先定錨後檢核策略運用在概似比檢定法之差異試題功能檢核效果

(1)

(2)

I

differential item functioning DIF

Type I error

DIF

Wang

2008

DIF-free-then-DIF

DFTD

DIF

likelihood ratio test LRT

DIF

power

DIF

DIF-free

DIF

DIF-free

(3)

II

The Effect of DIF-free-then-DIF Strategy on Likelihood Ratio

Test in Assessing Differential Item Functioning

Abstract

It was found the Type I error rate of differential item functioning

DIF

assessment was seriously influenced by the percentage of DIF items in the test. To

diminish this problem, the DIF-free-then-DIF

DFTD

strategy was strongly

recommended to implement in DIF assessment methods

Wang, 2008 . Though there

are many methods, the likelihood ratio test LRT method was found to perform better

in comparison with other DIF assessment methods, therefore it was used in this study.

The performance of DFTD Strategy on the LRT method was evaluated through

two-stage simulation studies.

The results indicated that the Type I error rates were well-controlled under LRT

method with setting DIF-free items as anchor. Furthermore, it was found the scale

purification procedure can yields higher accuracy than other methods on selecting a set

of DIF-free items. Taking these items as anchor of DFTD strategy, the subsequent

constant item method performed well on both Type I error control and power of DIF

assessment.

Keywords: differential item functioning, likelihood ratio test, DIF-free-then-DIF,

scale purification

(4)

III

--- I

Abstract --- II

--- III

--- IV

--- V

--- 1

--- 2

--- 3

--- 6

--- 10

--- 12

--- 15

DIF-free

--- 15

DIF-free

--- 20

--- 24

--- 25

DIF-free

--- 25

DIF-free

--- 31

--- 52

--- 53

--- 55

(5)

IV

1 --- 23

2 DIF-free

20 --- 29

3 DIF-free

40 --- 29

4 DIF

constant

0.4 --- 35

5 DIF

constant

0.6 --- 36

6 DIF

constant

0.4 --- 37

7 DIF

constant

0.6 --- 38

8 DIF

balanced

0.4 --- 39

9 DIF

balanced

0.6 --- 40

10 DIF

balanced

0.4 --- 41

11 DIF

balanced

0.6 --- 42

12 LRT-ST

--- 48

13 LRT-SP

--- 48

14 LRT-PA

--- 49

15 LRT-DFSP

--- 49

16 LRT-ST

--- 50

17 LRT-SP

--- 50

18 LRT-PA

--- 51

19 LRT-DFSP

--- 51

(6)

V

1 --- 9

2 --- 9

3 ASA

20 --- 30

4 ASA

40 --- 30

5 ASA

20 --- 30

6 ASA

40 --- 30

(7)

1

item response theory, IRT

differential item functioning , DIF

1987

Trends in International

Mathematics and Science Study, TIMSS

American Mathematics Competitions, AMC

DIF

(8)

2

Cole & Zieky, 2001

Educational Testing Service, ETS

DIF

power

Type I error

Finch, 2005; Lord, 1980; Stark, Chernyshenko, &

Drasgow, 2006

DIF

20%

DIF

inflated

scale purification

DIF

Candell & Drasgow, 1988; Clauser, Mazor, & Hambleton, 1993; French & Maller,

2007; Hidalgo-Montesinos & G mez-Benito, 2003; Holland & Thayer, 1988; Lord,

1980; Park & Lautenschlager, 1990; Miller & Oshima, 1992; Navas-Ara & G

mez-Benito, 2002; Wang & Su, 2004

DIF

20%

DIF

20%

DIF

20%

constant-item method, CI; Thissen, Steinberg, & Wainer, 1988;

Wang & Yeh, 2003

(9)

3

DIF

DIF-free

anchor

DIF

Wang

2008

DIF-free-then-DIF, DFTD

DIF

MIMIC

multiple indicators, multiple causes confirmatory

factor analysis methods; Oort, 1998)

Shih & Wang, 2009; Wang & Shih,

2010

DFTD

MIMIC

Woods, 2009

DIF

Woods

likelihood ratio test, LRT;

Thissen, Steinberg, & Wainer, 1988

graded response model,

GRM; Samejima,1969

DIF

rank-based

DIF

likelihood ratio test statistic, LR statistic

1 all-other-item method, AOI; Wang &

Yeh, 2003

2 f

LR statistic

3 LR statistic

f

4

3 g

4 g

DIF

g

DIF-free

rank-based

LR statistic

(10)

4

LR statistic

f

DIF-free

Stark et al., 2006;

Wang, 2004; Wang & Yeh, 2003

rank-based

Woods

2009

Wang, 2004; Wang & Yeh, 2003

Woods

rank-based

GRM

DIF

DFTD

DIF-free

rank-based

DFTD

DIF

IRT

DFTD

DIF

DIF-free

rank-based

LR statistic

rank-based

iterative constant item method, ICI method;

Wang, 2008

rank-based

DIF-free

DFTD

DIF-free

DFTD

DIF

(11)

5

DIF-free

2009

(12)

6

item characteristic

curves, ICCs

item bias

Ironson & Subkoviak, 1979; Rudner, Geston, & Knight, 1980; Shepard, Camiili, &

Averill, 1981

DIF

Camilli & Shepard, 1994; Drasgow & Kang, 1984; Holland & Wainer

1993; Lord, 1980

DIF

IRT

DIF

IRT

dichotomous

0

1 IRT

(13)

7

IRT

three-parameter logistic model, 3PLM; Birnbaum, 1968

two-parameter logistic model, 2PLM; Birnbaum, 1968

Rasch,

1980

3PLM



_n

i

1 





(

)



exp

1 )

(

exp

)

1 (

i n i i n i i i ni

b

a

b

a

c

p

















1

i

a

_i

_{discrimination parameter}

b

_i

i

difficulty parameter

c

i

_i

_guessing

parameter

3PLM

1 c

i

₀

2PLM







(

)



exp

1 )

(

exp

i n i i n i ni

b

a

b

a

p











2

2 2PLM

2

1 Rasch

)

exp(

1 )

exp(

i n i n ni

b

p











3 Rasch

Rasch

1960

(14)

8

0 IRT

sample independent

impact

DIF

IRTLRDIF

Thissen, 2001

DIF

2010

DIF

reference group

focal group

uniform DIF

nonuniform

DIF

Mellenberg, 1982

studied item

(15)

9

1 ICC

2

(16)

10

DIF

matching variable

studied item

DIF

IRT

Holland & Wainer, 1993

IRT

DIF

Mantel-Haenszel

Holland & Thayer,

1988

Dorans & Kulick, 1986

Swaminathan & Rogers,

1990

IRT

DIF

Lord’s



2

Lord, 1980

Raju’s

Raju, 1988

DIF

Bolt, 2002; Kim &

Cohen, 1995; Stark, Chernyshenko, & Drasgow, 2006; Wang, 2004; Wang & Yeh

2003

Thissen Steinberg

Gerrand 1986

Thissen Steinberg

Wainer 1988

likelihood ratio test LR Neyman & Pearson, 1928

IRT

DIF

polytomous

MULTILOG

Thissen, 1991

IRTLRDIF

DIF

IRT

Rasch

2PL

3PL

(17)

