# [R] Randomization Test

Ben Tupper btupper @end|ng |rom b|ge|ow@org
Thu Feb 28 01:59:05 CET 2019

```Hi,

I'm not very clear on what you are trying to achieve, but I think you could try the following for your Q1...

> Q1: Please how do I generate many samples as x above, say up to 5000
> or 10,000? I manually generated and stored as x1,x2, x3 up to x100.

ndta = nrow(dta)
x0 = 8890
x1 = 9500
xx = seq(from = x0, to = x1, by = 1)
N_many = 50 # make 5000 etc as required
m <- sapply(   seq_len(N_many), function(i) sample(xx, ndta, replace = TRUE))

str(m)
# int [1:1136, 1:50] 9147 8904 9062 8946 9330 9056 9239 9284 9290 9441 ...

summary(as.vector(m))
#   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
#   8890    9043    9195    9196    9348    9500

m[1:5, 1:5]
#     [,1] [,2] [,3] [,4] [,5]
#[1,] 9147 9124 9341 8999 9268
#[2,] 8904 9246 9087 9041 8943
#[3,] 9062 9184 9061 9119 9350
#[4,] 8946 9242 8932 9306 9270
#[5,] 9330 8979 9437 9030 9333

Each sample set of length ndta (in this case ndta = 1136) is found in a column of the matrix.   Is that what you are looking for?

Ben

> On Feb 27, 2019, at 4:53 PM, Ogbos Okike <giftedlife2014 using gmail.com> wrote:
>
> Dear Kind List,
>
> I am still battling with this. I have, however, made some progress
> with the suggestions of Micheal and others. At least, I have a better
> picture of what I want to do now as I will attempt a detailed
> description here.
>
> I am aware I should show you just a small part of my code and data.
> But when I copied out a small portion and run to see what you get when
> I send that,  I was not satisfied with the signal displayed. The epoch
> analysis averages data and is quite sensitive to leveraging,
> especially if a small sample is used.
>
> So please permit/exercise patience  me to display the series of epoch
> that give the averaged valued used. You can just run the code and see
> the signal of interest. Here is the code and the data:
>
> dta <- read.table( text ="n CR
> -5 8969
> -4 8932
> -3 8929
> -2 8916
> -1 8807
> 0 8449
> 1 8484
> 2 8148
> 3 8282
> 4 8305
> 5 8380
> 6 8530
> 7 8642
> 8 8780
> 9 8890
> 10 8962
> -5 8929
> -4 8916
> -3 8807
> -2 8449
> -1 8484
> 0 8148
> 1 8282
> 2 8305
> 3 8380
> 4 8530
> 5 8642
> 6 8780
> 7 8890
> 8 8962
> 9 8949
> 10 8974
> -5 8744
> -4 8786
> -3 8828
> -2 8807
> -1 8716
> 0 8520
> 1 8634
> 2 8640
> 3 8636
> 4 8658
> 5 8699
> 6 8682
> 7 8621
> 8 8626
> 9 8660
> 10 8737
> -5 8592
