annex 5: statistical data analysis -...

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Annex 5: Statistical data analysis Exchangeable cations (SA10) Acid cations, exchangeable acidity and Free H+ 5 th FSCC Interlaboratory Comparison 2007

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Annex 5: Statistical data

analysis

Exchangeable cations (SA10)

Acid cations, exchangeable acidity

and Free H+

5th FSCC Interlaboratory Comparison 2007

Exchangeable acidity

327

8442373436

3141330678135566845543164102160

8554059833826716311

0.0 0.5 1.0 1.5 2.0 2.5

Location

Labora

tory

Num

ber

6 - Exchangeable Acidity - Sample A

Dot plot sample A

327

843736

342303413671468214540548164563563

831605559108311387126

0 1 2 3 4

Location

Labora

tory

Num

ber

6 - Exchangeable Acidity - Sample B

Dot plot sample B

30

64

59

84

10

34

55

36

63

26

83

81

67

0.0 0.2 0.4 0.6 0.8

16.66;17.60;17.74

Location

Labora

tory

Num

ber

6 - Exchangeable Acidity - Sample C

Dot plot sample C

327

843442378136

3146430211310355468453831714067

85526116059638356

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Location

Labora

tory

Num

ber

6 - Exchangeable Acidity - Sample D

Dot plot sample D

34

11

42

38

21

7

32

36

30

68

13

31

14

84

59

40

3

10

8

83

45

35

64

60

67

71

26

63

54

55

56

5 10 15 20

30.9

Location

Labora

tory

Num

ber

6 - Exchangeable Acidity - Sample E

Dot plot sample E

0.0 0.5 1.0 1.5 2.0 2.5 3.0

05

10

15

6 - Exchangeable Acidity - Sample A - mean

N:

33

NA

: 0

Z:

0 E

: 0

U:

33

a:

1.4

23

m

: 1

.39

s:

0.5

55

7

6.1%12.1%

48.5%

15.2% 15.2%

3%

0 1 2 3 4

04

812

6 - Exchangeable Acidity - Sample B - mean

N:

33

NA

: 0

Z:

0 E

: 1

,0 U

: 3

2

a:

3.0

76

m

: 3

.19

3

s:

0.8

94

1

3.1%0% 0%

3.1% 3.1%

21.9%

43.8%

15.6%9.4%

0.0742(32)

0.0 0.2 0.4 0.6 0.8 1.0

02

46

8

6 - Exchangeable Acidity - Sample C - mean

N:

13

NA

: 0

Z:

0 E

: 0

,1 U

: 1

2

a:

1.4

94

m

: 0

.08

s:

4.7

64

75%

16.7%

0% 0%8.3%

17.33(67)

Histogram of the means of samples A, B and C

0.0 0.5 1.0 1.5 2.0 2.5 3.0

04

812

6 - Exchangeable Acidity - Sample D - mean

N:

33

NA

: 0

Z:

0 E

: 0

U:

33

a:

1.9

16

m

: 1

.99

7

s:

0.5

82

4

6.1%0%

9.1%

36.4% 39.4%

9.1%

0 5 10 15 20 25

05

10

15

6 - Exchangeable Acidity - Sample E - mean

N:

31

NA

: 0

Z:

0 E

: 0

U:

31

a:

7.9

56

m

: 7

.18

7

s:

4.2

66

22.6%

58.1%

16.1%

0% 3.2%

Histogram of the means of samples D and E

0.0 0.5 1.0 1.5 2.0 2.5

A

0.0336(32); 0.4323(7) 2.297(26); 2.34(71); 2.483(63); 2.55(11)

84;42;37;34;36;3;14<13;30;67;81;35;56<68;45;54>31;64;10;21;60;8;55>40;59;83;38

O:

2,4

/ U

: 3

3

1 2 3 4

B

0.4673(7); 1.893(84); 2.167(37) 4.32(71); 4.343(26)

36;3;42;30;34<13;67;14;68;21;45<40;54;81;64>56;35;63;8;31;60>55;59;10;83;11;38

O:

3,2

/ U

: 3

2

0.0 0.2 0.4 0.6 0.8

C

0.32(83); 0.8(81)

30;64;59<84;10<34;55>36;63>26

O:

0,2

/ U

: 1

2

6 - Exchangeable Acidity - mean

Box plot of the means of samples A, B and C

0.0 0.5 1.0 1.5 2.0 2.5 3.0

D

0.08763(32); 0.4187(7); 1.04(84) 2.88(83); 2.95(56)

34;42;37;81;36;3<14;64;30;21;13;10<35;54;68>45;38;31;71;40;67;8>55;26;11;60;59;63

O:

3,2

/ U

: 3

3

5 10 15 20

E

13.07(54); 14.13(55); 24.1(56)

34;11;42;38;21;7;32;36<30;68;13;31;14;84<59;40;3>10;8;83;45;35;64>60;67;71;26;63

O:

0,3

/ U

: 3

1

6 - Exchangeable Acidity - mean

Box plot of the means of samples D and E

Histogram of the standard deviations of samples A, B and C

0.0 0.05 0.10 0.15 0.20 0.25 0.30

05

10

15

6 - Exchangeable Acidity - Sample A - stdev

N: 31 N

A: 0 Z

: 0 E

: 0 U

: 31

a: 0

.06954 m

: 0

.04041 s: 0

.06471

54.8%

19.4% 16.1%

6.5%0% 3.2%

0.0 0.1 0.2 0.3

02

46

812

6 - Exchangeable Acidity - Sample B - stdev

N: 29 N

A: 0 Z

: 0 E

: 0 U

: 29

a: 0

.09623 m

: 0

.05508 s: 0

.09201

41.4%

20.7%13.8% 13.8%

0%3.4%

6.9%

0.0 0.01 0.02 0.03 0.04 0.05 0.06

01

23

4

6 - Exchangeable Acidity - Sample C - stdev

N: 8 N

A: 0 Z

: 0 E

: 0,1

U: 7

a: 0

.09072 m

: 0

.01524 s: 0

.2013

14.3%

57.1%

0%

14.3%

0%

14.3%

0.5873(67)

Histogram of the standard deviations of samples D and E

0.0 0.1 0.2 0.3 0.4

02

46

8

6 - Exchangeable Acidity - Sample D - stdev

N: 28 N

A: 0 Z

: 0 E

: 0 U

: 28

a: 0

.08568 m

: 0

.06208 s: 0

.08456

39.3%

25%21.4%

7.1%3.6%

0% 0% 0%3.6%

0.0 0.2 0.4 0.6 0.8

04

812

6 - Exchangeable Acidity - Sample E - stdev

N: 28 N

A: 0 Z

: 0 E

: 0,2

U: 26

a: 0

.397 m

: 0

.09918 s: 1

.122

53.8%

23.1%

7.7%3.8% 3.8% 3.8%

0%3.8%

1.134(67); 5.973(56)

Box plot of the standard deviations of samples A, B and C

0.0 0.05 0.10 0.15 0.20 0.25 0.30

A

0.1665(42); 0.2969(81)

32;45;30;54;8;64;31;68<40;34;55;56;10;13<7;21;84>37;59;36;71;63;35>11;38;14;60;26;67

O: 0,2

/ U

: 31

0.0 0.1 0.2 0.3

B

0.2517(37); 0.3332(42); 0.3487(71)

8;55;36;54;35;40;7;45<31;11;10;84;14<30;64;63>59;68;26;13;56;34>21;60;38;67

O: 0,3

/ U

: 29

0.0 0.01 0.02 0.03 0.04 0.05

C

0.05033(26)