11

compact model

likelihood deviance

= -2 × log

likelihood

2 C

G

₄

) log( 2 2 compact C likelihood G  

4 DIF

augmented model

likelihood deviance

G

A2

5

) log( 2 2 augmented A likelihood G  

5 likelihood deviance

G

2

6

2 2 2

G

_C



_A



6

2

G

2

DIF

20 2PL

1 DIF

20 DIF

20

2 C

G

1

19

2 A

G

1

2 C

G

2 A

G

2

G

₁

(18)

12 84 . 3 2 ) 1 ( 



2

G

_3.84

₁

_DIF

1

2

G

₁

DIF

2

G

₂

DIF

all-other item method, Wang & Yeh, 2003

DIF

constant item method, Thissen et al., 1988; Wang & Yeh,

2003

DIF

Clauser, Mazor, & Hambleton, 1993;

Kim & Cohen, 1992

DIF

(19)

13

scale purification

DIF

IRT

DIF

Ackerman, 1992; Clauser et al., 1993

Rasch

Miller & Oshima, 1992; Navas-Ara & Gómez-Benito, 2002

Holland

Thayer 1988

Mantel-Haenszel

two-step purification process

Mantel-Haenszel

DIF

iterative purification process

Candell & Drasgow, 1988; Kok, Mellenbergh, & Van der Flier, 1985; Van der

Flier, Mellenbergh, Ade`r, & Wijn, 1984

DIF

20%

DIF

20%

DIF

20%

DIF

Candell &

Drasgow, 1988; Cheung & Rensvold, 1999; Stark et al., 2006; Thissen et al., 1988,

Wang & Shih, 2009

DIF

equal-mean-difficulty method, EMD

Wang, 2004;

Wang & Shih, 2010; Wang & Yeh, 2003

DIF-free

(20)

14

DIF

DIF-free

Wang 2008

DIF-free-then-DIF

DIF

DIF-free

DIF

4 Thissen et al., 1988; Wang & Yeh, 2003 ; Shih & Wang, 2009

DFTD

MIMIC

Shih & Wang,

2009

IRT

DFTD

DIF-free

DIF

2009

MIMIC

IRT

DIF-free

DFTD

(21)

15

IRT

DFTD

DIF

DIF-free

Shih & Wang, 2009; Wang & Shih, 2010

rank-based

DIF-free

LRT-ST

DIF-free

DIF-free item by standard LRT method ; LRT-DFST,

DFST

LRT-SP

DIF-free

DIF-free item by LRT method

with scale purification ; LRT-DFSP,

DFSP

DIF-free

DIF-free item by LRT method with iterative constant ;

(22)

16

DIF-free

DFST

1 DIF

LR statistic

2

1 LR statistic

DIF-free

rank-based

LR statistic

DIF-free

DFSP

1 DIF

LR statistic

2

1 LR statistic

DIF-free

DFST

LR statistic

DIF-free

DFICI

1 LR statistic

LR statistic

2

1 DIF-free

DIF

LR statistic

1 LR statistic

DIF

DIF-free

Hanson

Beguin

2002

1 Matlab

40 IRTLRDIF

DIF

(23)

17

ability difference

sample size

test length

DIF

pattern

DIF

DIF percentage

DIF

0%

Wang

Su,

2004

DIF-free

reference group

R

focal group

F

0

1 -1

1 IRT

Tang

1994

IRT

200 R250/F250

R500/F500

R1000/F1000

DIF-free

20

40 DIF

DIF

constant

(24)

18

balanced

constant

DIF

20 20%

DIF

4 balanced

DIF

20 20%

DIF

2

2 balanced

balanced

DIF

constant

DIF

DIF-free

DIF

10%

20%

30%

40%

DIF

DIF-free

DIF

100 9600

DIF

0.6

0.1 DIF

DIF

DIF-free

DIF

1 DIF-free

(25)

19

0.75 DIF-free

0.5 DIF-free

0.25 DIF

DIF

Wang 2001

average signed area

ASA

Raju’s

signed area

ICC

signed area



i



iF iR



i

c

b

SA



1 



i

ASA

SA

I

ASA



iF iR



F R I i i

I

b

I

b

SA

ASA















/

1

ASA

0 DIF

ASA

0 DIF

Wang

2001

DIF

balanced

ASA

0 DIF

DIF

constant

ASA

DIF

20%

ASA

0.09

0.18 ASA

0 DIF

20%

50%

(26)

20

ASA

DIF-free

DIF

DIF-free

DIF

standard LRT method,

LRT-ST

LRT method with scale

purification,

LRT-SP

DFTD

pure anchor

DIF-free

DIF

pure anchor

DIF

LRT

method with pure anchor,

LRT-PA

DIF

LRT-PA

LRT-SP

1 DIF

2

1 DIF

matching variable

3 DIF

4

2

3 DIF

pure anchor

DIF

LRT-PA

DIF

(27)

21

DIF-free

DIF

1

60 Matlab

IRTLRDIF

DIF

ability difference

sample size

test

length

DIF

DIF pattern

DIF

DIF percentage

DIF

DIF amount

0

1 -1

1 R250/F250

R500/F500

R1000/F1000

Rogers & Swaminathan, 1993

20

40

60

(28)

22

DIF

constant

balanced

DIF

Finch, 2005; Wang & Yeh,

2003

DIF

0% 10%

20%

30%

40%

DIF

0.4

0.1 DIF

DIF

0.6

0.1 DIF

DIF

uniform DIF

100 36000

DIF

0.05

0.05 0.0073

9.27

100

0 0.0927

DIF

ASA

(29)

23

1

0.642 -2.522 31

1.257

0.116

2

0.806 -1.902 32

0.984

0.273

3

0.956 -1.351 33

1.174

0.840

4

0.972 -1.092 34

1.601

0.745

5

1.045 -0.234 35

1.876

1.485

6

0.834 -0.317 36

0.620 -1.208

7

0.614 0.037 37

0.994

0.189

8

0.796 0.268 38

1.246

0.345

9

1.171 -0.571 39

1.175

0.962

10

1.514 0.317 40

1.715

1.592

11

0.842 0.295 41

0.769 -1.944

12

1.754 0.778 42

0.934 -1.348

13

0.839 1.514 43

0.496 -1.348

14

0.998 1.744 44

0.888 -0.859

15

0.727 1.951 45

0.953 -0.190

16

0.892 -1.152 46

1.022 -0.116

17

0.789 -0.526 47

1.012

0.421

18

1.604 1.104 48

1.605

1.377

19

0.722 0.961 49

1.009 -1.126

20

1.549 1.314 50

1.310 -0.067

21

0.700 -2.198 51

0.957

0.192

22

0.799 -1.621 52

1.269

0.683

23

1.022 -0.761 53

1.664

1.107

24

0.860 -1.179 54

1.511

1.393

25

1.248 -0.610 55

0.561 -1.865

26

0.896 -0.291 56

0.728 -0.678

27

0.679 0.067 57

1.665 -0.036

28

0.996 0.706 58

1.401

0.117

29

0.420 -2.713 59

1.391

0.031

30

0.977 0.213 60

1.259

0.259

(30)

24

DIF

EZDIF

Waller, 1998

IRTLRDIF

IRTLFDIF

DIF

DOS

University of North Carolina at Chapel Hill

David Thissen

DIF

IRTLRDIF

item

hypothesis

test

deviance

G

2

degrees of freedom

(31)

