Table 1 Sample size and lowest, highest, and average θ for each true score interval

[ − 2 ; − 1.5 ]

12193

− 1.716215

− 1.500013

− 1.58

[ − 1.5 ; − 1 ]

121331

− 1.499992

− 1.000002

− 1.19

[ − 1 ; − 0.5 ]

211557

− 0.999995

− 0.500002

− 0.75

[ − 0.5 ; 0 ]

193117

− 0.499994

− 1e −06

− 0.25

[ 0 ; 0.5 ]

163131

1.3e −05

0.499995

0.24

[ 0.5 ; 1 ]

139804

0.500006

0.999997

0.74

[ 1 ; 1.5 ]

95364

1.000001

1.499987

1.23

[ 1.5 ; 2 ]

53275

1.500001

1.999989

1.71

[ 2 ; 2.5 ]

9435

2.000034

2.499647

2.16

[ 2.5 ; 3.5 ]

793

2.500007

3.083216

2.66