# Table 4 Chi square statistics and their standard deviations of stage 2

$$\bar{n}$$ Types k = 5 k = 10 k = 1
UNIr UNIz MGLS TSSEM UNIr UNIz MGLS TSSEM UNIr UNIz MGLS TSSEM
50 E 2.3 (3.9)b 2.4 (4.0)b 1.0 (1.6) 1.1 (1.6) 2.5 (3.3)b 2.6 (3.4)b 1.1 (1.6) 1.1 (1.7)a 2.7 (3.7)b 2.8 (3.7)b 1.1 (1.7) 1.2 (1.8)b
M 2.1 (2.8)b 2.2 (2.9)b 1.0 (1.4) 1.1 (1.5) 2.3 (3.2)b 2.3 (3.3)b 1.0 (1.4) 1.1 (1.4) 2.7 (3.7)b 2.7 (3.7)b 1.0 (1.4) 1.0 (1.4)
H 2.3 (3.26)b 2.3 (3.4)b 1.0 (1.5) 1.0 (1.6) 2.4 (3.3)b 2.5 (3.4)b 1.0 (1.4) 1.0 (1.4) 2.5 (3.5)b 2.5 (3.6)b 1.0 (1.4) 1.0 (1.5)
100 E 2.3 (3.1)b 2.3 (3.1)b 1.0 (1.5) 1.0 (1.5) 2.9 (3.8)b 2.9 (3.9)b 1.1 (1.6) 1.1 (1.6) 3.4 (4.4)b 3.4 (4.4)b 1.1 (1.5) 1.1 (1.5)a
M 2.4 (3.6)b 2.4 (3.6)b 1.0 (1.5) 1.0 (1.5) 2.8 (3.7)b 2.8 (3.7)b 1.0 (1.4) 1.0 (1.4) 3.4 (4.2)b 3.3 (4.2)b 1.0 (1.5) 1.0 (1.5)
H 2.4 (3.2)b 2.4 (3.3)b 1.0 (1.5) 1.0 (1.5) 2.8 (3.7)b 2.8 (3.6)b 1.0 (1.4) 1.0 (1.4) 3.2 (4.0)b 3.2 (4.0)b 1.0 (1.4) 1.0 (1.4)
200 E 2.8 (3.7)b 2.8 (3.7)b 1.0 (1.3) 1.0 (1.3) 3.9 (4.6)b 3.9 (4.6)b 1.1 (1.44) 1.1 (14) 5.1 (5.9)b 5.1 (5.9)b 1.1 (1.6) 1.1 (1.6)
M 2.7 (3.6)b 2.7 (3.7)b 1.0 (1.6) 1.1 (1.6) 3.6 (4.3)b 3.6 (4.3)b 1.0 (1.3) 0.9 (1.3) 4.8 (5.3)b 4.7 (5.3)b 1.1 (1.5) 1.1 (1.5)
H 2.8 (3.6)b 2.9 (3.6)b 1.1 (1.6)a 1.1 (1.6)a 3.7 (4.6)b 3.7 (4.6)b 1.0 (1.4) 1.0 (1.4) 5.0 (5.55)b 4.9 (5.5)b 1.0 (1.4) 1.0 (1.4)
500 E 4.1 (4.9)b 4.1 (4.9)b 1.0 (1.4) 1.0 (1.4) 6.4 (6.2)b 6.4 (6.2)b 0.9 (1.3) 1.0 (1.3) 9.2 (7.79)b 9.1 (7.8)b 1.0 (1.5) 1.0 (1.5)
M 4.1 (4.9)b 4.1 (4.9)b 1.0 (1.3) 1.0 (1.3) 6.8 (6.5)b 6.7 (6.5)b 0.9 (1.3)a 0.9 (1.3)a 9.8 (8.1)b 9.7 (8.0)b 1.0 (1.4) 1.0 (1.4)
H 4.2 (4.9)b 4.2 (4.9)b 1.0 (1.5) 1.0 (1.5) 6.8 (6.4)b 6.7 (6.4)b 0.9 (1.3) 1.0 (1.3) 9.2 (7.8)b 9.1 (7.8)b 1.0 (1.4) 1.0 (1.4)
1000 E 7.0 (6.8)b 7.0 (6.8)b 1.1 (1.5) 1.1 (1.5) 11.7 (9.0)b 11.7 (9.0)b 1.0 (1.4) 1.0 (1.4) 15.9 (10.5)b 15.8 (10.5)b 1.0 (1.4) 1.0 (1.4)
M 6.9 (6.4)b 6.9 (6.4)b 1.0 (1.4) 1.0 (1.4) 11.4 (8.7)b 11.3 (8.7)b 0.9 (1.3) 0.9 (1.3)a 15.9 (10.6)b 15.9 (10.6)b 1.1 (1.6) 1.1 (1.6)
H 6.6 (6.5)b 6.6 (6.5)b 0.9 (1.3) 1.0 (1.3) 11.7 (9.0)b 11.7 (9.0)b 1.0 (1.4) 1.0 (1.4) 16.4 (10.8)b 16.3 (10.8)b 1.0 (1.4) 1.0 (1.4)
1. Values enclosed in parentheses represent standard deviations (SD). Expected means and SDs of Chi squares are 1 and 1.41, respectively
2. ap < 0.05; b p < 0.01