25

DIF-free

2

3

20

40 DIF-free

DIF

constant

2 R250/F250

DIF

DFST

DIF

20%

0.9 DIF

20%

0.9 DIF

0.67 DFSP

DIF

30%

0.96 DIF

0.9 DFICI

DIF

0.9 DFST

DIF

0.9 DFSP

DIF

DFICI

0.9 DFSP

DIF

30%

DIF

40%

DFICI

DIF

40%

DFSP

1 DFICI

DIF

40%

3

40

(32)

26

20 DIF

DFST

DIF

20%

0.9 DFSP

DIF

30%

0.96

1 DIF

0.76 DFICI

DIF

40%

0.94 DFICI

DIF

0.92 DFST

DFSP

DIF

30%

1 DFST

DIF

0.66

0.83 DFSP

DIF

0.79

0.94 DFST

DFSP

DIF

40%

DFSP

1 DFICI

DIF

40%

0.93

0.98 DIF

40%

DFSP

0.96 DFSP

DIF

constant

DIF

DFICI

DIF

0.9 DIF

constant

ASA

DIF

ASA

DIF

balanced

DIF

balanced

DIF

2

0.94

1

(33)

27

DIF

1 DFICI

DIF

10%

0.8 DIF

40%

0.4

3

0.96

1 DFST

DFSP

DIF

0.89 DIF

1 DFICI

20 DIF

DIF

balanced

ASA

0 DIF

ASA

0.01 ASA

0 DIF-free

ASA

0

0.94 ASA

0 DIF

DFST

DFSP

0.9 DFICI

DIF

ASA

0 DIF

DIF

balanced

DFSP

DFST

DIF

constant

DFSP

DIF-free

DFST

DFICI

DFSP

DIF

constant

DFICI

DIF

(34)

28

balanced

DFICI

DIF

0.13 DIF-free

3

6 ASA

DFSP

ASA

0.24 DFICI

ASA

0.24 DFSP

ASA

0 DFICI

DFSP

DFICI

ASA

0.24 ASA

0 DIF

2009

ICI

DIF-free

ICI

DIF

DFICI

ASA

0 DIF

DIF-free

(35)

29

2 DIF-free

20

ability

difference DIF pattern DIF% ASA

R250/F250 R500/F500 R1000/F1000 DFST DFSP DFICI DFST DFSP DFICI DFST DFSP DFICI 0 Constant 10% 0.064 .99 .99 1.00 1.00 1.00 1.00 1.00 1.00 1.00 20% 0.117 .98 1.00 .99 .99 1.00 1.00 1.00 1.00 1.00 30% 0.183 .89 .96 .97 .96 1.00 .99 .99 1.00 1.00 40% 0.242 .67 .81 .90 .70 .84 .96 .80 .86 .95 balanced 10% 0.000 .99 .98 .99 1.00 1.00 1.00 1.00 1.00 1.00 20% 0.001 .97 .97 .98 1.00 .99 1.00 1.00 1.00 1.00 30% 0.003 .96 .96 .95 1.00 1.00 .97 1.00 1.00 .99 40% 0.007 .96 .95 .94 .99 .98 .97 1.00 1.00 .99 1 Constant _{10% 0.064} _.99 _.98 _{.89 1.00 1.00} _{.90 1.00 1.00} _.86 20% 0.117 .94 .96 .84 .97 1.00 .84 1.00 1.00 .83 30% 0.183 .82 .88 .79 .89 .97 .83 .95 1.00 .87 40% 0.242 .63 .63 .66 .62 .69 .72 .65 .58 .76 balanced 10% 0.000 .96 .96 .81 1.00 .99 .80 1.00 1.00 .80 20% 0.001 .96 .95 .71 1.00 .99 .70 1.00 1.00 .65 30% 0.003 .96 .93 .55 .98 .98 .57 1.00 1.00 .53 40% 0.007 .91 .88 .44 .96 .96 .47 1.00 .99 .43

3 DIF-free

40

ability

difference DIF pattern DIF% ASA

R250/F250 R500/F500 R1000/F1000 DFST DFSP DFICI DFST DFSP DFICI DFST DFSP DFICI 0 Constant 10% 0.060 .99 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 20% 0.123 .97 1.00 .99 1.00 1.00 1.00 1.00 1.00 1.00 30% 0.190 .86 .96 .94 .94 1.00 .99 .98 1.00 .99 40% 0.252 .66 .79 .94 .73 .92 .95 .83 .94 .92 balanced 10% 0.002 .99 .99 .99 1.00 1.00 1.00 1.00 1.00 1.00 20% 0.001 .98 .98 .97 1.00 1.00 1.00 1.00 1.00 1.00 30% 0.002 .96 .97 .96 .99 .99 .99 1.00 1.00 1.00 40% 0.006 .97 .96 .96 .99 .99 .99 1.00 1.00 1.00 1 Constant 10% 0.060 .98 .99 .98 1.00 1.00 .95 1.00 1.00 .97 20% 0.123 .95 .97 .94 .98 1.00 .93 1.00 1.00 .93 30% 0.190 .81 .89 .95 .88 .98 .94 .95 1.00 .95 40% 0.252 .68 .72 .96 .69 .82 .96 .73 .96 .94 balanced _{10% 0.002} _.98 _.98 _.87 _{1.00 1.00} _.84 _{1.00 1.00} _.76 20% 0.001 .96 .96 .74 1.00 1.00 .70 1.00 1.00 .60 30% 0.002 .94 .93 .57 .98 .97 .54 1.00 1.00 .49 40% 0.006 .90 .89 .43 .98 1.00 .33 1.00 .99 .13

(36)

30

3 ASA 20 4 ASA 40

(37)

31

DIF-free

DFSP

DIF-free

LRT-DFSP

LRT-ST

LRT-SP

LRT-PA

DIF

4

11 DIF

100 DIF

DIF

constant

4 DIF

0.4

20 LRT-ST

DIF

20%

LRT-PA

0.02 0.05 LRT-DFST

LRT-PA

LRT-SP

DIF

0.08

40 LRT-ST

DIF

20%

LRT-SP

R500/F500

DIF

LRT-DFST

LRT-PA

60 LRT-ST

DIF

20%

LRT-SP

R250/F250

DIF

LRT-DFSP

LRT-PA

LRT-DFSP

LRT-SP

DIF

LRT-SP

LRT-DFSP

(38)

32

5 DIF

0.4

0.6 LRT-ST

R1000/F1000

DIF

20%

LRT-DFSP

LRT-PA

0.4 LRT-SP

0.04

0.09 DIF

LRT-ST

R500/F500

R1000/F1000

DIF

20%

LRT-SP

R250/F250

DIF

40%

LRT-PA

LRT-DFSP

LRT-SP

LRT-ST

DIF

20%

LRT-SP

LRT-DFSP

LRT-SP

LRT-DFSP

6 DIF

0.4 LRT-ST

R500/F500

DIF

20%

LRT-SP

R500/F500

0.09 LRT-PA

LRT-DFSP

LRT-PA

LRT-ST

30%DIF

LRT-SP

R250/F250 R500/F500

DIF

40%

LRT-PA

LRT-DFSP

LRT-ST

DIF

20%

(39)

33

LRT-DFSP

DIF

7 DIF

0.6 LRT-ST

DIF

20%

LRT-SP

DIF

40%

LRT-PA

LRT-DFSP

DIF

LRT-PA

LRT-DFSP

DIF

0.83 LRT-DFSP

LRT-PA

4

7 DIF

constant

ASA

DIF

LRT-ST

ASA

0.12 DIF

balanced

8 DIF

0.4 balanced

DIF

balanced

ASA

0 DIF

Wang, 2001

ASA

0.015

0 LRT-ST

LRT-SP

LRT-PA

(40)