> -4 8612
> -3 8628
> -2 8589
> -1 8318
> 0 8264
> 1 8294
> 2 8410
> 3 8442
> 4 8416
> 5 8389
> 6 8412
> 7 8453
> 8 8563
> 9 8581
> 10 8613
> -5 8264
> -4 8294
> -3 8410
> -2 8442
> -1 8416
> 0 8389
> 1 8412
> 2 8453
> 3 8563
> 4 8581
> 5 8613
> 6 8647
> 7 8613
> 8 8508
> 9 7829
> 10 7499
> -5 8613
> -4 8647
> -3 8613
> -2 8508
> -1 7829
> 0 7499
> 1 8213
> 2 7993
> 3 7821
> 4 8316
> 5 8460
> 6 8533
> 7 8584
> 8 8586
> 9 8567
> 10 8573
> -5 8508
> -4 7829
> -3 7499
> -2 8213
> -1 7993
> 0 7821
> 1 8316
> 2 8460
> 3 8533
> 4 8584
> 5 8586
> 6 8567
> 7 8573
> 8 8617
> 9 8591
> 10 8661
> -5 8851
> -4 8893
> -3 8858
> -2 8803
> -1 8790
> 0 8468
> 1 8545
> 2 8570
> 3 8568
> 4 8624
> 5 8669
> 6 8236
> 7 8190
> 8 8313
> 9 8389
> 10 8421
> -5 8803
> -4 8790
> -3 8468
> -2 8545
> -1 8570
> 0 8568
> 1 8624
> 2 8669
> 3 8236
> 4 8190
> 5 8313
> 6 8389
> 7 8421
> 8 8468
> 9 8537
> 10 8580
> -5 8570
> -4 8568
> -3 8624
> -2 8669
> -1 8236
> 0 8190
> 1 8313
> 2 8389
> 3 8421
> 4 8468
> 5 8537
> 6 8580
> 7 8605
> 8 8646
> 9 8690
> 10 8770
> -5 8690
> -4 8770
> -3 8799
> -2 8821
> -1 8666
> 0 8539
> 1 8633
> 2 8617
> 3 8651
> 4 8693
> 5 8715
> 6 8738
> 7 8716
> 8 8677
> 9 8680
> 10 8700
> -5 8756
> -4 8632
> -3 8662
> -2 8596
> -1 8552
> 0 8502
> 1 8633
> 2 8702
> 3 8745
> 4 8730
> 5 8708
> 6 8817
> 7 8724
> 8 8688
> 9 8693
> 10 8746
> -5 8926
> -4 8888
> -3 8798
> -2 8651
> -1 8678
> 0 8578
> 1 8593
> 2 8598
> 3 8526
> 4 8181
> 5 8204
> 6 8373
> 7 8599
> 8 8773
> 9 8784
> 10 8746
> -5 8678
> -4 8578
> -3 8593
> -2 8598
> -1 8526
> 0 8181
> 1 8204
> 2 8373
> 3 8599
> 4 8773
> 5 8784
> 6 8746
> 7 8747
> 8 8757
> 9 8749
> 10 8767
> -5 8757
> -4 8749
> -3 8767
> -2 8754
> -1 8695
> 0 8631
> 1 8661
> 2 8653
> 3 8588
> 4 8562
> 5 8613
> 6 8595
> 7 8498
> 8 8404
> 9 8507
> 10 8599
> -5 8695
> -4 8631
> -3 8661
> -2 8653
> -1 8588
> 0 8562
> 1 8613
> 2 8595
> 3 8498
> 4 8404
> 5 8507
> 6 8599
> 7 8592
> 8 8600
> 9 8637
> 10 8635
> -5 8588
> -4 8562
> -3 8613
> -2 8595
> -1 8498
> 0 8404
> 1 8507
> 2 8599
> 3 8592
> 4 8600
> 5 8637
> 6 8635
> 7 8632
> 8 8674
> 9 8644
> 10 8687
> -5 8595
> -4 8498
> -3 8404
> -2 8507
> -1 8599
> 0 8592
> 1 8600
> 2 8637
> 3 8635
> 4 8632
> 5 8674
> 6 8644
> 7 8687
> 8 8721
> 9 8747
> 10 8748
> -5 8599
> -4 8592
> -3 8600
> -2 8637
> -1 8635
> 0 8632
> 1 8674
> 2 8644
> 3 8687
> 4 8721
> 5 8747
> 6 8748
> 7 8739
> 8 8763
> 9 8792
> 10 8558
> -5 8600
> -4 8637
> -3 8635
> -2 8632
> -1 8674
> 0 8644