30;36<55<84>63>59

O: 0,1

/ U

: 7

6 - Exchangeable Acidity - stdev

Box plot of the standard deviations of samples D and E

0.0 0.1 0.2 0.3 0.4

D

0.4045(56)

7;32;36;31;40;54;55<68;64;13;10;30;37<38;21>35;11;59;8;14;26>63;71;34;67;60;42

O: 0,1

/ U

: 28

0.0 0.2 0.4 0.6

E

0.2987(42); 0.3106(32); 0.4366(64); 0.5384(63); 0.7685(71)

36;38;31;30;55;54;45<35;68;10;40;7<59;84>13;11;60;8;14>26;21

O: 0,5

/ U

: 26

6 - Exchangeable Acidity - stdev

Laboratory

Mandel's

h

-3-2

-10

12

3

10

11

13

14

21

26 3

30

31

32

34

35

36

37

38

40

42

45

54

55

56

59

60

63

64

67

68 7

71 8

83

84

6 - Exchangeable Acidity - Sample AStep:2; Nlab:32; Mgen:1.428; Fval:162.9; Pval:0; sRep:0.07653; sLab:0.5622; sRpr:0.5674; CV:39.74

Laboratory

Mandel's

k

0.0

1.0

2.0

10

11

13

14

21

26 3

30

31

32

34

35

36

37

38

40

42

45

54

55

56

59

60

63

64

67

68 7

71 8

83

84

E: k81

Mandel’s h and k plots of sample A

Laboratory

Mandel's

h

-3-2

-10

12

3

10

11

13

14

21

26 3

30

31

34

35

36

37

38

40

45

54

55

56

59

60

63

64

67

68 8

81

83

84

6 - Exchangeable Acidity - Sample BStep:3; Nlab:29; Mgen:3.235; Fval:84.83; Pval:0; sRep:0.09691; sLab:0.5123; sRpr:0.5213; CV:16.12

Laboratory

Mandel's

k

0.0

0.5

1.0

1.5

2.0

2.5

10

11

13

14

21

26 3

30

31

34

35

36

37

38

40

45

54

55

56

59

60

63

64

67

68 8

81

83

84

S: 37

E: h32;k

71;k

42;h

7

Mandel’s h and k plots of sample B

Laboratory

Mandel's

h

-2-1

01

2

10

30

34

36

55

63

83

84

6 - Exchangeable Acidity - Sample CStep:4; Nlab:8; Mgen:0.1195; Fval:309.8; Pval:7.772e-014; sRep:0.009498; sLab:0.09636; sRpr:0.09682; CV:81.05

Laboratory

Mandel's

k

0.0

0.5

1.0

1.5

2.0

10

30

34

36

55

63

83

84

E: hk67;k

26;h

81;k

59

Mandel’s h and k plots of sample C

Laboratory

Mandel's

h

-3-2

-10

12

3

10

11

13

14

21

26 3

30

31

32

34

35

36

37

38

40

42

45

54

55

59

60

63

64

67

68 7

71 8

81

83

84

6 - Exchangeable Acidity - Sample DStep:2; Nlab:32; Mgen:1.884; Fval:128.5; Pval:0; sRep:0.0857; sLab:0.5587; sRpr:0.5652; CV:30

S: 32

Laboratory

Mandel's

k

0.0

1.0

2.0

10

11

13

14

21

26 3

30

31

32

34

35

36

37

38

40

42

45

54

55

59

60

63

64

67

68 7

71 8

81

83

84

E: k56

Mandel’s h and k plots of sample D

Laboratory

Mandel's

h

-3-2

-10

12

3

10

11

13

14

21

26 3

30

31

32

34

35

36

38

40

42

45

54

55

59

60

68 7 8

83

84

6 - Exchangeable Acidity - Sample EStep:6; Nlab:26; Mgen:6.934; Fval:1755; Pval:0; sRep:0.1229; sLab:2.972; sRpr:2.975; CV:42.9

Laboratory

Mandel's

k

0.0

0.5

1.0

1.5

2.0

2.5

10

11

13

14

21

26 3

30

31

32

34

35

36

38

40

42

45

54

55

59

60

68 7 8

83

84

S: 32,4

2

E: hk56;k

67;k

71;k

63;k

64

Mandel’s h and k plots of sample E

Exchangeable Aluminium

84644255858137346758

36

483638

73513301483826356106845403154322360

87121592611

0.5 1.0 1.5 2.0 2.5

Location

Labora

tory

Num

ber

6 - Exchangeable Al - Sample A

Dot plot sample A

81556484423734586785

33682

76

30481383386823143556453263544060

810315971262111

1 2 3 4

Location

Labora

tory

Num

ber

6 - Exchangeable Al - Sample B

Dot plot sample B

85

30

6

55

67

13

64

10

40

59

60

83

26

7

36

82

81

0.0 0.05 0.10 0.15

0.64;0.64;0.65

Location

Labora

tory

Num

ber

6 - Exchangeable Al - Sample C

Dot plot sample C

84645581428534378223145836

73

384867301310

66368355631408371325426

84521605911

0.5 1.0 1.5 2.0

Location

Labora

tory

Num

ber

6 - Exchangeable Al - Sample D

Dot plot sample D

34641167

755428558381021836036

368133556458214

64831402663233259

8547130

0.4 0.6 0.8 1.0 1.2

6.89;7.18;7.24

Location

Labora

tory

Num

ber

6 - Exchangeable Al - Sample E

Dot plot sample E

0.0 0.5 1.0 1.5 2.0 2.5

05

15

25

6 - Exchangeable Al - Sample A - mean

N:

39

NA

: 0

Z:

0 E

: 0

U:

39

a:

1.1

32

m

: 1

.14

3

s:

0.4

05

2

10.3% 12.8%

64.1%

10.3%2.6%

1 2 3 4

05

10

15

6 - Exchangeable Al - Sample B - mean

N:

39

NA

: 0

Z:

0 E

: 0

U:

39

a:

2.6

83

m

: 2

.8

s:

0.7

04

6

2.6%7.7%

5.1%10.3%

35.9% 33.3%

5.1%

0.0 0.02 0.04 0.06 0.08 0.10 0.12 0.14

02

46

6 - Exchangeable Al - Sample C - mean

N:

17

NA

: 0

Z:

0 E

: 0

,1 U

: 1

6

a:

0.0

82

69

m

: 0

.05

63

3

s:

0.1

50

6

43.8%

6.2%12.5%

18.8%

6.2%0%

12.5%

0.6433(81)

Histogram of the means of samples A, B and C

0.5 1.0 1.5 2.0

02

46

8

6 - Exchangeable Al - Sample D - mean

N:

39

NA

: 0

Z:

0 E

: 0

U:

39

a:

1.5

3

m:

1.6

4

s:

0.4

40

8

5.1%7.7%

2.6% 2.6%5.1%

20.5%23.1%

28.2%

5.1%

0.2 0.4 0.6 0.8 1.0 1.2

02

46

8

6 - Exchangeable Al - Sample E - mean

N:

36

NA

: 0

Z:

0 E

: 0

,1 U

: 3

5

a:

0.8

98

1

m:

0.7

51

7

s:

1.0

94

2.9%

20%

5.7%2.9%

8.6%

14.3%11.4%

22.9%

8.6%

2.9%

7.103(30)

Histogram of the means of samples D and E

0.5 1.0 1.5 2.0 2.5

A

0.2(84); 0.4533(64); 0.47(42); 0.4993(55); 0.548(85); 0.5767(81) 1.64(59); 1.707(26); 2.463(11)