34

LRT-ST

DIF

0.6

9

0.4 LRT-ST

10 DIF

0.4 LRT-DFSP

LRT-PA

LRT-DFSP

LRT-ST

LRT-SP

DIF

LRT-ST

11 DIF

0.6 LRT-ST

DIF

constant

LRT-DFSP

LRT-SP

(41)

35

4 DIF constant 0.4

Type I error Power

sample size DIF% ASA L-ST L-SP L-PA L-DFSP L-ST L-SP L-PA L-DFSP NI20 R250_F250 0% 0.000 0.06 0.05 0.05 0.04 10% 0.042 0.05 0.05 0.04 0.03 0.22 0.23 0.17 0.18 20% 0.079 0.06 0.05 0.02 0.03 0.27 0.28 0.24 0.22 30% 0.124 0.08 0.07 0.04 0.04 0.25 0.27 0.29 0.22 40% 0.165 0.09 0.08 0.03 0.05 0.20 0.21 0.31 0.18 R500_F500 0% 0.000 0.05 0.05 0.03 0.03 10% 0.042 0.05 0.04 0.04 0.03 0.33 0.34 0.30 0.29 20% 0.079 0.07 0.05 0.03 0.04 0.44 0.52 0.45 0.42 30% 0.124 0.11 0.06 0.03 0.04 0.45 0.54 0.52 0.48 40% 0.165 0.14 0.08 0.03 0.05 0.35 0.43 0.47 0.38 R1000_F1000 0% 0.000 0.05 0.04 0.03 0.03 10% 0.042 0.06 0.05 0.03 0.03 0.58 0.60 0.54 0.56 20% 0.079 0.08 0.05 0.03 0.03 0.70 0.78 0.67 0.72 30% 0.124 0.17 0.05 0.02 0.03 0.65 0.79 0.74 0.75 40% 0.165 0.24 0.08 0.03 0.04 0.52 0.66 0.67 0.61 NI40 R250_F250 0% 0.000 0.05 0.05 0.05 0.03 10% 0.040 0.05 0.05 0.05 0.03 0.31 0.33 0.30 0.26 20% 0.083 0.06 0.05 0.04 0.03 0.27 0.30 0.28 0.23 30% 0.125 0.11 0.07 0.04 0.04 0.32 0.37 0.43 0.28 40% 0.169 0.11 0.07 0.04 0.04 0.26 0.32 0.37 0.23 R500_F500 0% 0.000 0.04 0.04 0.04 0.02 10% 0.040 0.05 0.05 0.03 0.03 0.53 0.53 0.43 0.42 20% 0.083 0.06 0.05 0.04 0.03 0.46 0.52 0.49 0.43 30% 0.125 0.14 0.05 0.04 0.03 0.50 0.63 0.62 0.54 40% 0.169 0.20 0.10 0.04 0.05 0.39 0.50 0.59 0.43 R1000_F1000 0% 0.000 0.05 0.05 0.04 0.02 10% 0.040 0.06 0.05 0.04 0.03 0.78 0.79 0.73 0.74 20% 0.083 0.09 0.05 0.03 0.03 0.67 0.73 0.68 0.68 30% 0.125 0.24 0.05 0.04 0.02 0.65 0.81 0.80 0.76 40% 0.169 0.34 0.08 0.03 0.04 0.58 0.76 0.79 0.71 NI60 R250_F250 0% 0.000 0.05 0.05 0.05 0.03 10% 0.041 0.06 0.05 0.04 0.03 0.36 0.38 0.38 0.29 20% 0.084 0.07 0.06 0.04 0.03 0.39 0.45 0.45 0.37 30% 0.128 0.08 0.06 0.04 0.03 0.31 0.36 0.41 0.26 40% 0.166 0.12 0.10 0.05 0.06 0.25 0.28 0.40 0.20 R500_F500 0% 0.000 0.05 0.05 0.04 0.03 10% 0.041 0.06 0.05 0.05 0.03 0.60 0.62 0.59 0.56 20% 0.084 0.09 0.05 0.04 0.02 0.57 0.65 0.64 0.57 30% 0.128 0.13 0.06 0.04 0.03 0.50 0.61 0.64 0.55 40% 0.166 0.18 0.08 0.04 0.04 0.42 0.55 0.62 0.48 R1000_F1000 0% 0.000 0.05 0.05 0.04 0.02 10% 0.041 0.06 0.05 0.04 0.03 0.81 0.84 0.81 0.79 20% 0.084 0.13 0.05 0.04 0.03 0.75 0.84 0.83 0.79 30% 0.128 0.20 0.05 0.05 0.02 0.70 0.83 0.82 0.77 40% 0.166 0.31 0.07 0.05 0.03 0.59 0.79 0.81 0.73

(42)

36

5 DIF constant 0.6

Type I error Power

sample size DIF% ASA L-ST L-SP L-PA L-DFSP L-ST L-SP L-PA L-DFSP NI20 R250_F250 0% 0.000 0.05 0.05 0.05 0.03 10% 0.064 0.05 0.05 0.04 0.03 0.36 0.33 0.29 0.27 20% 0.117 0.08 0.06 0.04 0.04 0.46 0.49 0.46 0.42 30% 0.184 0.11 0.05 0.04 0.05 0.44 0.54 0.54 0.47 40% 0.242 0.15 0.08 0.03 0.06 0.38 0.47 0.54 0.43 R500_F500 0% 0.000 0.04 0.04 0.03 0.03 10% 0.064 0.05 0.05 0.04 0.03 0.57 0.59 0.44 0.52 20% 0.117 0.09 0.05 0.04 0.03 0.67 0.76 0.67 0.71 30% 0.184 0.17 0.06 0.03 0.04 0.64 0.77 0.75 0.73 40% 0.242 0.27 0.08 0.03 0.04 0.62 0.78 0.81 0.74 R1000_F1000 0% 0.000 0.04 0.04 0.02 0.02 10% 0.064 0.06 0.05 0.03 0.03 0.86 0.88 0.75 0.83 20% 0.117 0.13 0.05 0.03 0.03 0.83 0.90 0.87 0.87 30% 0.184 0.28 0.05 0.03 0.04 0.83 0.96 0.93 0.93 40% 0.242 0.44 0.06 0.03 0.04 0.82 0.95 0.95 0.94 NI40 R250_F250 0% 0.000 0.05 0.04 0.04 0.02 10% 0.059 0.05 0.05 0.04 0.03 0.51 0.57 0.48 0.46 20% 0.121 0.06 0.04 0.03 0.02 0.52 0.58 0.57 0.51 30% 0.188 0.15 0.08 0.04 0.04 0.50 0.63 0.66 0.53 40% 0.251 0.20 0.10 0.05 0.06 0.41 0.53 0.61 0.44 R500_F500 0% 0.000 0.05 0.05 0.04 0.02 10% 0.059 0.05 0.05 0.03 0.03 0.73 0.77 0.71 0.72 20% 0.121 0.10 0.05 0.04 0.03 0.77 0.84 0.81 0.81 30% 0.188 0.24 0.05 0.04 0.03 0.73 0.90 0.87 0.85 40% 0.251 0.35 0.07 0.04 0.04 0.64 0.85 0.86 0.80 R1000_F1000 0% 0.000 0.06 0.06 0.04 0.03 10% 0.059 0.06 0.05 0.03 0.02 0.92 0.94 0.91 0.92 20% 0.121 0.15 0.05 0.04 0.03 0.93 0.96 0.95 0.95 30% 0.188 0.43 0.05 0.04 0.03 0.88 0.98 0.97 0.97 40% 0.251 0.60 0.06 0.04 0.03 0.83 0.97 0.96 0.95 NI60 R250_F250 0% 0.000 0.05 0.05 0.04 0.03 10% 0.061 0.05 0.05 0.04 0.02 0.59 0.63 0.61 0.54 20% 0.126 0.09 0.05 0.04 0.02 0.62 0.71 0.71 0.62 30% 0.186 0.13 0.06 0.04 0.03 0.52 0.68 0.70 0.59 40% 0.247 0.20 0.09 0.05 0.05 0.46 0.61 0.68 0.51 R500_F500 0% 0.000 0.05 0.05 0.05 0.03 10% 0.061 0.06 0.05 0.05 0.03 0.85 0.87 0.86 0.84 20% 0.126 0.13 0.05 0.04 0.02 0.81 0.90 0.89 0.87 30% 0.186 0.23 0.05 0.04 0.03 0.75 0.89 0.88 0.84 40% 0.247 0.35 0.06 0.05 0.03 0.67 0.88 0.89 0.84 R1000_F1000 0% 0.000 0.05 0.05 0.04 0.03 10% 0.061 0.08 0.05 0.04 0.02 0.93 0.95 0.95 0.94 20% 0.126 0.21 0.05 0.04 0.02 0.93 0.97 0.97 0.96 30% 0.186 0.38 0.04 0.04 0.02 0.92 0.98 0.97 0.97 40% 0.247 0.58 0.05 0.03 0.03 0.86 0.98 0.98 0.97