> 1 8687
> 2 8721
> 3 8747
> 4 8748
> 5 8739
> 6 8763
> 7 8792
> 8 8558
> 9 8442
> 10 8555
> -5 8748
> -4 8739
> -3 8763
> -2 8792
> -1 8558
> 0 8442
> 1 8555
> 2 8622
> 3 8634
> 4 8698
> 5 8732
> 6 8713
> 7 8732
> 8 8681
> 9 8615
> 10 8624
> -5 8698
> -4 8732
> -3 8713
> -2 8732
> -1 8681
> 0 8615
> 1 8624
> 2 8649
> 3 8656
> 4 8678
> 5 8723
> 6 8693
> 7 8548
> 8 7803
> 9 7801
> 10 7724
> -5 8723
> -4 8693
> -3 8548
> -2 7803
> -1 7801
> 0 7724
> 1 7910
> 2 7829
> 3 7995
> 4 8156
> 5 8307
> 6 8377
> 7 8465
> 8 8506
> 9 8516
> 10 8536
> -5 8548
> -4 7803
> -3 7801
> -2 7724
> -1 7910
> 0 7829
> 1 7995
> 2 8156
> 3 8307
> 4 8377
> 5 8465
> 6 8506
> 7 8516
> 8 8536
> 9 8574
> 10 8623
> -5 8821
> -4 8856
> -3 8798
> -2 8772
> -1 8705
> 0 8682
> 1 8691
> 2 8720
> 3 8727
> 4 8789
> 5 8821
> 6 8811
> 7 8841
> 8 8849
> 9 8849
> 10 8860
> -5 8835
> -4 8829
> -3 8826
> -2 8799
> -1 8775
> 0 8756
> 1 8793
> 2 8814
> 3 8847
> 4 8838
> 5 8833
> 6 8841
> 7 8847
> 8 8903
> 9 8933
> 10 8918
> -5 8890
> -4 8875
> -3 8874
> -2 8865
> -1 8891
> 0 8839
> 1 8853
> 2 8888
> 3 8884
> 4 8890
> 5 8889
> 6 8839
> 7 8879
> 8 8908
> 9 8924
> 10 8882
> -5 8853
> -4 8888
> -3 8884
> -2 8890
> -1 8889
> 0 8839
> 1 8879
> 2 8908
> 3 8924
> 4 8882
> 5 8910
> 6 8903
> 7 8859
> 8 8858
> 9 8863
> 10 8847
> -5 8924
> -4 8882
> -3 8910
> -2 8903
> -1 8859
> 0 8858
> 1 8863
> 2 8847
> 3 8883
> 4 8869
> 5 8878
> 6 8897
> 7 8922
> 8 8895
> 9 8858
> 10 8858
> -5 8910
> -4 8903
> -3 8859
> -2 8858
> -1 8863
> 0 8847
> 1 8883
> 2 8869
> 3 8878
> 4 8897
> 5 8922
> 6 8895
> 7 8858
> 8 8858
> 9 8736
> 10 8905
> -5 8859
> -4 8858
> -3 8863
> -2 8847
> -1 8883
> 0 8869
> 1 8878
> 2 8897
> 3 8922
> 4 8895
> 5 8858
> 6 8858
> 7 8736
> 8 8905
> 9 8935
> 10 8974
> -5 8897
> -4 8922
> -3 8895
> -2 8858
> -1 8858
> 0 8736
> 1 8905
> 2 8935
> 3 8974
> 4 8946
> 5 8952
> 6 9010
> 7 8980
> 8 8976
> 9 8970
> 10 8961
> -5 9376
> -4 9336
> -3 9311
> -2 9287
> -1 9221
> 0 9087
> 1 9132
> 2 9175
> 3 9166
> 4 9240
> 5 9264
> 6 9271
> 7 9319
> 8 9324
> 9 9333
> 10 9351
> -5 9287
> -4 9221
> -3 9087
> -2 9132
> -1 9175
> 0 9166
> 1 9240
> 2 9264
> 3 9271
> 4 9319
> 5 9324
> 6 9333
> 7 9351
> 8 9362
> 9 9385
> 10 9354
> -5 9407
> -4 9414
> -3 9354
> -2 9298
> -1 9319
> 0 9147
> 1 9178
> 2 9196
> 3 9258
> 4 9303
> 5 9369
> 6 9382
> 7 9375
> 8 9389
> 9 9376
> 10 9264
> -5 9386
> -4 9396
> -3 9424
> -2 9391
> -1 9284
> 0 9267
> 1 9278
> 2 9318
> 3 9334
> 4 9275
> 5 9306
> 6 9308