37;34;67;58<3;6;48;36;38;7;35;13<30;14;83>82;63;56;10;68;45;40;31>54;32;23;60;8;71;21

O:

6,3

/ U

: 3

9

1.0 1.5 2.0 2.5 3.0 3.5

B

0.63(81); 1.084(55); 1.097(64); 1.19(84); 1.867(42) 3.853(11)

37;34;58;67;85<3;36;82;7;6;30;48;13<83;38;68>23;14;35;56;45;32;63;54>40;60;8;10;31;59;71;26;21

O:

5,1

/ U

: 3

9

0.0 0.02 0.04 0.06 0.08 0.10 0.12

C

85;30;6;55<67;13;64<10;40>59;60;83>26;7;36;82

O:

0,0

/ U

:16

6 - Exchangeable Al - mean

Box plot of the means of samples A, B and C

0.5 1.0 1.5 2.0

D

0.4067(84); 0.5933(64); 0.6527(55); 0.66(81); 0.7133(42); 0.8873(85)

34;37;82;23<14;58;36;7;3;38;48;67<30;13;10>6;63;68;35;56;31;40;83>71;32;54;26;8;45;21;60;59;11

O:

6,0

/ U

: 3

9

0.4 0.6 0.8 1.0

E

34;64;11;67;7;55;42;85;58<38;10;21;83;60;36;3<68;13;35>56;45;82;14;6;48;31>40;26;63;23;32;59;8;54;71

O:

0,0

/ U

:35

6 - Exchangeable Al - mean

Box plot of the means of samples D and E

Histogram of the standard deviations of samples A, B and C

0.0 0.02 0.04 0.06 0.08 0.10 0.12 0.14

05

10

15

6 - Exchangeable Al - Sample A - stdev

N: 39 N

A: 0 Z

: 0 E

: 0,1

U: 38

a: 0

.04162 m

: 0

.02 s: 0

.05625

50%

28.9%

5.3% 2.6% 0% 2.6%10.5%

0.2879(85)

0.0 0.05 0.10 0.15 0.20 0.25 0.30

05

10

15

6 - Exchangeable Al - Sample B - stdev

N: 39 N

A: 0 Z

: 0 E

: 0,1

U: 38

a: 0

.08024 m

: 0

.05132 s: 0

.0926

50%

26.3%

5.3%10.5%

2.6% 5.3%

0.4428(42)

0.0 0.005 0.010 0.015 0.020

01

23

45

6 - Exchangeable Al - Sample C - stdev

N: 11 N

A: 0 Z

: 0 E

: 0 U

: 11

a: 0

.007317 m

: 0

.005774 s: 0

.005414

36.4%

45.5%

0%

18.2%

Histogram of the standard deviations of samples D and E

0.0 0.05 0.10 0.15 0.20

04

812

6 - Exchangeable Al - Sample D - stdev

N: 39 N

A: 0 Z

: 0 E

: 0 U

: 39

a: 0

.04915 m

: 0

.0265 s: 0

.04464

35.9%

17.9%

10.3%12.8%

7.7%10.3%

2.6%0% 0%

2.6%

0.0 0.05 0.10 0.15 0.20

05

10

15

6 - Exchangeable Al - Sample E - stdev

N: 34 N

A: 0 Z

: 0 E

: 0 U

: 34

a: 0

.04475 m

: 0

.02082 s: 0

.04946

47.1%

14.7% 11.8%5.9% 5.9% 2.9% 5.9%

0% 2.9% 2.9%

Box plot of the standard deviations of samples A, B and C

0.02 0.04 0.06 0.08 0.10 0.12 0.14

A

0.0741(14); 0.1159(71); 0.1249(35); 0.13(42); 0.1301(63); 0.138(11)

81;21;3;38;45;56;55;37;54;83<58;64;13;7;30;40;60<84;31;48;34>26;10;8;68;6;59;67>32;82;23;36

O: 0,6

/ U

: 38

0.0 0.05 0.10 0.15 0.20 0.25

B

0.1518(71); 0.1601(21); 0.1664(38); 0.1817(6); 0.2066(63); 0.2719(85); 0.2779(35)

8;64;58;36;81;40;13;55;32;45<37;83;3;54;31;84;14<82;34;56;30>10;26;7;60;23;59;67>68;11;48

O: 0,7

/ U

: 38

0.0 0.005 0.010 0.015

C

0.01732(82)

6;40;55<13;64<81>7;36>60;26

O: 0,1

/ U

: 11

6 - Exchangeable Al - stdev

Box plot of the standard deviations of samples D and E

0.0 0.05 0.10 0.15 0.20

D

0.1358(23); 0.1973(82)

13;3;55;7;36;37;31;45;32;58<38;81;34;68;40;56;64;83<21;6;10>84;26;63;30;35;59;54;48>71;60;8;14;42;67;11;85

O: 0,2

/ U

: 39

0.0 0.05 0.10 0.15

E

0.1137(23); 0.1229(71); 0.1308(82); 0.1662(14); 0.1872(30)

55;36;13;21;3;32;7;40;11<64;10;83;31;8;45<6;38;35;54>67;26;34;68;85;48>42;63;59;56

O: 0,5

/ U

: 34

6 - Exchangeable Al - stdev

Labora

tory

Mandel's h

-2 0 2

10

11

13

14

21

23

26

3

30

31

32

34

35

36

37

38

40

42

45

48

54

55

56

58

59

6

60

63

64

67

68

7

71

8

81

82

83

84

6 - E

xch

an

ge

ab

le A

l - Sa

mp

le A

Ste

p:2

; Nla

b:3

8; M

gen:1

.148; F

val:1

72.9

; Pval:0

; sR

ep:0

.05254; s

Lab:0

.3977; s

Rpr:0

.4012; C

V:3

4.9

5

S: 11

Labora

tory

Mandel's k

0.0 1.0 2.0

10

11

13

14

21

23

26

3

30

31

32

34

35

36

37

38

40

42

45

48

54

55

56

58

59

6

60

63

64

67

68

7

71

8

81

82

83

84

S: 11

E: k85

Mande

l’s h

and k

plo

ts o

f sam

ple

A

Labora

tory

Mandel's h

-2 0 2

10

11

13

14

21

23

26

3

30

31

32

34

36

37

38

40

45

48

54

55

56

58

59

6

60

63

64

67

68

7

71

8

81

82

83

84

6 - E

xch

an

ge

ab

le A

l - Sa

mp

le B

Ste

p:4

; Nla

b:3

6; M

gen:2

.702; F

val:2

42.3

; Pval:0

; sR

ep:0

.0799; s

Lab:0

.7166; s

Rpr:0

.721; C

V:2

6.6

8

Labora

tory

Mandel's k

0.0 1.0 2.0

10

11

13

14

21

23

26

3

30

31

32

34

36

37

38

40

45

48

54

55

56

58

59

6

60

63

64

67

68

7

71

8

81

82

83

84

S: 63

E: k42;k35;k85

Mande

l’s h

and k

plo

ts o

f sam

ple

B

Laboratory

Mandel's

h

-2-1

01

2

10

13

26

30

36

40

55 6

60

64

67 7

82

83

6 - Exchangeable Al - Sample CStep:2; Nlab:14; Mgen:0.0501; Fval:100.3; Pval:0; sRep:0.007786; sLab:0.0448; sRpr:0.04547; CV:90.77

