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Journal of Statistical Distributions and Applications

Table 5 Descriptive statistics for the free marginals case under the null hypothesis

From: Testing the Rasch model with the conditional likelihood ratio test: sample size requirements and bootstrap algorithms

 

mean

%

var

%

cv

%

skew

%

kurt

%

q50

%

q90

%

q95

%

q99

%

limiting: df=4

4.00

 

8.00

 

0.71

 

1.41

 

3.00

 

3.36

 

7.78

 

9.49

 

13.28

 

k=5/n=100

4.38

9.6

9.11

13.8

0.69

−2.6

1.29

−8.9

2.43

−18.8

3.76

12.0

8.43

8.4

10.18

7.3

14.10

6.2

k=5/n=250

4.16

4.1

8.76

9.6

0.71

0.5

1.39

−1.5

2.77

−7.7

3.47

3.4

8.16

4.9

9.98

5.2

13.81

4.0

k=5/n=500

4.08

2.0

8.35

4.4

0.71

0.2

1.41

−0.2

2.93

−2.3

3.42

1.9

7.97

2.4

9.71

2.3

13.58

2.3

k=5/n=750

4.03

0.8

8.16

2.0

0.71

0.2

1.43

1.4

3.16

5.5

3.39

1.0

7.84

0.8

9.52

0.3

13.46

1.4

k=5/n=1000

4.03

0.7

8.09

1.2

0.71

−0.2

1.38

−2.1

2.85

−4.8

3.38

0.7

7.87

1.2

9.55

0.7

13.27

−0.1

k=5/n=2500

4.01

0.1

7.95

−0.6

0.70

−0.5

1.39

−1.9

2.84

−5.4

3.36

0.1

7.78

0.0

9.46

−0.3

13.27

−0.0

k=5/n=5000

4.00

0.1

8.01

0.1

0.71

−0.1

1.44

2.1

3.28

9.2

3.37

0.4

7.79

0.1

9.47

−0.2

13.29

0.1

avg. (df=4)

4.10

2.5

8.35

4.4

0.71

−0.4

1.39

−1.6

2.89

−3.5

3.45

2.8

7.98

2.5

9.70

2.2

13.54

2.0

limiting: df=9

9.00

 

18.00

 

0.47

 

0.94

 

1.33

 

8.34

 

14.68

 

16.92

 

21.67

 

k=10/n=100

9.53

5.9

20.14

11.9

0.47

−0.1

0.92

−2.0

1.27

−5.0

8.86

6.2

15.54

5.8

17.89

5.7

22.82

5.3

k=10/n=250

9.14

1.5

18.51

2.8

0.47

−0.1

0.95

0.7

1.36

2.2

8.47

1.5

14.90

1.5

17.16

1.4

22.05

1.8

k=10/n=500

9.04

0.4

18.04

0.2

0.47

−0.3

0.93

−1.5

1.29

−3.6

8.40

0.7

14.70

0.1

16.91

−0.1

21.75

0.4

k=10/n=750

9.05

0.6

18.13

0.7

0.47

−0.2

0.93

−1.5

1.26

−5.5

8.38

0.4

14.78

0.7

16.97

0.3

21.68

0.1

k=10/n=1000

9.00

0.0

18.02

0.1

0.47

0.0

0.95

0.5

1.34

0.7

8.34

−0.0

14.70

0.1

16.94

0.1

21.66

−0.0

k=10/n=2500

9.03

0.3

18.23

1.3

0.47

0.4

0.95

0.4

1.36

1.8

8.38

0.4

14.70

0.1

17.02

0.6

21.80

0.6

k=10/n=5000

9.02

0.2

18.08

0.5

0.47

−0.0

0.96

1.7

1.39

3.9

8.37

0.3

14.71

0.2

16.98

0.4

21.82

0.7

avg. (df=9)

9.12

1.3

18.45

2.5

0.47

−0.0

0.94

−0.2

1.32

−0.8

8.46

1.4

14.86

1.2

17.12

1.2

21.94

1.3

limiting: df=14

14.00

 

28.00

 

0.38

 

0.76

 

0.86

 

13.34

 

21.06

 

23.68

 

29.14

 

k=15/n=100

14.58

4.2

30.67

9.5

0.38

0.5

0.76

0.8

0.85

−0.3

13.88

4.1

21.98

4.3

24.74

4.5

30.43

4.4

k=15/n=250

14.15

1.1

28.51

1.8

0.38

−0.1

0.76

0.2

0.85

−0.8

13.49

1.1

21.27

1.0

23.91

1.0

29.56

1.4

k=15/n=500

14.05

0.4

28.17

0.6

0.38

−0.1

0.77

2.0

0.94

9.7

13.39

0.4

21.14

0.4

23.76

0.3

29.31

0.6

k=15/n=750

14.03

0.2

27.91

−0.3

0.38

−0.4

0.74

−2.6

0.78

−9.4

13.37

0.2

21.11

0.2

23.66

−0.1

29.11

−0.1

k=15/n=1000

14.03

0.2

27.86

−0.5

0.38

−0.5

0.75

−0.7

0.84

−2.0

13.38

0.3

21.11

0.2

23.67

−0.1

29.04

−0.3

k=15/n=2500

14.01

0.1

28.04

0.1

0.38

−0.0

0.77

1.9

0.88

2.2

13.35

0.1

21.09

0.1

23.75

0.3

29.25

0.4

k=15/n=5000

14.02

0.2

28.19

0.7

0.38

0.2

0.77

1.6

0.89

4.4

13.34

0.0

21.09

0.1

23.76

0.3

29.23

0.3

avg. (df=14)

14.12

0.9

28.48

1.7

0.38

−0.1

0.76

0.5

0.86

0.5

13.46

0.9

21.26

0.9

23.89

0.9

29.42

1.0

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