> 7 9358
> 8 9335
> 9 9373
> 10 9379
> -5 9284
> -4 9267
> -3 9278
> -2 9318
> -1 9334
> 0 9275
> 1 9306
> 2 9308
> 3 9358
> 4 9335
> 5 9373
> 6 9379
> 7 9355
> 8 9340
> 9 9327
> 10 9320
> -5 9327
> -4 9320
> -3 9315
> -2 9336
> -1 9371
> 0 9259
> 1 9330
> 2 9355
> 3 9334
> 4 9353
> 5 9370
> 6 9394
> 7 9400
> 8 9318
> 9 9037
> 10 8994
> -5 9394
> -4 9400
> -3 9318
> -2 9037
> -1 8994
> 0 8943
> 1 8964
> 2 8997
> 3 9158
> 4 8964
> 5 8564
> 6 8736
> 7 8818
> 8 8938
> 9 9034
> 10 9132
> -5 8943
> -4 8964
> -3 8997
> -2 9158
> -1 8964
> 0 8564
> 1 8736
> 2 8818
> 3 8938
> 4 9034
> 5 9132
> 6 9167
> 7 9200
> 8 9257
> 9 9266
> 10 9306
> -5 9338
> -4 9354
> -3 9372
> -2 9338
> -1 9308
> 0 9282
> 1 9324
> 2 9318
> 3 9342
> 4 9370
> 5 9331
> 6 9327
> 7 9338
> 8 9381
> 9 9394
> 10 9332
> -5 9372
> -4 9338
> -3 9308
> -2 9282
> -1 9324
> 0 9318
> 1 9342
> 2 9370
> 3 9331
> 4 9327
> 5 9338
> 6 9381
> 7 9394
> 8 9332
> 9 9331
> 10 9293
> -5 9338
> -4 9381
> -3 9394
> -2 9332
> -1 9331
> 0 9293
> 1 9309
> 2 9325
> 3 9406
> 4 9409
> 5 9413
> 6 9426
> 7 9440
> 8 9449
> 9 9512
> 10 9494
> -5 9361
> -4 9354
> -3 9299
> -2 9282
> -1 9250
> 0 9242
> 1 9254
> 2 9321
> 3 9390
> 4 9414
> 5 9435
> 6 9437
> 7 9426
> 8 9398
> 9 9383
> 10 9354
> -5 9365
> -4 9421
> -3 9416
> -2 9355
> -1 9338
> 0 9324
> 1 9325
> 2 9322
> 3 9319
> 4 9381
> 5 9315
> 6 9314
> 7 9359
> 8 9403
> 9 9419
> 10 9474
> -5 9355
> -4 9338
> -3 9324
> -2 9325
> -1 9322
> 0 9319
> 1 9381
> 2 9315
> 3 9314
> 4 9359
> 5 9403
> 6 9419
> 7 9474
> 8 9525
> 9 9501
> 10 9447
> -5 9325
> -4 9322
> -3 9319
> -2 9381
> -1 9315
> 0 9314
> 1 9359
> 2 9403
> 3 9419
> 4 9474
> 5 9525
> 6 9501
> 7 9447
> 8 9424
> 9 9396
> 10 9388
> -5 9447
> -4 9424
> -3 9396
> -2 9388
> -1 9396
> 0 9346
> 1 9358
> 2 9353
> 3 9350
> 4 9378
> 5 9372
> 6 9354
> 7 9349
> 8 9392
> 9 9440
> 10 9467
> -5 9388
> -4 9396
> -3 9346
> -2 9358
> -1 9353
> 0 9350
> 1 9378
> 2 9372
> 3 9354
> 4 9349
> 5 9392
> 6 9440
> 7 9467
> 8 9519
> 9 9550
> 10 9565
> -5 9353
> -4 9350
> -3 9378
> -2 9372
> -1 9354
> 0 9349
> 1 9392
> 2 9440
> 3 9467
> 4 9519
> 5 9550
> 6 9565
> 7 9565
> 8 9497
> 9 9500
> 10 9472
> -5 9522
> -4 9529
> -3 9492
> -2 9432
> -1 9382
> 0 9355
> 1 9361
> 2 9350
> 3 9382
> 4 9451
> 5 9491
> 6 9506
> 7 9529
> 8 9543
> 9 9556
> 10 9553
> -5 9492
> -4 9432
> -3 9382
> -2 9355
> -1 9361
> 0 9350
> 1 9382
> 2 9451
> 3 9491
> 4 9506
> 5 9529
> 6 9543
> 7 9556
> 8 9553
> 9 9502
> 10 9470
> -5 9551