Laboratory

Mandel's

k

0.0

0.5

1.0

1.5

2.0

2.5

10

13

26

30

36

40

55 6

60

64

67 7

82

83

S: 82

E: h81

Mandel’s h and k plots of sample C

Labora

tory

Mandel's h

-2 0 2

10

11

13

14

21

23

26

3

30

31

32

34

35

36

37

38

40

42

45

48

54

55

56

58

59

6

60

63

64

67

68

7

71

8

81

83

84

85

6 - E

xch

an

ge

ab

le A

l - Sa

mp

le D

Ste

p:2

; Nla

b:3

8; M

gen:1

.535; F

val:1

73; P

val:0

; sR

ep:0

.05872; s

Lab:0

.4445; s

Rpr:0

.4484; C

V:2

9.2

2

Labora

tory

Mandel's k

0.0 1.0 2.0

10

11

13

14

21

23

26

3

30

31

32

34

35

36

37

38

40

42

45

48

54

55

56

58

59

6

60

63

64

67

68

7

71

8

81

83

84

85

E: k82

Mande

l’s h

and k

plo

ts o

f sam

ple

D

Laboratory

Mandel's

h

-20

2

10

11

13

21

23

26 3

31

32

34

35

36

38

40

42

45

48

54

55

56

58

59 6

60

63

64

67

68 7

71 8

82

83

85

6 - Exchangeable Al - Sample EStep:3; Nlab:34; Mgen:0.7164; Fval:82.07; Pval:0; sRep:0.05034; sLab:0.2617; sRpr:0.2665; CV:37.19

Laboratory

Mandel's

k

0.0

1.0

2.0

10

11

13

21

23

26 3

31

32

34

35

36

38

40

42

45

48

54

55

56

58

59 6

60

63

64

67

68 7

71 8

82

83

85

S: 82

E: hk30;k

14

Mandel’s h and k plots of sample E

Exchangeable Fe

541330

632

3485864

8856845344283551135596756

7212331634026601271828177

0.0 0.02 0.04 0.06 0.08 0.10 0.12

1.91;2.76;3.540.36;0.39;0.40

0.21;0.22

Location

Labora

tory

Num

ber

6 - Exchangeable Fe - Sample A

Dot plot sample A

64553742

38336

6143448305823456756132135635432

7316810

88559407126121160828177

0.05 0.10 0.15 0.20

7.03; 8.38;11.160.39;0.40;0.410.32;0.32;0.39

Location

Labora

tory

Num

ber

6 - Exchangeable Fe - Sample B

Dot plot sample B

32

68

64

13

55

85

67

45

59

63

83

21

40

12

26

60

7

34

23

82

77

81

0.0 0.02 0.04 0.06 0.08 0.10 0.12

0.30;0.39;0.51

0.40;0.41;0.41

0.16;0.17

Location

Labora

tory

Num

ber

6 - Exchangeable Fe - Sample C

Dot plot sample C

32

30

85

68

13

64

55

67

63

83

40

7

35

54

21

26

23

12

60

82

81

77

0.0 0.02 0.04 0.06 0.08 0.10 0.12 0.14

0.36;0.51;1.01

0.39;0.39;0.40

0.16;0.19

Location

Labora

tory

Num

ber

6 - Exchangeable Fe - Sample D

Dot plot sample D

64678555112134

74283581435362348306810

35613406063

626313271455954

8128277

0.1 0.2 0.3 0.4 0.5

23.08;23.59;24.36

Location

Labora

tory

Num

ber

6 - Exchangeable Fe - Sample E

Dot plot sample E

0.0 0.02 0.04 0.06 0.08 0.10

05

10

15

20

6 - Exchangeable Fe - Sample A - mean

N:

35

NA

: 0

Z:

0 E

: 0

,3 U

: 3

2

a:

0.1

17

7

m:

0.0

2

s:

0.4

60

9

62.5%

21.9%

3.1% 6.2% 6.2%

0.1867(82); 0.3833(81); 2.737(77)

0.05 0.10 0.15 0.20

04

812

6 - Exchangeable Fe - Sample B - mean

N:

39

NA

: 0

Z:

0 E

: 0

,3 U

: 3

6

a:

0.3

47

6

m:

0.1

06

7

s:

1.4

2.8% 2.8%

11.1%

19.4%

36.1%

19.4%

0%5.6%

2.8%

0.3433(82); 0.4(81); 8.857(77)

0.0 0.005 0.010 0.015 0.020 0.025 0.030

02

46

8

6 - Exchangeable Fe - Sample C - mean

N:

22

NA

: 0

Z:

0 E

: 0

,3 U

: 1

9

a:

0.0

53

55

m

: 0

.01

16

7

s:

0.1

17

6

42.1%

15.8%

5.3%

15.8%10.5% 10.5%

0.1533(82); 0.4(77); 0.4067(81)

Histogram of the means of samples A, B and C

0.0 0.01 0.02 0.03 0.04 0.05

02

46

8

6 - Exchangeable Fe - Sample D - mean

N:

22

NA

: 0

Z:

0 E

: 0

,3 U

: 1

9

a:

0.0

66

2

m:

0.0

13

17

s:

0.1

52

52.6%

26.3%

5.3% 5.3%10.5%

0.1633(82); 0.3933(81); 0.6267(77)

0.1 0.2 0.3 0.4 0.5

02

46

8

6 - Exchangeable Fe - Sample E - mean

N:

37

NA

: 0

Z:

0 E

: 0

,1 U

: 3

6

a:

0.8

39

9

m:

0.1

93

3

s:

3.8

6

13.9%16.7%

25%

19.4%

8.3% 8.3%5.6%

0% 0%2.8%

23.68(77)

Histogram of the means of samples D and E

0.02 0.04 0.06 0.08

A

0.06333(26); 0.06333(60); 0.09333(12); 0.095(71)

54;13;30;6;32;3;48;58<64;8;85;68;45;34<42;83;55;11>35;59;67;56;7;21>23;31;63;40

O:

0,4

/ U

: 3

2

0.05 0.10 0.15

B

0.04(64); 0.04667(55) 0.1733(12); 0.18(11); 0.1867(60)

37;42;3;83;36;6;14<34;48;30;58;23;45;67<56;13;21;35>63;54;32;7;31;68;10>8;85;59;40;71;26

O:

2,3

/ U

: 3

6

0.0 0.005 0.010 0.015 0.020 0.025 0.030

C

32;68;64;13;55<85;67;45;59<63>83;21;40;12>26;60;7;34;23

O:

0,0

/ U

:19

6 - Exchangeable Fe - mean

Box plot of the means of samples A, B and C

0.0 0.01 0.02 0.03 0.04

D

0.03333(23); 0.04333(12); 0.04667(60)

32;30;85;68;13<64;55;67;63<83>40;7;35;54>21;26

O:

0,3

/ U

: 1

9

0.1 0.2 0.3 0.4 0.5

E

0.3967(12); 0.51(82)

64;67;85;55;11;21;34;7;42<83;58;14;35;36;23;48<30;68;10;3>56;13;40;60;63;6;26>31;32;71;45;59;54;8

O:

0,2

/ U

: 3

6

6 - Exchangeable Fe - mean

Box plot of the means of samples D and E

Histogram of the standard deviations of samples A, B and C

0.0 0.005 0.010 0.015 0.020 0.025

04

812

6 - Exchangeable Fe - Sample A - stdev

N: 28 N

A: 0 Z

: 0 E

: 0,2

U: 26

a: 0

.03664 m

: 0

.005774 s: 0

.1529

46.2%38.5%

0%3.8%

11.5%

0.04933(82); 0.8153(77)

