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Table 2 Statistical tests for the significance of the power-law property in distributions of rest bouts according to the method described by Clauset et al. (CCFS)

From: Temporal organization of rest defined by actigraphy data in healthy and childhood chronic fatigue syndrome children

No.

Basic parameters

Power Law vs. exponential

Power law test

24h

UP

DOWN

n

<x>

Total

sd

LR

p

LR

p

LR

p

xmax

xmin

α

ntail

p’

1

2286

7.7

17608

21.8

8.7

0.00

2.0

0.04

0.7

0.50

301

4

1.91

758

0.02

2

783

7.9

6218

28.7

12.1

0.00

0.8

0.41

-0.2

0.83

344

1

1.87

783

0.00

3

449

21.4

9595

56.2

17.4

0.00

2.0

0.04

-0.8

0.41

426

1

1.61

449

0.00

4

366

12.3

4514

37.1

8.0

0.00

1.4

0.15

0.6

0.56

401

1

1.64

366

0.42

5

642

8.5

5466

40.4

6.6

0.00

1.8

0.07

-1.2

0.23

549

1

1.81

642

0.00

6

509

13.1

6668

53.2

10.8

0.00

1.6

0.11

-1.0

0.34

512

1

1.78

509

0.01

7

322

17.5

5646

62.7

6.6

0.00

1.4

0.16

-0.3

0.78

592

2

1.69

215

0.26

8

965

13.0

12566

43.5

12.3

0.00

3.3

0.00

-1.5

0.13

541

2

1.73

555

0.05

9

1264

10.8

13604

55.1

12.5

0.00

3.0

0.00

-1.5

0.14

683

1

1.88

1264

0.00

10

1239

9.3

11475

44.5

13.9

0.00

3.2

0.00

-2.0

0.05

501

2

2.02

631

0.00

11

507

11.2

5678

55.8

5.7

0.00

-0.3

0.73

-0.3

0.73

558

2

1.85

298

0.00

12

577

13.5

7806

46.7

15.1

0.00

1.6

0.12

-1.7

0.09

371

1

1.76

577

0.02

13

1625

8.9

14494

31.2

16.3

0.00

0.1

0.95

-0.6

0.52

356

1

1.79

1625

0.00

14

1168

11.8

13771

40.5

7.6

0.00

0.2

0.81

-0.7

0.51

573

7

2.13

383

0.02

15

1050

12.0

12567

49.0

15.4

0.00

1.4

0.15

-1.8

0.07

469

1

1.81

1050

0.00

16

1529

10.6

16184

36.0

9.8

0.00

4.0

0.00

-1.3

0.19

537

3

1.83

696

0.28

17

1226

9.9

12123

51.7

11.3

0.00

1.1

0.27

-1.5

0.14

592

2

2.00

656

0.00

18

491

9.6

4723

42.9

7.6

0.00

2.6

0.01

0.4

0.72

470

1

1.83

491

0.00

19

842

10.5

8850

39.0

10.1

0.00

1.8

0.07

-0.9

0.38

488

2

1.82

483

0.73

20

1787

8.5

15131

36.1

14.9

0.00

4.3

0.00

-1.4

0.15

479

1

1.87

1787

0.00

21

171

21.9

3741

72.4

9.2

0.00

1.0

0.30

0.2

0.85

579

1

1.66

171

0.00

22

572

12.7

7241

40.6

13.0

0.00

2.4

0.02

-0.2

0.88

375

1

1.70

572

0.02

23

555

10.6

5870

36.3

10.6

0.00

1.7

0.09

0.5

0.61

468

1

1.74

555

0.01

24

2244

8.1

18070

33.3

12.3

0.00

4.4

0.00

-2.3

0.02

457

2

1.92

1262

0.00

25

1029

7.5

7738

27.1

9.1

0.00

1.2

0.24

-0.7

0.47

351

2

1.92

575

0.38

26

1073

11.8

12610

28.8

17.9

0.00

1.4

0.17

-1.7

0.09

233

1

1.63

1073

0.00

27

550

10.8

5964

43.5

10.4

0.00

4.1

8.00

-0.6

0.58

454

2

1.88

294

0.01

28

706

9.2

6495

24.4

10.0

0.00

1.7

0.08

-1.3

0.20

227

2

1.80

438

0.10

29

545

13.8

7527

32.3

12.3

0.00

5.7

0.00

0.2

0.82

384

1

1.59

545

0.00

30

1050

9.3

9756

33.4

8.5

0.00

4.7

0.00

-0.6

0.56

383

3

1.90

463

0.37

31

1278

8.9

11314

19.1

3.2

0.00

1.3

0.21

-1.2

0.22

207

7

1.99

348

0.00

32

903

10.7

9647

39.3