> -4 9505
> -3 9389
> -2 9406
> -1 9377
> 0 9284
> 1 9365
> 2 9424
> 3 9412
> 4 9403
> 5 9384
> 6 9394
> 7 9404
> 8 9413
> 9 9407
> 10 9405
> -5 9579
> -4 9576
> -3 9543
> -2 9451
> -1 9421
> 0 9361
> 1 9394
> 2 9400
> 3 9387
> 4 9366
> 5 9346
> 6 9360
> 7 9385
> 8 9435
> 9 9443
> 10 9430
> -5 9361
> -4 9394
> -3 9400
> -2 9387
> -1 9366
> 0 9346
> 1 9360
> 2 9385
> 3 9435
> 4 9443
> 5 9430
> 6 9454
> 7 9531
> 8 9547
> 9 9581
> 10 9540
> -5 9510
> -4 9546
> -3 9564
> -2 9508
> -1 9422
> 0 9369
> 1 9395
> 2 9438
> 3 9423
> 4 9392
> 5 9368
> 6 9366
> 7 9348
> 8 9340
> 9 9375
> 10 9391
> -5 9423
> -4 9392
> -3 9368
> -2 9366
> -1 9348
> 0 9340
> 1 9375
> 2 9391
> 3 9466
> 4 9545
> 5 9574
> 6 9564
> 7 9527
> 8 9513
> 9 9494
> 10 9542
> -5 9511
> -4 9491
> -3 9457
> -2 9453
> -1 9402
> 0 9382
> 1 9407
> 2 9437
> 3 9403
> 4 9404
> 5 9425
> 6 9486
> 7 9457
> 8 9451
> 9 9423
> 10 9401
> -5 9425
> -4 9486
> -3 9457
> -2 9451
> -1 9423
> 0 9401
> 1 9429
> 2 9422
> 3 9431
> 4 9462
> 5 9475
> 6 9474
> 7 9487
> 8 9493
> 9 9495
> 10 9499
> -5 9404
> -4 9385
> -3 9363
> -2 9399
> -1 9411
> 0 9355
> 1 9357
> 2 9363
> 3 9382
> 4 9387
> 5 9408
> 6 9429
> 7 9456
> 8 9487
> 9 9526
> 10 9487
> -5 9493
> -4 9439
> -3 9400
> -2 9378
> -1 9371
> 0 9369
> 1 9374
> 2 9305
> 3 9298
> 4 9298
> 5 9325
> 6 9381
> 7 9477
> 8 9508
> 9 9496
> 10 9517
> -5 9371
> -4 9369
> -3 9374
> -2 9305
> -1 9298
> 0 9298
> 1 9325
> 2 9381
> 3 9477
> 4 9508
> 5 9496
> 6 9517
> 7 9561
> 8 9570
> 9 9546
> 10 9544
> -5 9510
> -4 9506
> -3 9530
> -2 9441
> -1 9427
> 0 9393
> 1 9420
> 2 9444
> 3 9468
> 4 9484
> 5 9525
> 6 9542
> 7 9557
> 8 9548
> 9 9550
> 10 9593
> -5 9589
> -4 9598
> -3 9527
> -2 9417
> -1 9390
> 0 9374
> 1 9386
> 2 9407
> 3 9453
> 4 9447
> 5 9419
> 6 9386
> 7 9373
> 8 9364
> 9 9376
> 10 9389
> -5 9453
> -4 9447
> -3 9419
> -2 9386
> -1 9373
> 0 9364
> 1 9376
> 2 9389
> 3 9376
> 4 9375
> 5 9370
> 6 9391
> 7 9458
> 8 9446
> 9 9456
> 10 9463
> -5 9364
> -4 9376
> -3 9389
> -2 9376
> -1 9375
> 0 9370
> 1 9391
> 2 9458
> 3 9446
> 4 9456
> 5 9463
> 6 9500
> 7 9486
> 8 9474
> 9 9495
> 10 9531
> -5 9491
> -4 9441
> -3 9388
> -2 9380
> -1 9369
> 0 9354
> 1 9367
> 2 9369
> 3 9341
> 4 9305
> 5 9308
> 6 9324
> 7 9385
> 8 9451
> 9 9496
> 10 9527
> -5 9369
> -4 9354
> -3 9367
> -2 9369
> -1 9341
> 0 9305
> 1 9308
> 2 9324
> 3 9385
> 4 9451
> 5 9496
> 6 9527
> 7 9544
> 8 9543
> 9 9535
> 10 9536
> -5 9586
> -4 9583
> -3 9572
> -2 9533
> -1 9454
> 0 9392
> 1 9420