0.0 0.005 0.010 0.015

02

46

8

6 - Exchangeable Fe - Sample B - stdev

N: 32 N

A: 0 Z

: 0 E

: 0,4

U: 28

a: 0

.07491 m

: 0

.005774 s: 0

.3708

10.7%

28.6%

35.7%

0%

14.3%

3.6%0%

7.1%

0.04041(82); 0.04359(71); 0.04536(85); 2.106(77)

0.0 0.005 0.010 0.015 0.020 0.025

02

46

8

6 - Exchangeable Fe - Sample C - stdev

N: 13 N

A: 0 Z

: 0 E

: 0,1

U: 12

a: 0

.01209 m

: 0

.002887 s: 0

.02854

66.7%

25%

0% 0%8.3%

0.1054(77)

Histogram of the standard deviations of samples D and E

0.0 0.005 0.010 0.015 0.020 0.025 0.030

02

46

8

6 - Exchangeable Fe - Sample D - stdev

N: 19 N

A: 0 Z

: 0 E

: 0,1

U: 18

a: 0

.02218 m

: 0

.002646 s: 0

.07727

55.6%

33.3%

5.6%0% 0%

5.6%

0.3403(77)

0.0 0.01 0.02 0.03

02

46

8

6 - Exchangeable Fe - Sample E - stdev

N: 29 N

A: 0 Z

: 0 E

: 0,2

U: 27

a: 0

.0314 m

: 0

.005774 s: 0

.1183

33.3%29.6%

22.2%

11.1%

0% 0%3.7%

0.04583(71); 0.6444(77)

Box plot of the standard deviations of samples A, B and C

0.0 0.005 0.010 0.015 0.020

A

0.01528(26); 0.02082(63); 0.02082(81); 0.02121(71)

68;13;54;30;45;6;34<32;55;67;56;7<85;23>42;83;21;12;60>40;31;35

O: 0,4

/ U

: 26

0.0 0.01 0.02 0.03 0.04

B

0.01155(35); 0.01528(60); 0.01528(54); 0.04041(82)

32;45;67;13;55;68;6;36<40;56;7;30;34<12;21;23>31;42;10;48;59;14>81;11;63

O: 0,4

/ U

: 29

0.0 0.005 0.010 0.015 0.020

C

0.02082(82)

68;55;85<13;34<67;7>40;81>60;21

O: 0,1

/ U

: 12

6 - Exchangeable Fe - stdev

Box plot of the standard deviations of samples D and E

0.0 0.005 0.010 0.015 0.020 0.025

D

0.01155(35); 0.02517(82)

68;32;30;55;67<85;13;7<64;40>26;23;54>60;12;81

O: 0,2

/ U

: 18

0.0 0.01 0.02 0.03 0.04

E

0.01732(63); 0.03053(85); 0.04583(71)

55;40;45;6;36;32;56<7;67;21;10;54;59<8;26>35;68;42;82;14;12>23;30;48;34

O: 0,3

/ U

: 28

6 - Exchangeable Fe - stdev

Labora

tory

Mandel's h

-3 -2 -1 0 1 2 3

11

13

21

23

3

30

31

32

34

35

40

42

45

48

54

55

56

58

59

6

64

67

68

7

8

83

85

6 - E

xch

an

ge

ab

le F

e - S

am

ple

AS

tep:6

; Nla

b:2

7; M

gen:0

.01714; F

val:2

1.6

8; P

val:0

; sR

ep:0

.003923; s

Lab:0

.0103; s

Rpr:0

.01102; C

V:6

4.2

9

Labora

tory

Mandel's k

0.0 0.5 1.0 1.5 2.0 2.5

11

13

21

23

3

30

31

32

34

35

40

42

45

48

54

55

56

58

59

6

64

67

68

7

8

83

85

S: 35

E: hk77;hk81;hk82;h12;k63;hk26;h60

Mande

l’s h

and k

plo

ts o

f sam

ple

A

Labora

tory

Mandel's h

-2 0 2

10

11

12

13

14

21

23

26

3

30

31

32

34

35

36

37

40

42

45

48

54

55

56

58

59

6

60

63

64

67

68

7

8

83

6 - E

xch

an

ge

ab

le F

e - S

am

ple

BS

tep:3

; Nla

b:3

4; M

gen:0

.1084; F

val:8

1.5

1; P

val:0

; sR

ep:0

.006059; s

Lab:0

.03139; s

Rpr:0

.03197; C

V:2

9.5

Labora

tory

Mandel's k

0.0 1.0 2.0

10

11

12

13

14

21

23

26

3

30

31

32

34

35

36

37

40

42

45

48

54

55

56

58

59

6

60

63

64

67

68

7

8

83

S: 54,60

E: hk77;k71;h81;hk82;k85

Mande

l’s h

and k

plo

ts o

f sam

ple

B

Laboratory

Mandel's

h

-3-2

-10

12

3

12

13

21

23

26

34

40

45

55

60

64

67

68 7

83

85

6 - Exchangeable Fe - Sample CStep:3; Nlab:16; Mgen:0.01235; Fval:52.7; Pval:0; sRep:0.002582; sLab:0.01072; sRpr:0.01103; CV:89.27

Laboratory

Mandel's

k

0.0

0.5

1.0

1.5

2.0

2.5

12

13

21

23

26

34

40

45

55

60

64

67

68 7

83

85

E: hk77;h

81;h

k82

Mandel’s h and k plots of sample C

Laboratory

Mandel's

h

-3-2

-10

12

3

12

13

21

23

26

30

32

40

54

55

60

63

64

67

68 7

83

85

6 - Exchangeable Fe - Sample DStep:4; Nlab:18; Mgen:0.01425; Fval:62.13; Pval:0; sRep:0.003178; sLab:0.01434; sRpr:0.01469; CV:103.1

Laboratory

Mandel's

k

0.0

0.5

1.0

1.5

2.0

2.5

12

13

21

23

26

30

32

40

54

55

60

63

64

67

68 7

83

85

E: hk77;h

81;h

k82;k

35

Mandel’s h and k plots of sample D

Laboratory

Mandel's

h

-20

2

10

11

12

13

14

21

23

26 3

30

31

32

34

35

36

40

42

45

48

54

55

56

58

59 6

60

63

64

67

68 7 8

82

83

6 - Exchangeable Fe - Sample EStep:4; Nlab:34; Mgen:0.2068; Fval:509.3; Pval:0; sRep:0.007456; sLab:0.09706; sRpr:0.09734; CV:47.08

S: 82

Laboratory

Mandel's

k

0.0

1.0

2.0

10

11

12

13

14

21

23

26 3

30

31

32

34

35

36

40

42

45

48

54

55

56

58

59 6

60

63

64

67

68 7 8

82

83

E: hk77;k

71;k

85

Mandel’s h and k plots of sample E

Exchangeable Mn

644255853723

348563640671368106371

73034

63121265883123214

86045545981821177

0.02 0.04 0.06 0.08

0.16;0.16;0.1616.87;16.91;17.04

Location

Labora

tory

Num

ber

6 - Exchangeable Mn - Sample A

Dot plot sample A

6455108342378568216334365667

726

34858

8133045

640542331321159601282148177

0.01 0.02 0.03 0.04 0.05 0.06

13.36;13.66;13.67

Location

Labora

tory

Num

ber

6 - Exchangeable Mn - Sample B

Dot plot sample B

64

85

68

13

30

31

40

55

54

6

60

67

7

32

34

23

63

82

45

81

11

12

77

0.0 0.01 0.02 0.03 0.04

0.61;0.81;1.03

Location

Labora

tory

Num

ber

6 - Exchangeable Mn - Sample C

Dot plot sample C

8464558510234271343768

3633658213856

76730831340

6318132484526

85954601282111477

0.05 0.10 0.15 0.20 0.25 0.30

66.12;70.25;76.32

Location

Labora

tory

Num

ber

6 - Exchangeable Mn - Sample D

Dot plot sample D

112164348542

76855671058837156

34860632345361326543031

64059

83212821477

0.02 0.04 0.06 0.08

23.55;24.17;24.46

Location

Labora

tory

Num

ber

6 - Exchangeable Mn - Sample E

Dot plot sample E

0.02 0.04 0.06 0.08

05

10

15

6 - Exchangeable Mn - Sample A - mean

N:

38

NA

: 0

Z:

0 E

: 0

,2 U

: 3

6

a:

0.4

95

6

m:

0.0

45

17

s:

2.7

4

2.8%8.3% 11.1%

50%

11.1%5.6%

11.1%

0.16(11); 16.94(77)

0.01 0.02 0.03 0.04 0.05

05

10

15

6 - Exchangeable Mn - Sample B - mean

N:

37

NA

: 0

Z:

0 E

: 0

,1 U

: 3

6

a:

0.3

96

7

m:

0.0

3

s:

2.2

25

2.8% 0%

8.3%2.8%

41.7%

22.2%

11.1%5.6% 2.8% 2.8%

13.56(77)

0.0 0.01 0.02 0.03

05

10

15

6 - Exchangeable Mn - Sample C - mean

N:

23

NA

: 0

Z:

0 E

: 0

,1 U

: 2

2

a:

0.0

42

6

m:

0.0

03

s:

0.1

69

68.2%

13.6%4.5% 4.5% 0% 0%

9.1%

0.8167(77)

Histogram of the means of samples A, B and C

0.0 0.05 0.10 0.15 0.20 0.25 0.30

05

10

15

6 - Exchangeable Mn - Sample D - mean

N:

40

NA

: 0

Z:

0 E

: 0

,1 U

: 3

9

a:

1.9

55

m

: 0

.19

27

s:

11

.18

2.6% 2.6%

10.3%

41%35.9%

7.7%

70.9(77)

0.02 0.04 0.06 0.08

02

46

6 - Exchangeable Mn - Sample E - mean

N:

36

NA

: 0

Z:

0 E

: 0

,1 U

: 3

5

a:

0.7

15

6

m:

0.0

5

s:

4.0

02

8.6%

14.3% 14.3%17.1%

14.3%

20%

11.4%

24.06(77)

Histogram of the means of samples D and E

0.02 0.03 0.04 0.05 0.06 0.07

A

0.02(64) 0.06867(45); 0.07133(54); 0.07333(59); 0.07667(81); 0.07667(82)

42;55;85;37;23;3;48;56<36;40;67;13;68;10;63<71;7;30;34>6;31;21;26;58;83;12>32;14;8;60

O:

1,5

/ U

: 3

6

0.01 0.02 0.03 0.04 0.05

B

0.01(64); 0.017(55) 0.04333(12); 0.04333(82); 0.047(14); 0.05333(81)

10;83;42;37;85;68;21<63;34;36;56;67;7;26<3;48;58;8>13;30;45;6;40;54;23>31;32;11;59;60

O:

2,4

/ U

: 3

6

0.0 0.01 0.02 0.03

C

0.02(81); 0.03333(11); 0.03333(12)

64;85;68;13;30;31<40;55;54;6<60;67>7;32;34;23>63;82;45

O:

0,3

/ U

: 2

2

6 - Exchangeable Mn - mean

Box plot of the means of samples A, B and C

0.05 0.10 0.15 0.20 0.25

D

0.04633(84); 0.07(64); 0.1003(55) 0.286(14)

85;10;23;42;71;34;37<68;3;63;36;58;21;38;56<7;67;30>83;13;40;6;31;81;32;48>45;26;8;59;54;60;12;82;11

O:

3,1

/ U

: 3

9

0.02 0.03 0.04 0.05 0.06 0.07

E

11;21;64;34;85;42;7;68;55<67;10;58;83;71;56;3<48;60;63>23;45;36;13;26;54;30>31;6;40;59;8;32;12;82;14

O:

0,0

/ U

:35

6 - Exchangeable Mn - mean

Box plot of the means of samples D and E

Histogram of the standard deviations of samples A, B and C

0.0 0.005 0.010 0.015

02

46

8

6 - Exchangeable Mn - Sample A - stdev

N: 28 N

A: 0 Z

: 0 E

: 0,1

U: 27

a: 0

.007704 m

: 0

.005774 s: 0

.01632

37%

3.7%

40.7%

3.7% 3.7%7.4%

0%3.7%

0.08888(77)

0.0 0.002 0.004 0.006 0.008 0.010 0.012

02

46

8

6 - Exchangeable Mn - Sample B - stdev

N: 21 N

A: 0 Z

: 0 E

: 0,1

U: 20

a: 0

.01124 m

: 0

.001732 s: 0

.03791

55%

10%

30%

0% 0%5%

0.1762(77)

0.0 0.001 0.002 0.003 0.004 0.005 0.006

01

23

45

6 - Exchangeable Mn - Sample C - stdev

N: 8 N

A: 0 Z

: 0 E

: 0,1

U: 7

a: 0

.02795 m

: 0

.0005774 s: 0

.07363

71.4%

0%

28.6%

0.2101(77)

Histogram of the standard deviations of samples D and E

0.0 0.005 0.010 0.015 0.020 0.025 0.030

05

10

15

6 - Exchangeable Mn - Sample D - stdev

N: 38 N

A: 0 Z

: 0 E

: 0,2

U: 36

a: 0

.1437 m

: 0

.005971 s: 0

.8309

33.3%

47.2%

8.3% 5.6% 2.8% 2.8%

0.04373(85); 5.131(77)

0.0 0.005 0.010 0.015 0.020 0.025

02

46

812

6 - Exchangeable Mn - Sample E - stdev

N: 20 N

A: 0 Z

: 0 E

: 0,1

U: 19

a: 0

.02756 m

: 0

.003649 s: 0

.1031

63.2%

26.3%

0%5.3% 5.3%

0.4649(77)

Box plot of the standard deviations of samples A, B and C

0.002 0.004 0.006 0.008 0.010 0.012 0.014

A

0.01415(85)

13;40;31;68;37;55;7<54;45;32;56;30<14;12;59>42;10;67;71;63>60;34;6;36;81;82

O: 0,1

/ U

: 27

0.0 0.002 0.004 0.006 0.008 0.010

B

0.01155(42)

68;32;37;7;34<40;54;67;56<45;6>85;14;81;21>63;12;23;82

O: 0,1

/ U

: 20

0.0001 0.0002 0.0003 0.0004 0.0005

C

68;32<34>7>85

O: 0,0

/ U

:5

6 - Exchangeable Mn - stdev

Box plot of the standard deviations of samples D and E

0.0 0.005 0.010 0.015 0.020 0.025

D

0.01528(8); 0.01604(67); 0.02082(82); 0.02887(71)

6;45;55;54;37;84;68;40;36<13;7;56;10;58;26;3<59;83;34;30>14;32;12;21;23;31;60>63;81;11;48;42

