Sampling Based on Trading Probability in a Given Period: Nonparametric tests

PIT: Wilcoxon Rank Sum Test

 

Decile

2

3

4

5

6

7

8

9

10

Period 1

1

0.195

0.814

1.753

1.668

1.992

1.071

0.928

2.722

1.006

2

0.243

0.046

0.129

0.414

0.271

0.350

0.584

0.414

3

1.014

0.386

0.386

0.684

0.700

0.593

0.988

4

1.357

1.643

1.022

0.986

0.198

0.487

5

0.471

0.565

0.834

0.167

0.511

6

0.289

0.411

1.475

1.232

7

0.130

0.350

0.877

8

0.076

0.441

9

0.054

Period 2

1

1.234

0.776

0.227

0.541

0.869

2.110

1.495

1.071

2.661

2

0.131

0.174

0.744

2.233

2.503

1.471

1.080

0.269

3

1.699

0.952

1.364

0.382

0.289

0.348

1.566

4

0.019

1.101

1.064

0.654

0.035

0.867

5

0.584

0.865

0.958

1.112

1.900

6

0.986

0.989

2.184

2.186

7

1.213

0.382

2.509

8

0.682

0.054

9

1.141

Period 3

1

0.579

0.357

1.529

2.727

0.000

1.818

0.015

2.338

1.251

2

1.425

0.000

1.536

0.471

0.521

0.106

0.260

1.104

3

0.871

0.592

1.157

1.506

1.071

1.323

0.227

4

1.507

0.806

1.384

0.928

0.043

0.000

5

1.957

0.441

1.201

2.745

1.931

6

1.329

0.260

0.414

0.958

7

0.700

0.586

1.493

8

1.414

0.519

9

0.195

 

Period

2

3

Decile 1

1

0.357

0.915

 

2

 

0.974

Decile 2

1

1.243

0.909

 

2

 

0.660

Decile 3

1

0.541

1.214

 

2

 

1.614

Decile 4

1

0.654

0.441

 

2

 

0.292

Decile 5

1

2.126

2.018

 

2

 

1.445

Decile 6

1

3.247

2.206

 

2

 

1.929

Decile 7

1

2.144

0.441

 

2

 

1.100

Decile 8

1

0.390

0.228

 

2

 

0.015

Decile 9

1

0.776

0.714

 

2

 

1.453

Decile 10

1

0.443

0.289

 

2

 

0.897

All Deciles

1

3.087

0.459

 

2

 

3.248


PIT: Kruskal-Wallis Test

Test Deciles

Stat

P-value

Period 1

9.995

0.351

Period 2

17.751

0.038

Period 3

13.292

0.150

All Data

10.774

0.292

Test Time

Stat

P-value

Decile 1

0.798

0.671

Decile 2

0.788

0.674

Decile 3

2.691

0.260

Decile 4

4.853

0.088

Decile 5

12.515

0.002

Decile 6

11.983

0.003

Decile 7

6.048

0.049

Decile 8

1.100

0.577

Decile 9

2.075

0.354

Decile 10

0.288

0.866

All Deciles

14.320

0.001

alpha (α): Kruskal-Wallis Test

Test Deciles

Stat

P-value

Period 1

8.553

0.480

Period 2

7.709

0.564

Period 3

9.825

0.365

All Data

6.277

0.712

Test Time

Stat

P-value

Decile 1

8.405

0.015

Decile 2

1.015

0.602

Decile 3

0.010

0.995

Decile 4

4.789

0.091

Decile 5

0.934

0.627

Decile 6

2.417

0.299

Decile 7

4.227

0.121

Decile 8

5.921

0.052

Decile 9

2.458

0.293

Decile 10

0.836

0.658

All Deciles

12.280

0.002

delta (δ): Kruskal-Wallis Test

Test Deciles

Stat

P-value

Period 1

10.024

0.349

Period 2

19.482

0.021

Period 3

10.346

0.323

All Data

12.926

0.166

Test Time

Stat

P-value

Decile 1

0.304

0.859

Decile 2

3.099

0.212

Decile 3

7.957

0.019

Decile 4

18.571

0.000

Decile 5

18.301

0.000

Decile 6

12.493

0.002

Decile 7

7.514

0.023

Decile 8

6.939

0.031

Decile 9

4.047

0.132

Decile 10

4.292

0.117

All Deciles

55.765

0.000