> 2 9451
> 3 9475
> 4 9514
> 5 9561
> 6 9542
> 7 9502
> 8 9461
> 9 9468
> 10 9463
> -5 9587
> -4 9562
> -3 9530
> -2 9445
> -1 9404
> 0 9395
> 1 9417
> 2 9449
> 3 9467
> 4 9470
> 5 9524
> 6 9512
> 7 9448
> 8 9398
> 9 9431
> 10 9467
> -5 9467
> -4 9470
> -3 9524
> -2 9512
> -1 9448
> 0 9398
> 1 9431
> 2 9467
> 3 9490
> 4 9517
> 5 9526
> 6 9574
> 7 9573
> 8 9562
> 9 9563
> 10 9566
>
> data<-matrix(c(dta\$CR),ncol=71)
> A<-matrix(rep(-5:10,71))
> B<-matrix(data)
>
> oodf<-data.frame(A,B)
> a<--5:10
> oodf<-data.frame(A,B)
> library(plotrix)
> std.error<-function(x) return(sd(x)/(sum(!is.na(x))))
> oomean<-as.vector(by(oodf\$B,oodf\$A,mean))
> oose<-as.vector(by(oodf\$B,oodf\$A,std.error))
> plot(-5:10,oomean,type="l",ylim=c(8890,9100),
> )
> A<-oomean-1.96*oose
> B<-oomean+1.96*oose
> lines(a,A,col="red")
> lines(a,B,col="red")
>
> My Question:
> I wish to conduct a randomization test of significance (90 and 99
> percentile) of the reductions/decreases as displayed by the signal.
>
> I am attempting using:
> x<-sample(8890:9500,1136,replace=T )
>
> to generate the random numbers, where 8890, 9500 and 1136 are the
> minimum  and maximum of the signal and 1136 the length of sample data.
> Q1: Please how do I generate many samples as x above, say up to 5000
> or 10,000? I manually generated and stored as x1,x2, x3 up to x100.
>
> Q2: Please how do I use this randomly generated numbers to test the
> statistical significance level of the signal generated by
> plot(-5:10,oomean,type="l",ylim=c(8890,9100),  )?
>
> I wish to test for 90% and 99% percentile.
>
> I am sorry that this is too long.
>
> Many thanks for your kind contributions
>
> Best
> Ogbos
>
>
>
>
>
>
>
> On Sun, Feb 10, 2019 at 3:55 PM Ogbos Okike <giftedlife2014 using gmail.com> wrote:
>>
>> Dear Michael,
>> This is great! Thank you.
>>
>> I have not really got any response other than yours.
>>
>> I have long before now included what I have in a paper submitted to a journal.
>>
>> I am awaiting the feedback of the reviewer. I will compare the
>> comments with your input here and determine the corrections to make
>>
>> Best wishes
>> Ogbos
>>
>> On Fri, Feb 8, 2019 at 4:31 PM Meyners, Michael <meyners.m using pg.com> wrote:
>>>
>>> Ogbos,
>>>
>>> You do not seem to have received a reply over the list yet, which might be due to the fact that this seems rather a stats than an R question. Neither got your attachment (Figure) through - see posting guide.