(43)

37

6 DIF constant 0.4

Type I error Power

sample size DIF% ASA L-ST L-SP L-PA L-DFSP L-ST L-SP L-PA L-DFSP NI20 R250_F250 0% 0.000 0.06 0.06 0.04 0.04 10% 0.042 0.05 0.05 0.03 0.04 0.20 0.20 0.13 0.12 20% 0.079 0.05 0.05 0.04 0.03 0.18 0.20 0.17 0.13 30% 0.124 0.08 0.07 0.04 0.05 0.19 0.20 0.21 0.10 40% 0.165 0.09 0.07 0.04 0.05 0.17 0.17 0.18 0.11 R500_F500 0% 0.000 0.05 0.05 0.04 0.03 10% 0.042 0.05 0.05 0.04 0.03 0.37 0.38 0.21 0.24 20% 0.079 0.07 0.05 0.03 0.03 0.35 0.38 0.28 0.22 30% 0.124 0.10 0.08 0.04 0.04 0.31 0.39 0.29 0.24 40% 0.165 0.12 0.09 0.03 0.06 0.21 0.24 0.27 0.13 R1000_F1000 0% 0.000 0.05 0.05 0.04 0.04 10% 0.042 0.06 0.06 0.04 0.04 0.55 0.54 0.42 0.45 20% 0.079 0.09 0.05 0.03 0.03 0.60 0.68 0.41 0.48 30% 0.124 0.16 0.06 0.04 0.03 0.53 0.68 0.57 0.54 40% 0.165 0.20 0.08 0.02 0.04 0.40 0.55 0.47 0.41 NI40 R250_F250 0% 0.000 0.05 0.05 0.04 0.03 10% 0.040 0.06 0.05 0.04 0.03 0.22 0.23 0.13 0.14 20% 0.083 0.06 0.05 0.03 0.03 0.22 0.23 0.20 0.13 30% 0.125 0.09 0.08 0.04 0.06 0.22 0.27 0.26 0.13 40% 0.169 0.11 0.10 0.04 0.06 0.16 0.18 0.22 0.08 R500_F500 0% 0.000 0.05 0.05 0.04 0.03 10% 0.040 0.06 0.06 0.04 0.03 0.43 0.43 0.28 0.24 20% 0.083 0.07 0.06 0.05 0.04 0.36 0.42 0.34 0.25 30% 0.125 0.12 0.07 0.04 0.04 0.37 0.49 0.40 0.31 40% 0.169 0.17 0.10 0.04 0.06 0.28 0.38 0.39 0.22 R1000_F1000 0% 0.000 0.05 0.05 0.05 0.03 10% 0.040 0.06 0.05 0.04 0.04 0.72 0.77 0.65 0.55 20% 0.083 0.09 0.05 0.05 0.04 0.58 0.68 0.54 0.51 30% 0.125 0.20 0.06 0.04 0.04 0.56 0.74 0.68 0.54 40% 0.169 0.28 0.09 0.04 0.05 0.46 0.64 0.64 0.48 NI60 R250_F250 0% 0.000 0.05 0.05 0.05 0.03 10% 0.041 0.05 0.05 0.04 0.03 0.34 0.35 0.32 0.20 20% 0.084 0.07 0.06 0.05 0.03 0.29 0.34 0.32 0.18 30% 0.128 0.08 0.07 0.05 0.04 0.24 0.27 0.30 0.15 40% 0.166 0.10 0.09 0.04 0.04 0.18 0.20 0.29 0.10 R500_F500 0% 0.000 0.05 0.05 0.04 0.03 10% 0.041 0.06 0.05 0.04 0.04 0.47 0.52 0.43 0.32 20% 0.084 0.08 0.05 0.05 0.03 0.45 0.55 0.48 0.33 30% 0.128 0.11 0.06 0.05 0.04 0.39 0.50 0.48 0.28 40% 0.166 0.15 0.08 0.05 0.04 0.31 0.39 0.48 0.21 R1000_F1000 0% 0.000 0.05 0.05 0.04 0.03 10% 0.041 0.06 0.05 0.04 0.03 0.75 0.80 0.73 0.61 20% 0.084 0.11 0.05 0.04 0.02 0.68 0.78 0.74 0.62 30% 0.128 0.18 0.06 0.05 0.04 0.59 0.75 0.70 0.57 40% 0.166 0.25 0.09 0.05 0.05 0.49 0.67 0.72 0.48

(44)