12.4

0.00

2.1

0.04

-1.6

0.11

470

1

1.75

903

0.03

33

1994

7.7

15294

35.8

11.0

0.00

5.0

0.00

-2.5

0.01

504

2

1.97

1069

0.00

34

1472

15.7

23068

55.8

5.6

0.00

2.7

0.01

-1.0

0.31

1007

7

1.83

454

0.01

35

1119

10.8

12141

58.5

11.3

0.00

3.1

0.00

-1.3

0.18

866

2

2.00

610

0.00

36

543

15.4

8387

58.5

12.8

0.00

2.8

0.01

-1.6

0.11

501

1

1.73

543

0.00

37

594

11.8

7038

46.9

9.4

0.00

2.1

0.04

0.2

0.82

568

1

1.73

594

0.29

38

1077

10.8

11591

38.0

14.3

0.00

2.7

0.01

-1.2

0.22

422

1

1.75

1077

0.07

39

1812

10.0

18073

32.8

17.6

0.00

2.0

0.05

-2.1

0.04

345

2

1.84

1051

0.00

40

1690

10.0

16965

27.9

13.9

0.00

3.1

0.00

-0.5

0.61

372

2

1.75

1009

0.07

41

756

9.2

6991

33.3

8.4

0.00

2.6

0.01

-0.9

0.35

434

3

1.94

324

0.07

42

1646

10.8

17749

35.0

14.4

0.00

1.8

0.07

-1.2

0.24

483

2

1.78

1004

0.09

43

1542

12.0

18481

52.4

13.0

0.00

1.4

0.17

-0.8

0.43

809

2

1.82

867

0.00

44

1850

8.2

15235

27.3

12.2

0.00

2.2

0.03

0.2

0.81

444

3

1.91

739

0.00

45

1542

12.0

18481

52.4

13.0

0.00

1.4

0.17

-0.8

0.43

809

2

1.82

867

0.00

46

1096

8.0

8746

31.3

13.5

0.00

1.5

0.14

-1.9

0.06

364

2

1.98

568

0.00

47

1316

11.7

15350

49.4

17.5

0.00

2.4

0.02

-1.2

0.21

567

2

1.92

727

0.00

48

425

9.8

4153

30.7

7.9

0.00

3.8

0.00

-0.4

0.70

281

1

1.70

425

0.18

49

1159

9.3

10780

26.3

6.8

0.00

2.8

0.01

-0.8

0.41

267

5

1.90

356

0.20

50

785

11.7

9212

39.8

12.1

0.00

4.8

0.00

-0.2

0.81

439

1

1.70

785

0.18

51

580

10.8

6272

58.0

6.8

0.00

4.5

0.00

-0.9

0.39

704

2

1.94

328

0.02

52

2239

9.4

20994

52.5

10.4

0.00

0.9

0.36

-1.6

0.12

720

3

2.06

945

0.00

53

562

16.7

9385

56.3

16.9

0.00

1.2

0.22

-0.5

0.63

520

1

1.74

562

0.00

54

916

16.1

14710

50.6

24.4

0.00

8.6

0.00

-2.3

0.02

410

1

1.73

916

0.00

55

798

13.0

10413

37.6

14.2

0.00

5.4

0.00

0.2

0.85

502

1

1.64

798

0.09

56

1272

8.9

11302

38.0

12.2

0.00

2.2

0.03

-2.2

0.03

396

1

1.83

1272

0.00

57

612

9.8

5996

39.4

5.6

0.00

0.8

0.45

0.9

0.39

435

4

2.05

250

0.01

mean

1047

11.3

11008

 

11.5

0.05>

2.5

0.05>

-0.9

0.05>

482

2.0

1.83

694

0.1<

s.d.

530

3.1

4761

 

3.9

57

1.6

31

0.8

6

156

1.5

0.1

341

11

  1. n, number of all of the rest bouts; <x>, average length of the rest bout (min); total, total length of rest bout (min); sd, standard deviation of the length of the rest bout (min); LR, log likelihood ratio of the power-law distribution to exponential distribution; p, p-value, positive values of the LR with p<0.05 indicate that the power-law distribution is statistically favored over the alternative distribution. p-values less than 0.05 are indicated in italic. In the power law test, we calculated the p′-value for the best power-law fit for the empirical data set. p′-values larger than 0.1 are indicated in italic. xmax, maximum value of fitted portion; xmin, minimum value of fitted portion; a, exponent of the fitted power law function; ntail, number of bouts with x ≥ xmin.