476
CHSH is 0.9569
Experiment 24
corr11 = 0
corr12 = 0.0714
corr21 = 0.1429
corr22 = 0.0909
CHSH is 0.1234
Experiment 25
corr11 = 0.3043
corr12 = 0.3333
corr21 = 0.2
corr22 = 0.125
CHSH is 0.7127
Experiment 26
corr11 = 0.2258
corr12 = 0.4286
corr21 = 0.1429
corr22 = 0.1176
CHSH is 0.6796
Experiment 27
corr11 = 0.3077
corr12 = 0.1724
corr21 = 0.36
corr22 = -0.3
CHSH is 1.1401
Experiment 28
corr11 = 0.5833
corr12 = 0.3
corr21 = 0.2258
corr22 = -0.2
CHSH is 1.3091
Experiment 29
corr11 = 0.6
corr12 = 0.3913
corr21 = 0.0968
corr22 = -0.2308
CHSH is 1.3188
Experiment 30
corr11 = 0.3333
corr12 = 0.2857
corr21 = 0.1111
corr22 = 0
CHSH is 0.7302
Experiment 31
corr11 = 0.7778
corr12 = 0.4
corr21 = -0.0323
corr22 = 0.0476
CHSH is 1.0979
Experiment 32
corr11 = 0.4167
corr12 = 0.5652
corr21 = 0.1333
corr22 = -0.3043
CHSH is 1.4196
Experiment 33
corr11 = 0.1579
corr12 = 0.2143
corr21 = 0.36
corr22 = 0.2857
CHSH is 0.4465
Experiment 34
corr11 = 0.04
corr12 = 0.2903
corr21 = 0.1429
corr22 = 0.0435
CHSH is 0.4297
Experiment 35
corr11 = 0.2593
corr12 = 0.8182
corr21 = 0
corr22 = -0.04
CHSH is 1.1174
Experiment 36
corr11 = 0.2414
corr12 = 0.25
corr21 = 0.2174
corr22 = 0
CHSH is 0.7088
Experiment 37
corr11 = 0.4286
corr12 = 0.6522
corr21 = 0.375
corr22 = -0.0303
CHSH is 1.486
Experiment 38
corr11 = 0.1538
corr12 = 0.3636
corr21 = 0.1111
corr22 = -0.2
CHSH is 0.8286
Experiment 39
corr11 = 0.5
corr12 = 0.5
corr21 = 0.3636
corr22 = -0.2667
CHSH is 1.6303
Experiment 40
corr11 = 0.1892
corr12 = 0.5556
corr21 = 0.5
corr22 = -0.12
CHSH is 1.3647
Experiment 41
corr11 = 0.3103
corr12 = 0.5238
corr21 = 0.1579
corr22 = -0.0968
CHSH is 1.0888
Experiment 42
corr11 = 0.3333
corr12 = 0.6842
corr21 = -0.1111
corr22 = -0.1111
CHSH is 1.0175
Experiment 43
corr11 = 0.3333
corr12 = 0.4286
corr21 = 0.12
corr22 = 0.0476
CHSH is 0.8343
Experiment 44
corr11 = 0.2632
corr12 = 0.44
corr21 = -0.0435
corr22 = -0.2121
CHSH is 0.8718
Experiment 45
corr11 = 0.5385
corr12 = 0.3043
corr21 = 0.0667
corr22 = 0
CHSH is 0.9095
Experiment 46
corr11 = 0.3077
corr12 = 0.28
corr21 = 0.3333
corr22 = -0.2
CHSH is 1.121
Experiment 47
corr11 = 0.2414
corr12 = 0.2727
corr21 = 0.1852
corr22 = -0.1818
CHSH is 0.8811
Experiment 48
corr11 = 0.1034
corr12 = 0.25
corr21 = 0.2941
corr22 = -0.2727
CHSH is 0.9203
Experiment 49
corr11 = 0.1852
corr12 = 0.5
corr21 = 0.0909