38

7 DIF constant 0.6

Type I error Power

sample size DIF% ASA L-ST L-SP L-PA L-DFSP L-ST L-SP L-PA L-DFSP NI20 R250_F250 0% 0.000 0.06 0.05 0.04 0.03 10% 0.064 0.05 0.05 0.04 0.04 0.33 0.31 0.24 0.18 20% 0.117 0.07 0.06 0.04 0.04 0.39 0.42 0.29 0.23 30% 0.184 0.12 0.09 0.04 0.05 0.29 0.35 0.30 0.19 40% 0.242 0.15 0.13 0.03 0.09 0.23 0.24 0.27 0.13 R500_F500 0% 0.000 0.05 0.05 0.04 0.03 10% 0.064 0.06 0.05 0.04 0.05 0.48 0.51 0.24 0.37 20% 0.117 0.08 0.05 0.05 0.04 0.56 0.67 0.46 0.47 30% 0.184 0.16 0.07 0.04 0.04 0.49 0.61 0.49 0.39 40% 0.242 0.22 0.13 0.03 0.07 0.38 0.47 0.54 0.30 R1000_F1000 0% 0.000 0.05 0.05 0.04 0.03 10% 0.064 0.06 0.05 0.04 0.03 0.65 0.70 0.53 0.57 20% 0.117 0.15 0.07 0.03 0.04 0.76 0.84 0.69 0.72 30% 0.184 0.26 0.06 0.04 0.05 0.74 0.89 0.81 0.75 40% 0.242 0.37 0.13 0.04 0.07 0.62 0.78 0.79 0.66 NI40 R250_F250 0% 0.000 0.05 0.05 0.04 0.03 10% 0.059 0.05 0.05 0.05 0.03 0.43 0.47 0.29 0.22 20% 0.121 0.07 0.05 0.04 0.03 0.38 0.43 0.32 0.23 30% 0.188 0.11 0.07 0.04 0.04 0.33 0.40 0.37 0.20 40% 0.251 0.16 0.13 0.04 0.07 0.26 0.29 0.36 0.18 R500_F500 0% 0.000 0.05 0.05 0.05 0.04 10% 0.059 0.06 0.05 0.05 0.04 0.66 0.70 0.46 0.46 20% 0.121 0.10 0.05 0.04 0.03 0.59 0.71 0.52 0.50 30% 0.188 0.19 0.09 0.04 0.06 0.52 0.68 0.62 0.41 40% 0.251 0.25 0.12 0.03 0.08 0.42 0.59 0.62 0.33 R1000_F1000 0% 0.000 0.05 0.05 0.04 0.03 10% 0.059 0.07 0.05 0.05 0.03 0.85 0.88 0.77 0.75 20% 0.121 0.14 0.05 0.04 0.03 0.83 0.92 0.85 0.79 30% 0.188 0.31 0.05 0.04 0.03 0.74 0.93 0.86 0.81 40% 0.251 0.43 0.08 0.04 0.05 0.64 0.86 0.85 0.72 NI60 R250_F250 0% 0.000 0.06 0.05 0.05 0.03 10% 0.061 0.06 0.05 0.04 0.04 0.58 0.61 0.55 0.35 20% 0.126 0.09 0.06 0.05 0.04 0.50 0.60 0.55 0.38 30% 0.186 0.11 0.06 0.05 0.04 0.38 0.50 0.49 0.31 40% 0.247 0.16 0.10 0.04 0.05 0.29 0.37 0.49 0.22 R500_F500 0% 0.000 0.06 0.05 0.04 0.03 10% 0.061 0.06 0.05 0.04 0.03 0.85 0.91 0.82 0.69 20% 0.126 0.12 0.05 0.04 0.03 0.72 0.85 0.80 0.63 30% 0.186 0.18 0.06 0.04 0.04 0.58 0.78 0.72 0.61 40% 0.247 0.27 0.10 0.05 0.07 0.49 0.67 0.73 0.48 R1000_F1000 0% 0.000 0.05 0.05 0.05 0.03 10% 0.061 0.07 0.05 0.05 0.04 0.91 0.94 0.92 0.83 20% 0.126 0.17 0.05 0.05 0.03 0.86 0.94 0.92 0.84 30% 0.186 0.28 0.06 0.05 0.04 0.79 0.95 0.91 0.87 40% 0.247 0.43 0.05 0.03 0.04 0.71 0.94 0.93 0.83

(45)

39

8 DIF balanced 0.4

Type I error Power

sample size DIF% ASA L-ST L-SP L-PA L-DFSP L-ST L-SP L-PA L-DFSP NI20 R250_F250 0% 0.000 0.04 0.04 0.03 0.02 10% 0.004 0.05 0.05 0.04 0.03 0.27 0.25 0.18 0.19 20% 0.004 0.05 0.04 0.03 0.03 0.38 0.36 0.28 0.27 30% 0.014 0.07 0.06 0.04 0.04 0.46 0.43 0.34 0.37 40% 0.007 0.06 0.05 0.04 0.03 0.42 0.40 0.32 0.33 R500_F500 0% 0.000 0.05 0.05 0.03 0.03 10% 0.004 0.05 0.05 0.04 0.03 0.54 0.51 0.40 0.44 20% 0.004 0.05 0.04 0.03 0.03 0.64 0.62 0.50 0.52 30% 0.014 0.07 0.05 0.03 0.03 0.70 0.67 0.56 0.60 40% 0.007 0.06 0.05 0.03 0.04 0.62 0.59 0.49 0.52 R1000_F1000 0% 0.000 0.04 0.05 0.03 0.03 10% 0.004 0.04 0.04 0.03 0.02 0.75 0.74 0.64 0.69 20% 0.004 0.05 0.05 0.03 0.03 0.84 0.81 0.71 0.74 30% 0.014 0.06 0.05 0.02 0.03 0.91 0.85 0.77 0.78 40% 0.007 0.06 0.05 0.03 0.04 0.80 0.78 0.71 0.73 NI40 R250_F250 0% 0.000 0.05 0.06 0.05 0.03 10% 0.002 0.05 0.05 0.04 0.03 0.38 0.36 0.29 0.27 20% 0.003 0.05 0.05 0.04 0.03 0.43 0.42 0.35 0.33 30% 0.002 0.05 0.05 0.04 0.03 0.46 0.45 0.38 0.33 40% 0.004 0.05 0.06 0.04 0.03 0.44 0.42 0.36 0.32 R500_F500 0% 0.000 0.05 0.05 0.04 0.03 10% 0.002 0.05 0.04 0.04 0.03 0.57 0.57 0.47 0.48 20% 0.003 0.05 0.05 0.04 0.03 0.63 0.62 0.53 0.53 30% 0.002 0.07 0.06 0.04 0.04 0.69 0.67 0.60 0.57 40% 0.004 0.06 0.05 0.04 0.03 0.66 0.65 0.57 0.57 R1000_F1000 0% 0.000 0.05 0.05 0.04 0.03 10% 0.002 0.05 0.04 0.04 0.02 0.85 0.85 0.74 0.75 20% 0.003 0.05 0.05 0.04 0.03 0.83 0.83 0.75 0.77 30% 0.002 0.05 0.04 0.03 0.02 0.87 0.86 0.82 0.80 40% 0.004 0.06 0.05 0.03 0.02 0.85 0.84 0.80 0.79 NI60 R250_F250 0% 0.000 0.04 0.04 0.04 0.02 10% 0.005 0.05 0.05 0.05 0.03 0.44 0.43 0.39 0.35 20% 0.001 0.05 0.05 0.04 0.03 0.48 0.47 0.43 0.35 30% 0.005 0.05 0.05 0.04 0.03 0.43 0.42 0.37 0.32 40% 0.001 0.05 0.05 0.04 0.03 0.47 0.46 0.39 0.35 R500_F500 0% 0.000 0.05 0.05 0.04 0.02 10% 0.005 0.06 0.05 0.05 0.03 0.67 0.66 0.60 0.58 20% 0.001 0.04 0.04 0.03 0.02 0.69 0.68 0.64 0.60 30% 0.005 0.05 0.05 0.04 0.03 0.68 0.68 0.64 0.61 40% 0.001 0.05 0.06 0.04 0.03 0.69 0.67 0.62 0.58 R1000_F1000 0% 0.000 0.05 0.05 0.04 0.02 10% 0.005 0.06 0.05 0.04 0.03 0.89 0.86 0.84 0.80 20% 0.001 0.06 0.06 0.05 0.03 0.87 0.87 0.84 0.82 30% 0.005 0.05 0.05 0.04 0.02 0.86 0.86 0.84 0.81 40% 0.001 0.05 0.05 0.04 0.03 0.86 0.86 0.84 0.83

