Table 6 Rate of rejection of the Rasch model assumption with the Q1 test as a function of the rate of missing data per item (π), the value of the correlation coefficient ρ between the latent variable Θ and the propensity to have missing data ξ for each method for handling missing data (results for w = 0/w = 1) [*: values significantly different of 5%]

5.2/6.5

5.2/6.6*

4.9/6.3*

5.7/9.2*

5.9/9.7*

6.2/8.1*

4.6/22.3*

6.3/17.6*

6.2/18.5*

5.6/5.2

6.0/5.6

4.0/4.7

3.9/8.0*

4.3/6.4

6.2/6.0

5.2/8.5*

5.9/8.3*

6.7*/8.2*

5.6/3.9

5.4/4.6

6.0/5.8

4.5/4.6

6.3/4.4

6.1/5.3

3.9/4.5

3.9/5.0

6.1/5.8

6.0/6.0

6.0/6.1

4.5/5.0

6.2/6.7*

4.4/5.7

4.9/5.1

4.7/7.4*

5.9/5.5

4.3/6.8

11.4*/9.7*

8.5*/9.3*

9.0*/8.2*

19.6*/19.5*

15.5*/18.5*

14.2*/19.1*

22.9*/29.0*

22.2*/28.8*

23.6*/32.7*

5.9/3.7

4.9/4.4

5.2/4.4

6.9*/4.4

6.9*/5.6

6.6*/4.5

6.9*/5.5

6.8/4.9

8.0*/6.3

49.6*/54.8*

51.5*/55.2*

51.7*/54.0*

85.0*/87.9*

86.0*/88.6*

85.0*/89.0*

94.1*/97.6*

93.7*/96.5*

95.6*/97.7*

33.0*/37.3*

34.9*/34.6*

35.8*/37.2*

64.2*/63.6*

63.2*/67.4*

61.5*/65.9*

65.5*/65.6*

63.2*/68.1*

60.4*/66.9*

10.6*/12.6*

13.1*/11.1*

11.9*/11.6*

19.1*/19.8*

19.5*/18.7*

17.7*/19.0*

22.2*/26.4*

24.5*/24.8*

22.6*/24.0*

16.1*/17.3*

17.9*/18.6*

19.2*/19.4*

42.2*/51.3*

44.3*/54.2*

49.4*/56.9*

58.5*/72.4*

60.2*/75.0*

67.8*/82.0*

21.8*/23.8*

22.8*/24.3*

21.5*/26.1*

61.2*/69.9*

63.9*/67.6*

64.2*/67.5*

80.6*/87.7*

83.3*/88.7*

81.0*/86.3*

4.7/4.9

5.9/5.3

6.2/6.2

6.0/6.2

6.9*/6.9*

7.3*/6.0

6.6*/6.6*

6.7*/16.9*

6.8*/5.7

21.9*/24.3*

22.9*/24.3*

22.6*/27.5*

17.8*/45.0*

19.6*/40.2*

18.3*/36.9*

10.1*/61.0*

14.1*/52.5*

15.4*/45.0*

6.8*/5.5

6.1/5.8*

5.1/3.2*

6.7*/6.9*

6.2/4.4

5.0/4.8

10.0*/6.9*

9.2*/5.8

8.0*/4.0

6.5/7.8*

7.5*/8.2*

6.9*/7.6*

9.2*/9.7*

11.0*/10.9*

10.2*/9.4*

13.3*/14.8*

13.8*/14.0*

9.6*/9.5*

4.9/5.1

4.0/5.2

5.1/4.9

4.8/5.2

5.1/5.0

4.3/4.4

3.4*/3.3*

3.4*/4.5

3.3*/2.5*

5.2/5.5

4.8/4.4

5.1/5.0

5.4/4.6

4.1/3.9

4.9/4.9

4.0/4.8

4.7/4.5

4.9/3.8*