corr22 = 0.1852
CHSH is 0.5909
Experiment 50
corr11 = -0.1034
corr12 = 0.4
corr21 = -0.04
corr22 = 0
CHSH is 0.2566
Experiment 51
corr11 = 0.44
corr12 = 0.3846
corr21 = 0.2174
corr22 = -0.0769
CHSH is 1.1189
Experiment 52
corr11 = 0.4737
corr12 = 0.3333
corr21 = 0.36
corr22 = 0
CHSH is 1.167
Experiment 53
corr11 = -0.0909
corr12 = 0.3333
corr21 = -0.037
corr22 = -0.3333
CHSH is 0.5387
Experiment 54
corr11 = 0.1111
corr12 = 0.3913
corr21 = 0.0909
corr22 = 0.5
CHSH is 0.0933
Experiment 55
corr11 = 0.3913
corr12 = 0.2174
corr21 = 0.2381
corr22 = 0.1515
CHSH is 0.6953
Experiment 56
corr11 = 0.2857
corr12 = 0.4815
corr21 = 0.0667
corr22 = 0.2
CHSH is 0.6339
Experiment 57
corr11 = 0.3333
corr12 = 0.3043
corr21 = -0.1852
corr22 = -0.3043
CHSH is 0.7568
Experiment 58
corr11 = 0.1111
corr12 = 0.36
corr21 = 0.3043
corr22 = -0.28
CHSH is 1.0555
Experiment 59
corr11 = 0.2632
corr12 = 0.0968
corr21 = 0
corr22 = -0.1429
CHSH is 0.5028
Experiment 60
corr11 = 0.36
corr12 = 0.1818
corr21 = 0.04
corr22 = 0
CHSH is 0.5818
Experiment 61
corr11 = 0.1538
corr12 = 0.1818
corr21 = 0.1111
corr22 = -0.36
CHSH is 0.8068
Experiment 62
corr11 = 0.4545
corr12 = 0.3333
corr21 = 0.2353
corr22 = 0.1304
CHSH is 0.8927
Experiment 63
corr11 = 0.12
corr12 = 0.1667
corr21 = 0.1538
corr22 = -0.12
CHSH is 0.5605
Experiment 64
corr11 = 0.3077
corr12 = 0.0345
corr21 = -0.2
corr22 = -0.12
CHSH is 0.2622
Experiment 65
corr11 = 0.2593
corr12 = 0.2414
corr21 = 0.3043
corr22 = 0.1429
CHSH is 0.6621
Experiment 66
corr11 = 0.1852
corr12 = 0.2381
corr21 = 0.2414
corr22 = 0.0435
CHSH is 0.6212
Experiment 67
corr11 = 0.0323
corr12 = 0
corr21 = 0.4545
corr22 = -0.1724
CHSH is 0.6592
Experiment 68
corr11 = 0.3333
corr12 = -0.0588
corr21 = -0.3333
corr22 = -0.0345
CHSH is -0.0243
Experiment 69
corr11 = 0.3
corr12 = 0.3939
corr21 = 0
corr22 = -0.0526
CHSH is 0.7466
Experiment 70
corr11 = 0.1852
corr12 = 0.4615
corr21 = 0.0714
corr22 = -0.2632
CHSH is 0.9813
Experiment 71
corr11 = 0.2381
corr12 = 0.68
corr21 = -0.0667
corr22 = -0.1667
CHSH is 1.0181
Experiment 72
corr11 = 0.619
corr12 = 0.5385
corr21 = -0.0769
corr22 = 0.037
CHSH is 1.0435
Experiment 73
corr11 = 0.2593
corr12 = 0.6429
corr21 = 0.2174
corr22 = 0
CHSH is 1.1195
Experiment 74
corr11 = 0.2414
corr12 = 0.3846
corr21 = 0
corr22 = 0.1429
CHSH is 0.4831
Experiment 75
corr11 = 0.5
corr12 = 0.6522
corr21 = 0.1852