(46)

40

9 DIF balanced 0.6

Type I error Power

(47)

41

10 DIF balanced 0.4

Type I error Power

(48)

42

11 DIF balanced 0.6

Type I error Power

sample size DIF% ASA L-ST L-SP L-PA L-DFSP L-ST L-SP L-PA L-DFSP NI20 R250_F250 0% 0.000 0.04 0.04 0.03 0.03 10% 0.008 0.06 0.05 0.04 0.04 0.39 0.37 0.21 0.22 20% 0.011 0.05 0.05 0.03 0.02 0.51 0.47 0.27 0.26 30% 0.003 0.06 0.06 0.03 0.04 0.55 0.53 0.33 0.32 40% 0.007 0.06 0.05 0.03 0.04 0.56 0.53 0.35 0.37 R500_F500 0% 0.000 0.04 0.04 0.03 0.04 10% 0.008 0.04 0.04 0.03 0.04 0.70 0.68 0.46 0.52 20% 0.011 0.06 0.06 0.04 0.04 0.78 0.73 0.49 0.53 30% 0.003 0.06 0.05 0.03 0.03 0.77 0.76 0.59 0.59 40% 0.007 0.05 0.04 0.03 0.04 0.78 0.74 0.56 0.56 R1000_F1000 0% 0.000 0.04 0.04 0.03 0.03 10% 0.008 0.05 0.05 0.04 0.03 0.87 0.83 0.69 0.73 20% 0.011 0.06 0.05 0.03 0.04 0.93 0.91 0.78 0.80 30% 0.003 0.08 0.05 0.04 0.04 0.95 0.94 0.82 0.83 40% 0.007 0.07 0.05 0.04 0.05 0.95 0.93 0.81 0.85 NI40 R250_F250 0% 0.000 0.05 0.05 0.06 0.03 10% 0.005 0.06 0.05 0.04 0.04 0.54 0.53 0.35 0.35 20% 0.004 0.06 0.05 0.05 0.03 0.55 0.54 0.37 0.35 30% 0.005 0.06 0.05 0.04 0.03 0.63 0.63 0.45 0.40 40% 0.009 0.06 0.05 0.04 0.03 0.60 0.58 0.41 0.39 R500_F500 0% 0.000 0.04 0.04 0.04 0.03 10% 0.005 0.05 0.05 0.04 0.03 0.77 0.76 0.54 0.53 20% 0.004 0.05 0.05 0.04 0.04 0.79 0.77 0.61 0.61 30% 0.005 0.06 0.05 0.03 0.03 0.84 0.84 0.70 0.67 40% 0.009 0.08 0.05 0.05 0.03 0.82 0.80 0.67 0.65 R1000_F1000 0% 0.000 0.06 0.06 0.05 0.04 10% 0.005 0.05 0.04 0.03 0.03 0.93 0.92 0.82 0.80 20% 0.004 0.05 0.05 0.03 0.04 0.94 0.93 0.87 0.86 30% 0.005 0.08 0.05 0.04 0.03 0.97 0.96 0.90 0.88 40% 0.009 0.10 0.06 0.04 0.04 0.95 0.95 0.88 0.86 NI60 R250_F250 0% 0.000 0.05 0.05 0.04 0.03 10% 0.001 0.05 0.05 0.04 0.04 0.58 0.58 0.48 0.33 20% 0.003 0.05 0.04 0.04 0.03 0.64 0.64 0.49 0.41 30% 0.002 0.05 0.06 0.05 0.04 0.59 0.59 0.52 0.41 40% 0.004 0.04 0.05 0.04 0.03 0.63 0.61 0.51 0.40 R500_F500 0% 0.000 0.05 0.05 0.04 0.03 10% 0.001 0.05 0.05 0.04 0.03 0.86 0.83 0.77 0.61 20% 0.003 0.05 0.05 0.04 0.03 0.87 0.86 0.79 0.68 30% 0.002 0.06 0.06 0.04 0.04 0.84 0.84 0.76 0.66 40% 0.004 0.05 0.05 0.04 0.03 0.84 0.83 0.77 0.68 R1000_F1000 0% 0.000 0.05 0.06 0.05 0.03 10% 0.001 0.06 0.05 0.05 0.03 0.98 0.97 0.95 0.92 20% 0.003 0.06 0.05 0.05 0.04 0.98 0.98 0.95 0.91 30% 0.002 0.06 0.05 0.05 0.03 0.94 0.95 0.92 0.88 40% 0.004 0.05 0.05 0.04 0.04 0.96 0.96 0.92 0.88

(49)

43

DIF

constant

LRT-ST

20%

DIF

Finch, 2005; Stark et al., 2006

LRT-SP

DIF

LRT-PA

DIF-free

DIF

pure anchor

DIF

Shih

Wang

2009

MIMIC

LRT-DFSP

LRT-PA

LRT-SP

2001

LRT-PA

LRT-DFSP

LRT-SP

LRT-DFSP

DIF

balanced

LRT-ST

LRT-SP

LRT-DFSP

LRT-SP

DIF

constant

balanced

LRT-SP

DIF

30%

LRT-ST

DIF

(50)

44

Analysis of Variance

1. LRT-ST

ANOVA

F

η

2

η

2

_0.14

_{Cohen ,1998}

12 LRT-ST

ANOVA

ASA

F

_7,298

=1350.600

η

2

=0.969

F

2,298

=953.677

η

2

=0.865

F

2,298

=76.158

η

2

=0.338

F

_1,298

=115.979

η

2

=0.280

ASA

F

14,298

=170.627

η

2

=0.889

ASA

F

14,298

=14.407

η

2

_=0.404

_ASA

_F

7,298

=29.051

η

2

=0.406

LRT-ST

ASA

0.12 DIF

constant

ASA

2. LRT-SP

13 LRT-SP

ANOVA

ASA

F

7,298

=180.886

η

2

=0.809

F

1,298

=68.463

(51)

45

η

2

_=0.187

_F

2,298

=28.828

η

2

=0.162

ASA

F

_7,298

=23.487

η

2

=0.356

ASA

F

_14,298

=7.596

η

2

=0.263

ASA

F

_14,298

=6.708

η

2

=0.240

LRT-SP

ASA

0.24 3. LRT-PA

LRT-PA

ANOVA

14 F

_2,298

=72.477

η

2

=0.327

LRT-PA

20

60

0.01 LRT-PA

4. LRT-DFSP

15 LRT-DFSP

ANOVA

ASA

F

_7,298

=83.505

η

2

=0.662

F

1,298

=128.912

η

2

=0.302

F

2,298

=33.314

η

2

=0.183

F

_2,298

=27.532

η

2

=0.156

ASA

F

14,298

=4.701

η

2

=0.181

LRT-DFSP

ASA

DIF

constant

ASA

1. LRT-ST

16 LRT-ST

ANOVA

F

_2,155

=414.824

η

2

=0.843

ASA

F

_7,155

=32.913

η

2

=0.598

DIF

F

1,155

=104.779

η

2

=0.403

(52)