O: 0,4

/ U

: 36

0.0 0.002 0.004 0.006 0.008 0.010 0.012 0.014

E

0.01504(56)

31;34;45;54;55<6;32;7<85;67>30;14;12>23;82;42;71

O: 0,1

/ U

: 18

6 - Exchangeable Mn - stdev

Labora

tory

Mandel's h

-2 0 2

10

12

13

14

21

23

26

3

30

31

32

34

36

37

40

42

45

48

54

55

56

58

59

6

60

63

64

67

68

7

71

8

81

82

83

6 - E

xch

an

ge

ab

le M

n - S

am

ple

AS

tep:3

; Nla

b:3

5; M

gen:0

.04872; F

val:2

6.1

9; P

val:0

; sR

ep:0

.004634; s

Lab:0

.01343; s

Rpr:0

.0142; C

V:2

9.1

5

Labora

tory

Mandel's k

0.0 1.0 2.0

10

12

13

14

21

23

26

3

30

31

32

34

36

37

40

42

45

48

54

55

56

58

59

6

60

63

64

67

68

7

71

8

81

82

83

S: 81,82

E: hk77;h11;k85

Mande

l’s h

and k

plo

ts o

f sam

ple

A

Laboratory

Mandel's

h

-20

2

10

11

12

13

14

21

23

26 3

30

31

32

34

36

37

40

45

48

54

55

56

58

59 6

60

63

64

67

68 7 8

81

82

83

85

6 - Exchangeable Mn - Sample BStep:3; Nlab:35; Mgen:0.03117; Fval:33.03; Pval:0; sRep:0.002519; sLab:0.00823; sRpr:0.008606; CV:27.61

Laboratory

Mandel's

k

0.0

1.0

2.0

10

11

12

13

14

21

23

26 3

30

31

32

34

36

37

40

45

48

54

55

56

58

59 6

60

63

64

67

68 7 8

81

82

83

85

E: hk77;k

42

Mandel’s h and k plots of sample B

Laboratory

Mandel's

h

-3-2

-10

12

3

13

23

30

31

32

34

40

45

54

55 6

60

63

64

67

68 7

82

85

6 - Exchangeable Mn - Sample CStep:4; Nlab:19; Mgen:0.004023; Fval:641.8; Pval:0; sRep:0.000234; sLab:0.003419; sRpr:0.003427; CV:85.2

Laboratory

Mandel's

k

0.0

0.5

1.0

1.5

2.0

2.5

13

23

30

31

32

34

40

45

54

55 6

60

63

64

67

68 7

82

85

S: 34,7

,85

E: hk77;h

k11;h

k12;h

81

Mandel’s h and k plots of sample C

Labora

tory

Mandel's h

-2 0 2

10

11

12

13

14

21

23

26

3

30

31

32

34

36

37

38

40

42

45

48

54

55

56

58

59

6

60

63

64

67

68

7

8

81

82

83

84

6 - E

xch

an

ge

ab

le M

n - S

am

ple

DS

tep:4

; Nla

b:3

7; M

gen:0

.189; F

val:1

00.8

; Pval:0

; sR

ep:0

.008285; s

Lab:0

.04778; s

Rpr:0

.04849; C

V:2

5.6

5

Labora

tory

Mandel's k

0.0 1.0 2.0

10

11

12

13

14

21

23

26

3

30

31

32

34

36

37

38

40

42

45

48

54

55

56

58

59

6

60

63

64

67

68

7

8

81

82

83

84

S: 82

E: hk77;k85;k71

Mande

l’s h

and k

plo

ts o

f sam

ple

D

Laboratory

Mandel's

h

-20

2

10

11

12

13

14

21

23

26 3

30

31

32

34

36

40

42

45

48

54

55

58

59 6

60

63

64

67 7

71 8

82

83

85

6 - Exchangeable Mn - Sample EStep:3; Nlab:33; Mgen:0.04923; Fval:139.4; Pval:0; sRep:0.002623; sLab:0.01782; sRpr:0.01801; CV:36.58

Laboratory

Mandel's

k

0.0

1.0

2.0

10

11

12

13

14

21

23

26 3

30

31

32

34

36

40

42

45

48

54

55

58

59 6

60

63

64

67 7

71 8

82

83

85

E: hk77;k

56;k

68

Mandel’s h and k plots of sample E

Free H+

54

56

67

14

31

48

32

64

13

37

3

68

8

34

59

21

10

35

26

84

81

63

38

71

55

-0.2 0.0 0.2 0.4 0.6 0.8 1.0

1.155;1.179;1.189

1.13

Location

Labora

tory

Num

ber

6 - Free H - Sample A

Dot plot sample A

54

67

48

42

14

64

32

31

13

3

68

37

56

8

59

34

84

35

10

21

26

63

71

38

81

55

-0.2 0.0 0.2 0.4 0.6 0.8

2.495;2.512;2.517

Location

Labora

tory

Num

ber

6 - Free H - Sample B

Dot plot sample B

71

37

56

21

48

68

67

10

84

55

81

54

64

26

-0.2 0.0 0.2 0.4 0.6

Location

Labora

tory

Num

ber

6 - Free H - Sample C

Dot plot sample C

54

37

67

64

14

42

48

31

56

13

32

3

68

8

59

26

21

10

34

84

35

71

81

55

63

-0.2 0.0 0.2 0.4

1.603;1.632;1.638

5.384;5.926;6.746

Location

Labora

tory

Num

ber

6 - Free H - Sample D

Dot plot sample D

37

34

42

67

21

38

36

14

68

40

30

32

31

13

84

59

10

8

3

64

35

26

71

54

55

56

63

0 5 10 15

100.7;107.9;123.9

Location

Labora

tory

Num

ber

6 - Free H - Sample E

Dot plot sample E

0.0 0.5 1.0

05

10

15

6 - Free H - Sample A - mean

N:

25

NA

: 0

Z:

0 E

: 0

,1 U

: 2

4

a:

0.2

07

5

m:

0.0

7

s:

0.3

43

8

4.2% 4.2%

66.7%

12.5%

0%8.3%

0% 4.2%

1.174(55)

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

04

812

6 - Free H - Sample B - mean

N:

26

NA

: 0

Z:

0 E

: 0

,1 U

: 2

5

a:

0.2

89

3

m:

0.1

27

8

s:

0.5

01

6

4%0%

56%

28%

4% 4% 4%

2.508(55)

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8

02

46

6 - Free H - Sample C - mean

N:

14

NA

: 0

Z:

0 E

: 0

U:

14

a:

0.1

07

6

m:

0.0

28

83

s:

0.2

52

8

7.1%

35.7% 35.7%

7.1%0%

14.3%

Histogram of the means of samples A, B and C

-0.2 0.0 0.2 0.4

02

46

8

6 - Free H - Sample D - mean

N:

25

NA

: 0

Z:

0 E

: 0

,2 U

: 2

3

a:

0.3

96

1

m:

0.0

95

63

s:

1.2

16

4.3%0%

4.3%

47.8%

26.1%

13%

4.3%

1.624(55); 6.019(63)

0 5 10 15

02

46

8

6 - Free H - Sample E - mean

N:

26

NA

: 0

Z:

0 E

: 0

,1 U

: 2

5

a:

10

.25

m

: 4

.79

7

s:

20

.79

4%

16%

40%

20%

8%4% 4% 4%

110.8(63)

Histogram of the means of samples D and E

-0.2 0.0 0.2 0.4 0.6 0.8 1.0

A

-0.25(54) 0.3933(81); 0.63(63); 0.77(38); 1.05(71)

