Sample

Pr.

Proposed

Mardia

SJ

Royston

Q'

Q

K²

Z

H

H'

1

N₁E₁C₁L₁

ϕ

0.9996

0.9989

1

0.9998

0.9219

0.8884

2

N₂E₂C₂L₂

ϕ

1

0.9999

1

0.9993

0.9451

0.9244

3

N₃E₃C₃L₃

ϕ

1

1

1

0.9978

1

0.9999

4

N₄E₄C₄L₄

ϕ

1

1

0.9995

0.9999

0.9730

0.9582

5

N₁E₂C₃L₄

ϕ

1

1

0.9890

0.6167

1

0.9999

6

N₁N₂N₃N₄

β

0.7516

0.8587

0.2687

0.9755

0.6176

0.6185

7

4N rel.

β

0.9334

0.9500

0.3671

0.8404

0.8677

0.8492

8

4E ind

ϕ

1

1

0.9974

0.7330

1

0.9999

9

4C ind

ϕ

1

1

0.9849

0.8269

1

1

10

4L ind

ϕ

1

1

0.9999

0.8264

1

1

11

N₁N₂E₁C₁

ϕ

0.9975

0.9793

0.9998

0.9993

0.8687

0.8171

12

N₁N₂E₁L₁

ϕ

0.9885

0.9968

0.9971

0.9998

0.7969

0.7385

13

N₁N₂C₁L₁

ϕ

0.9985

0.9888

1

0.9999

0.9175

0.8889

14

N₁N₃E₂C₂

ϕ

0.9967

0.9621

0.9970

0.9981

0.9623

0.9490

15

N₁N₃E₂L₂

ϕ

0.9975

0.9976

0.9996

0.9876

0.9355

0.9154

16

N₁N₃C₂L₂

ϕ

0.9998

0.9942

0.9998

0.6161

0.9899

0.9828

17

N₁N₄E₃C₃

ϕ

1

1

1

0.9979

1

0.9998

18

N₁N₄E₃L₃

ϕ

1

1

0.9702

0.9946

0.9995

0.9982

19

N₁N₄C₃L₃

ϕ

1

1

1

0.9870

1

0.9999

20

N₂N₃E₄C₄

ϕ

0.9800

0.9545

0.9904

0.8979

0.9766

0.9663

21

N₂N₃E₄L₄

ϕ

1

1

0.9798

0.0500

0.9816

0.9898

22

N₂N₃C₄L₄

ϕ

0.9988

0.9978

0.9938

0.4893

0.9909

0.9846

23

N₂N₄E₁C₃

ϕ

1

1

0.8843

0.9872

0.9989

0.9964

24

N₂N₄E₁L₃

ϕ

1

1

0.9666

0.7357

0.9994

0.9976

25

N₂N₄C₁L₃

ϕ

1

1

0.9865

0.3634

0.9996

0.9987

26

N₃N₄E₂C₁

ϕ

1

0.99998

0.9321

0.3630

0.9738

0.9667

27

N₃N₄E₂L₁

ϕ

0.9951

0.9954

0.9393

0.6199

0.9915

0.9874

28

N₃N₄C₂L₁

ϕ

0.9997

0.9983

0.9953

0.3637

0.9907

0.9859

29

3NE rel

ϕ

0.5444

0.5842

0.4909

0.2515

0.5685

0.4633

30

3NC rel

ϕ

0.9572

0.8650

0.7551

0.1591

0.6984

0.6555

31

3NL rel

ϕ

0.6181

0.6983

0.6562

0.9432

0.8009

0.7332

32

4N rel

β

0.8822

0.8796

0.2782

0.6377

0.9013

0.9077

33

4N rel

β

0.9082

0.9249

0.0612

0.8409

0.8526

0.8496

34

4N rel

β

0.8344

0.6814

0.4174

0.7505

0.6934

0.7279

35

4Logist ind

ϕ

0.3846

0.3538

0.7429

0.0109

0.5109

0.5171

36

4Lap ind

ϕ

0.6833

0.7130

0.8456

0.0109

0.8250

0.8092

37

4B (10, 0.1) ind

ϕ

1.0000

1.0000

0.7956

0.0108

0.9999

0.9996

38

4t [100] ind

β

0.7194

0.6863

0.4734

0.9998

0.8090

0.7993

39

4χ² [100] ind

β

0.6423

0.6945

0.4215

0.9890

0.7484

0.7466

40

4B (20, 0.5) ind

β

0.3549

0.3628

0.3415

0.9891

0.4726

0.5652

41

4N ind

β

0.6360

0.6750

0.2585

0.7481

0.6993

0.7342

42

2N2N⁻¹ ind

ϕ

1

1

1

0.9993

1

0.9999

43

2N2χ² (2, 4) ind

ϕ

0.7991

0.8737

0.8159

0.0936

0.9203

0.8948

44

2N2χ² [1] ind

ϕ

0.9991

0.9997

0.9166

0.1598

0.9978

0.9947

45

2N2C ind

ϕ

0.9996

0.9978

0.6199

0.2506

0.9750

0.9601

46

4N ind

β

0.4665

0.3009

0.5901

0.9755

0.8038

0.8033

47

3N1N⁻¹ ind

ϕ

1

1

0.9999

0.9998

0.9995

0.9981

48

3N1χ² [2] ind

ϕ

0.7880

0.8968

0.3631

0.2504

0.8121

0.7306

49

3N1χ² [1] ind

ϕ

1

0.9972

0.9449

0.0500

0.9877

0.9733

50

3N1C ind

ϕ

1

1

0.9872

0.9946

0.9946

0.9868