corr22 = 0.1538
CHSH is 1.1835
Experiment 76
corr11 = 0
corr12 = 0.3333
corr21 = -0.1304
corr22 = -0.1429
CHSH is 0.3458
Experiment 77
corr11 = 0.2857
corr12 = 0.4615
corr21 = 0.1111
corr22 = 0.1579
CHSH is 0.7005
Experiment 78
corr11 = 0.5556
corr12 = 0.3043
corr21 = -0.2414
corr22 = -0.3333
CHSH is 0.9519
Experiment 79
corr11 = 0.4286
corr12 = 0.3333
corr21 = 0.12
corr22 = -0.1304
CHSH is 1.0123
Experiment 80
corr11 = 0.1852
corr12 = 0.3
corr21 = 0.5238
corr22 = -0.1875
CHSH is 1.1965
Experiment 81
corr11 = 0.1818
corr12 = 0.3684
corr21 = 0
corr22 = -0.2903
CHSH is 0.8406
Experiment 82
corr11 = 0.4118
corr12 = 0.3077
corr21 = 0.2903
corr22 = -0.1538
CHSH is 1.1636
Experiment 83
corr11 = 0.5714
corr12 = 0.4783
corr21 = 0.1304
corr22 = -0.2308
CHSH is 1.4109
Experiment 84
corr11 = 0.4615
corr12 = 0.3333
corr21 = 0.037
corr22 = 0.1
CHSH is 0.7319
Experiment 85
corr11 = 0.5294
corr12 = 0.2857
corr21 = -0.1429
corr22 = -0.037
CHSH is 0.7093
Experiment 86
corr11 = 0.2143
corr12 = 0.3571
corr21 = 0.2941
corr22 = -0.3333
CHSH is 1.1989
Experiment 87
corr11 = 0.1765
corr12 = 0.4444
corr21 = 0.2593
corr22 = -0.0476
CHSH is 0.9278
Experiment 88
corr11 = 0.3077
corr12 = 0.4815
corr21 = -0.1304
corr22 = 0.0833
CHSH is 0.5754
Experiment 89
corr11 = 0.2174
corr12 = 0.3571
corr21 = 0.0769
corr22 = -0.3043
CHSH is 0.9558
Experiment 90
corr11 = 0.0476
corr12 = 0.2308
corr21 = -0.0714
corr22 = 0.04
CHSH is 0.167
Experiment 91
corr11 = 0.1111
corr12 = 0.4286
corr21 = 0.0345
corr22 = -0.1304
CHSH is 0.7046
Experiment 92
corr11 = 0.4615
corr12 = 0.4286
corr21 = -0.25
corr22 = 0.1724
CHSH is 0.4677
Experiment 93
corr11 = 0.1818
corr12 = 0.6552
corr21 = -0.0714
corr22 = 0.0476
CHSH is 0.7179
Experiment 94
corr11 = 0.1111
corr12 = 0.4074
corr21 = 0
corr22 = 0.0909
CHSH is 0.4276
Experiment 95
corr11 = 0.2308
corr12 = 0.3333
corr21 = -0.1304
corr22 = -0.1667
CHSH is 0.6003
Experiment 96
corr11 = 0.5
corr12 = 0.2174
corr21 = 0.1111
corr22 = -0.3846
CHSH is 1.2131
Experiment 97
corr11 = 0.2381
corr12 = 0.4839
corr21 = 0.1304
corr22 = 0.04
CHSH is 0.8124
Experiment 98
corr11 = 0.1
corr12 = 0.2941
corr21 = 0.2571
corr22 = -0.0714
CHSH is 0.7227
Experiment 99
corr11 = -0.1034
corr12 = 0.6154
corr21 = -0.0526
corr22 = -0.2308
CHSH is 0.6901
Experiment 100
corr11 = 0.5455
corr12 = 0.2857
corr21 = 0.5
corr22 = -0.3846
CHSH is 1.7158