56;67;14;31;48<32;64;13;37;3<68;8>34;59;21;10;35>26;84

O:

1,4

/ U

: 2

4

-0.2 0.0 0.2 0.4 0.6 0.8

B

0.6267(38); 0.8133(81)

54;67;48;42;14;64;32<31;13;3;68<37;56;8>59;34;84;35;10>21;26;63;71

O:

0,2

/ U

: 2

5

-0.2 0.0 0.2 0.4 0.6

C

-0.23(71) 0.3033(54); 0.6033(64); 0.6733(26)

37;56;21<48;68<67;10>84;55>81

O:

1,3

/ U

: 1

4

6 - Free H - mean

Box plot of the means of samples A, B and C

-0.2 -0.1 0.0 0.1 0.2 0.3

D

-0.25(54) 0.2667(35); 0.2933(71); 0.3667(81)

37;67;64;14;42<48;31;56;13<32;3;68>8;59;26;21>10;34;84

O:

1,3

/ U

: 2

3

2 4 6 8 10 12 14

E

9.68(71); 11.35(54); 13.76(55); 15.4(56)

34;42;67;21;38;36;14<68;40;30;32<31;13;84>59;10;8;3;64>35;26

O:

0,4

/ U

: 2

5

6 - Free H - mean

Box plot of the means of samples D and E

Histogram of the standard deviations of samples A, B and C

0.0 0.02 0.04 0.06 0.08

02

46

8

6 - Free H - Sample A - stdev

N: 17 N

A: 0 Z

: 0 E

: 0 U

: 17

a: 0

.01803 m

: 0

.01 s: 0

.02209

47.1%

23.5%

5.9%11.8%

0%5.9%

0%5.9%

0.0 0.01 0.02 0.03 0.04 0.05 0.06

02

46

8

6 - Free H - Sample B - stdev

N: 22 N

A: 0 Z

: 0 E

: 0 U

: 22

a: 0

.02042 m

: 0

.01013 s: 0

.01994

50%

9.1% 9.1% 9.1%13.6%

9.1%

0.0 0.02 0.04 0.06 0.08

01

23

4

6 - Free H - Sample C - stdev

N: 6 N

A: 0 Z

: 0 E

: 0 U

: 6

a: 0

.02248 m

: 0

.01369 s: 0

.0247

66.7%

16.7%

0%

16.7%

Histogram of the standard deviations of samples D and E

0.0 0.01 0.02 0.03 0.04 0.05 0.06

02

46

8

6 - Free H - Sample D - stdev

N: 18 N

A: 0 Z

: 0 E

: 0,1

U: 17

a: 0

.05405 m

: 0

.01443 s: 0

.1586

47.1%

29.4%

5.9%0%

5.9%11.8%

0.6857(63)

0.0 0.2 0.4 0.6

02

46

8

6 - Free H - Sample E - stdev

N: 23 N

A: 0 Z

: 0 E

: 0,2

U: 21

a: 0

.8398 m

: 0

.155 s: 2

.496

38.1%

28.6%

4.8%9.5% 9.5%

4.8% 4.8%

3.4(56); 11.84(63)

Box plot of the standard deviations of samples A, B and C

0.0 0.02 0.04 0.06 0.08

A

0.08(71)

37;31;14;13;67<32;68;21<38>64;81;55;59>84;63;26

O: 0

,1 / U

: 1

7

0.0 0.01 0.02 0.03 0.04 0.05 0.06

B

0.05774(38); 0.05774(26)

32;31;13;68;37;64<48;8;67;56<14;55>21;81;35;59>63;42;84;71

O: 0

,2 / U

: 2

2

0.005 0.010 0.015 0.020 0.025 0.030

C

0.03215(54)

67;64<55>81

O: 0

,1 / U

: 5

6 - Free H - stdev

Box plot of the standard deviations of samples D and E

0.0 0.01 0.02 0.03 0.04 0.05

D

0.04619(71); 0.05132(59); 0.05686(81)

31;68;14;13;67<56;32;64<21>26;84;48;55>35

O: 0,3

/ U

: 17

0.0 0.1 0.2 0.3 0.4 0.5 0.6

E

0.6087(67)

31;38;36;55;34;13<42;54;68;10<40;8>14;21;35;32>71;26;64;84

O: 0,1

/ U

: 21

6 - Free H - stdev

Laboratory

Mandel's

h

-2-1

01

2

10

13

14

21 3

31

32

34

37

48

56

67

68 8

6 - Free H - Sample AStep:7; Nlab:14; Mgen:0.04531; Fval:1468; Pval:0; sRep:0.002289; sLab:0.05062; sRpr:0.05067; CV:111.8

Laboratory

Mandel's

k

0.0

0.5

1.0

1.5

2.0

2.5

10

13

14

21 3

31

32

34

37

48

56

67

68 8

O: 21

E: hk71;k

26;h

k55;h

k63;h

k38;k

59;k

84;h

k81;h

54;k

64

Mandel’s h and k plots of sample A

Laboratory

Mandel's

h

-3-2

-10

12

3

10

13

14

21

26 3

31

32

34

35

37

38

48

54

56

59

63

64

67

68

71 8

81

84

6 - Free H - Sample BStep:2; Nlab:24; Mgen:0.2068; Fval:230.2; Pval:0; sRep:0.02549; sLab:0.2228; sRpr:0.2242; CV:108.4

Laboratory

Mandel's

k

0.0

0.5

1.0

1.5

2.0

2.5

10

13

14

21

26 3

31

32

34

35

37

38

48

54

56

59

63

64

67

68

71 8

81

84

E: h55

Mandel’s h and k plots of sample B

Laboratory

Mandel's

h

-2-1

01

2

10

21

37

48

56

67

68

71

84

6 - Free H - Sample CStep:5; Nlab:9; Mgen:-0.02926; Fval:82458; Pval:0; sRep:0.0005092; sLab:0.08442; sRpr:0.08442; CV:-288.5

S: 71

Laboratory

Mandel's

k

0.0

1.0

2.0

3.0

10

21

37

48

56

67

68

71

84

O: 67

E: hk26;k

54;h

k64;k

81;k

55

Mandel’s h and k plots of sample C

Laboratory

Mandel's

h

-3-2

-10

12

3

10

13

14

21

26 3

31

32

34

37

48

56

64

67

68 8

84

6 - Free H - Sample DStep:5; Nlab:17; Mgen:0.0841; Fval:184.6; Pval:0; sRep:0.00818; sLab:0.064; sRpr:0.06452; CV:76.71

Laboratory

Mandel's

k

0.0

0.5

1.0

1.5

2.0

2.5

10

13

14

21

26 3

31

32

34

37

48

56

64

67

68 8

84

E: hk63;h

55;k

81h;k

59;k

71;3

5k;h

54

Mandel’s h and k plots of sample D

Laboratory

Mandel's

h

-3-2

-10

12

3

10

13

14

21

26 3

30

31

32

34

35

36

37

38

40

42

54

55

59

64

67

68

71 8

84

6 - Free H - Sample EStep:3; Nlab:25; Mgen:5.611; Fval:495.1; Pval:0; sRep:0.2377; sLab:3.05; sRpr:3.059; CV:54.52

Laboratory

Mandel's

k

0.0

0.5

1.0

1.5

2.0

2.5

10

13

14

21

26 3

30

31

32

34

35

36

37

38

40

42

54

55

59

64

67

68

71 8

84

S: 67

E: hk63;k

56

Mandel’s h and k plots of sample E