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Table 4 Descriptive statistics for the fixed 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

4.42

10.4

8.86

10.7

0.67

−4.7

1.23

−12.8

2.17

−27.7

3.81

13.5

8.45

8.6

10.17

7.2

13.82

4.1

k=5/n=250

4.19

4.7

8.88

10.9

0.71

0.6

1.39

−1.9

2.74

−8.6

3.47

3.4

8.22

5.7

9.99

5.3

13.91

4.8

k=5/n=500

4.10

2.4

8.53

6.7

0.71

0.9

1.44

1.8

3.10

3.2

3.42

1.9

7.98

2.6

9.81

3.4

13.70

3.2

k=5/n=750

4.06

1.5

8.26

3.3

0.71

0.2

1.43

1.2

3.12

3.9

3.40

1.3

7.90

1.5

9.60

1.2

13.46

1.4

k=5/n=1000

4.02

0.6

8.05

0.7

0.71

−0.3

1.40

−0.7

2.96

−1.3

3.38

0.7

7.81

0.4

9.54

0.6

13.29

0.1

k=5/n=2500

4.02

0.5

8.19

2.3

0.71

0.7

1.43

1.2

3.03

1.2

3.37

0.4

7.83

0.6

9.57

0.9

13.51

1.8

k=5/n=5000

4.00

−0.1

7.99

−0.2

0.71

−0.0

1.43

0.9

3.19

6.4

3.36

0.1

7.76

−0.2

9.47

−0.2

13.14

−1.0

avg. (df=4)

4.12

2.9

8.39

4.9

0.70

−0.4

1.39

−1.5

2.90

−3.3

3.46

3.0

7.99

2.7

9.74

2.6

13.55

2.1

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

9.54

6.0

20.05

11.4

0.47

−0.4

0.89

−5.9

1.10

−17.7

8.88

6.4

15.55

5.9

17.87

5.6

22.77

5.1

k=10/n=250

9.14

1.6

18.67

3.7

0.47

0.3

0.95

1.2

1.36

2.3

8.47

1.5

14.93

1.7

17.23

1.8

22.07

1.9

k=10/n=500

9.08

0.9

18.32

1.8

0.47

−0.0

0.95

0.6

1.42

6.4

8.43

1.0

14.80

0.8

17.07

0.9

21.83

0.8

k=10/n=750

9.02

0.2

18.22

1.2

0.47

0.4

0.95

0.3

1.30

−2.6

8.33

−0.2

14.75

0.5

16.97

0.3

21.81

0.7

k=10/n=1000

9.01

0.1

17.93

−0.4

0.47

−0.3

0.94

0.1

1.37

2.8

8.34

−0.0

14.69

0.0

16.92

0.0

21.64

−0.1

k=10/n=2500

9.02

0.2

17.97

−0.2

0.47

−0.3

0.93

−1.1

1.26

−5.5

8.36

0.2

14.73

0.3

16.95

0.2

21.48

−0.9

k=10/n=5000

9.01

0.1

17.87

−0.7

0.47

−0.5

0.93

−0.9

1.30

−2.3

8.37

0.3

14.69

0.0

16.88

−0.2

21.65

−0.1

avg. (df=9)

9.12

1.3

18.43

2.4

0.47

−0.1

0.93

−0.8

1.30

−2.4

8.45

1.3

14.88

1.3

17.13

1.2

21.89

1.1

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

14.60

4.3

30.69

9.6

0.38

0.4

0.75

−1.2

0.79

−7.8

13.92

4.4

21.99

4.4

24.74

4.5

30.52

4.7

k=15/n=250

14.13

1.0

28.75

2.7

0.38

0.4

0.77

2.1

0.92

7.0

13.45

0.8

21.28

1.0

23.91

1.0

29.53

1.3

k=15/n=500

14.07

0.5

27.84

−0.6

0.37

−0.8

0.74

−2.0

0.78

−9.4

13.40

0.5

21.15

0.4

23.73

0.2

29.26

0.4

k=15/n=750

14.03

0.2

28.39

1.4

0.38

0.5

0.77

2.3

0.95

10.3

13.36

0.2

21.16

0.5

23.82

0.6

29.26

0.4

k=15/n=1000

14.04

0.3

28.44

1.6

0.38

0.5

0.77

2.0

0.92

7.5

13.37

0.2

21.11

0.2

23.79

0.4

29.49

1.2

k=15/n=2500

14.02

0.2

28.19

0.7

0.38

0.2

0.75

−0.9

0.78

−9.4

13.35

0.1

21.13

0.3

23.76

0.3

29.25

0.4

k=15/n=5000

14.01

0.0

28.06

0.2

0.38

0.1

0.75

−0.4

0.83

−3.3

13.34

0.0

21.09

0.1

23.70

0.1

29.15

0.0

avg. (df=14)

14.13

0.9

28.62

2.2

0.38

0.2

0.76

0.3

0.85

−0.7

13.46

0.9

21.27

1.0

23.92

1.0

29.49

1.2