>>>
>>> I'm not familiar with epoch analysis, so not sure what exactly you are doing / trying to achieve, but some general thoughts:
>>>
>>> * You do NOT want to restrict your re-randomizations in a way that "none of the dates corresponds with the ones in the real event" - actually, as a general principle, the true data must be an admissible re-randomization as well. You seem to have excluded that (and a lot of other randomizations at the same time which might have occurred, i.e. dates 1 and 2 reversed but all others the same), thereby rendering the test invalid. Any restrictions you have on your re-randomizations must've applied to the original randomization as well.
>>> * If you have rather observational data (which I suspect, but not sure), Edgington & Onghena (2007) would rather refer to this as a permutation test - the difference being that you have to make strong assumptions (similar to parametric tests) on the nature of the data, which are designed-in to be true for randomization tests. It might be a merely linguistic discrimination, but it is important to note which assumptions have to be (implicitly) made.
>>> * I'm not sure what you mean by "mean differences" of the events - is that two groups you are comparing? If so, that seems reasonable, but just make sure the test statistic you use is reasonable and sensitive against the alternatives you are mostly interested in. The randomization/permutation test will never proof that, e.g., means are significantly different, but only that there is SOME difference. By selecting the appropriate test statistic, you can influence what will pop up more easily and what not, but you can never be sure (unless you make strong assumptions about everything else, like in many parametric tests).
>>> * For any test statistic, you would then determine the proportion of its values among the 5000 samples where it is as large or larger than the one observed (or as small or smaller, or either, depending on the nature of the test statistic and whether you aim for a one- or a two-sided test). That is your p value. If small enough, conclude significance. At least conceptually important: The observed test statistic is always part of the re-randomization (i.e. your 5000) - so you truly only do 4999 plus the one you observed. Otherwise the test may be more or less liberal. Your p value is hence no smaller than 1/n, where n is the total number of samples you looked at (including the observed one), a p value of 0 is not possible in randomization tests (nor in other tests, of course).
>>>
>>> I hope this is helpful, but you will need to go through these and refer to your own setup to check whether you adhered to the principles or not, which is impossible for me to judge based on the information provided (and I won't be able to look at excessive code to check either).
>>>
>>> Michael
>>>
>>>> -----Original Message-----
>>>> From: R-help <r-help-bounces using r-project.org> On Behalf Of Ogbos Okike
>>>> Sent: Montag, 28. Januar 2019 19:42
>>>> To: r-help <r-help using r-project.org>
>>>> Subject: [R] Randomization Test
>>>>
>>>> Dear Contributors,
>>>>
>>>> I conducting epoch analysis. I tried to test the significance of my result using
>>>> randomization test.
>>>>
>>>> Since I have 71 events, I randomly selected another 71 events, making sure
>>>> that none of the dates in the random events corresponds with the ones in
>>>> the real event.
>>>>
>>>> Following the code I found here
>>>> (https://www.uvm.edu/~dhowell/StatPages/R/RandomizationTestsWithR/R
>>>> andom2Sample/TwoIndependentSamplesR.html),
>>>> I combined these two data set and used them to generate another 5000
>>>> events. I then plotted the graph of the mean differences for the 5000
>>>> randomly generated events. On the graph, I indicated the region of the
>>>> mean difference between the real 71 epoch and the randomly selected 71
>>>> epoch.
>>>>
>>>> Since the two tail test shows that the mean difference falls at the extreme of
>>>> the randomly selected events, I concluded that my result is statistically
>>>> significant.
>>>>
>>>>
>>>>
>>>> I am attaching the graph to assistance you in you suggestions.
>>>>
>>>> I can attach both my code and the real and randomly generated events if you
>>>>
>>>> My request is that you help me to understand if I am on the right track or no.
>>>> This is the first time I am doing this and except the experts decide, I am not
>>>> quite sure whether I am right or not.
>>>>
>>>> Many thanks for your kind concern.
>>>>
>>>> Best
>>>> Ogbos
>>>> ______________________________________________
>>>> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>> guide.html
>>>> and provide commented, minimal, self-contained, reproducible code.
>
> ______________________________________________
> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> and provide commented, minimal, self-contained, reproducible code.

Ben Tupper
Bigelow Laboratory for Ocean Sciences
60 Bigelow Drive, P.O. Box 380
East Boothbay, Maine 04544
http://www.bigelow.org

Ecological Forecasting: https://eco.bigelow.org/

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