46

F

_2,155

=32.304

η

2

=0.294

ASA

F

_12,155

=3.775

η

2

=0.226

LRT-ST

R250/F250

R1000/F1000

100%

180%

DIF

0.4

0.6 50%

ASA

0.12 ASA

ASA

2. LRT-SP

17 LRT-SP

ANOVA

F

_2,213

=1129.682

η

2

=0.914

DIF

F

1,213

=799.640

η

2

=0.790

F

2,213

=105.311

η

2

=0.497

ASA

F

_7,213

=28.130

η

2

=0.480

F

_1,213

=104.760

η

2

=0.330

ASA

F

14,213

=5.083

η

2

=0.250

LRT-SP

R250/F250

R1000/F1000

100%

200%

LRT-SP

ASA

0.18 ASA

LRT-ST

3. LRT-PA

LRT-PA

ANOVA

18 F

2,226

=898.528

η

2

=0.888

DIF

F

_1,226

=718.257

η

2

=0.761

F

_2,226

=226.244

η

2

=0.667

F

1,226

=380.928

η

2

=0.628

ASA

F

7,226

=14.237

η

2

=0.306

ASA

F

_{14, 226}

=4.560

η

2

=0.220

LRT-PA

LRT-SP

LRT-PA

(53)

47

LRT-SP

LRT-PA

LRT-SP

14%

4. LRT-DFSP

19 LRT-DFSP

ANOVA

F

_2,226

=1349.239

η

2

=0.923

DIF

F

_1,226

=912.125

η

2

=0.801

F

_1,226

=778.850

η

2

=0.775

ASA

F

_7,226

=34.885

η

2

=0.519

F

_2,226

=98.560

η

2

=0.466

ASA

F

_7,226

=7.487

η

2

=0.188

ASA

F

14, 226

=2.970

η

2

=0.155

LRT-DFSP

R250/F250

R1000/F1000

200%

300%

DIF

0.4

0.6 50%

2001

DIF

DFTD

(54)

48

12 LRT-ST

F Eta testlength 2 0.013 76.158 0.000 0.338 samplesize 2 0.160 953.677 0.000 0.865 abilitydifference 1 0.019 115.979 0.000 0.280 DIFamount 1 0.000 0.024 0.876 0.000 ASA 7 0.226 1350.600 0.000 0.969 testlength * samplesize 4 0.001 5.816 0.000 0.072 testlength * abilitydifference 2 0.001 4.767 0.009 0.031 testlength * DIFamount 2 0.000 0.677 0.509 0.005 testlength * ASA 14 0.002 14.407 0.000 0.404 samplesize * abilitydifference 2 0.001 6.319 0.002 0.041 samplesize * DIFamount 2 0.000 0.290 0.748 0.002 samplesize * ASA 14 0.029 170.627 0.000 0.889 abilitydifference * DIFamount 1 0.000 0.056 0.813 0.000 abilitydifference * ASA 7 0.005 29.051 0.000 0.406 298 0.000 360

13 LRT-SP

F Eta testlength 2 0.000 8.034 0.000 0.051 samplesize 2 0.001 28.828 0.000 0.162 abilitydifference 1 0.002 68.463 0.000 0.187 DIFamount 1 0.000 5.160 0.024 0.017 ASA 7 0.007 180.886 0.000 0.809 testlength * samplesize 4 0.000 0.557 0.694 0.007 testlength * abilitydifference 2 0.000 1.555 0.213 0.010 testlength * DIFamount 2 0.000 0.420 0.658 0.003 testlength * ASA 14 0.000 6.708 0.000 0.240 samplesize * abilitydifference 2 0.000 0.941 0.392 0.006 samplesize * DIFamount 2 0.000 3.671 0.027 0.024 samplesize * ASA 14 0.000 7.596 0.000 0.263 abilitydifference * DIFamount 1 0.000 0.272 0.603 0.001 abilitydifference * ASA 7 0.001 23.487 0.000 0.356 298 0.000 360

(55)

49

14 LRT-PA

F Eta testlength 2 0.002 72.477 0.000 0.327 samplesize 2 0.000 6.284 0.002 0.040 abilitydifference 1 0.000 12.717 0.000 0.041 DIFamount 1 0.000 0.120 0.729 0.000 ASA 7 0.000 1.489 0.171 0.034 testlength * samplesize 4 0.000 0.938 0.442 0.012 testlength * abilitydifference 2 0.000 0.625 0.536 0.004 testlength * DIFamount 2 0.000 0.188 0.829 0.001 testlength * ASA 14 0.000 1.276 0.221 0.057 samplesize * abilitydifference 2 0.000 7.488 0.001 0.048 samplesize * DIFamount 2 0.000 0.369 0.692 0.002 samplesize * ASA 14 0.000 0.275 0.996 0.013 abilitydifference * DIFamount 1 0.000 0.095 0.758 0.000 abilitydifference * ASA 7 0.000 1.442 0.188 0.033 298 0.000 360

15 LRT-DFSP

F Eta testlength 2 0.001 33.314 0.000 0.183 samplesize 2 0.001 27.532 0.000 0.156 abilitydifference 1 0.003 128.912 0.000 0.302 DIFamount 1 0.000 0.445 0.505 0.001 ASA 7 0.002 83.505 0.000 0.662 testlength * samplesize 4 0.000 0.398 0.810 0.005 testlength * abilitydifference 2 0.000 0.935 0.394 0.006 testlength * DIFamount 2 0.000 0.504 0.605 0.003 testlength * ASA 14 0.000 2.872 0.000 0.119 samplesize * abilitydifference 2 0.000 5.718 0.004 0.037 samplesize * DIFamount 2 0.000 2.505 0.083 0.017 samplesize * ASA 14 0.000 4.701 0.000 0.181 abilitydifference * DIFamount 1 0.000 0.235 0.628 0.001 abilitydifference * ASA 7 0.000 6.776 0.000 0.137 298 0.000 360

(56)

50

16 LRT-ST

F Eta testlength 2 0.089 32.304 0.000 0.294 samplesize 2 1.145 414.824 0.000 0.843 abilitydifference 1 0.013 4.643 0.033 0.029 DIFamount 1 0.289 104.779 0.000 0.403 ASA 7 0.091 32.913 0.000 0.598 testlength * samplesize 4 0.004 1.350 0.254 0.034 testlength * abilitydifference 2 0.001 0.289 0.749 0.004 testlength * DIFamount 2 0.002 0.829 0.438 0.011 testlength * ASA 12 0.010 3.775 0.000 0.226 samplesize * abilitydifference 2 0.000 0.054 0.947 0.001 samplesize * DIFamount 2 0.028 10.003 0.000 0.114 samplesize * ASA 12 0.003 1.220 0.274 0.086 abilitydifference * DIFamount 1 0.004 1.528 0.218 0.010 abilitydifference * ASA 5 0.001 0.278 0.925 0.009 155 0.003 211

17 LRT-SP

F Eta testlength 2 0.213 105.311 0.000 0.497 samplesize 2 2.285 1129.682 0.000 0.914 abilitydifference 1 0.212 104.760 0.000 0.330 DIFamount 1 1.618 799.640 0.000 0.790 ASA 7 0.057 28.130 0.000 0.480 testlength * samplesize 4 0.005 2.371 0.054 0.043 testlength * abilitydifference 2 0.006 3.096 0.047 0.028 testlength * DIFamount 2 0.002 0.874 0.419 0.008 testlength * ASA 14 0.010 5.083 0.000 0.250 samplesize * abilitydifference 2 0.005 2.239 0.109 0.021 samplesize * DIFamount 2 0.033 16.479 0.000 0.134 samplesize * ASA 14 0.002 1.068 0.388 0.066 abilitydifference * DIFamount 1 0.008 3.898 0.050 0.018 abilitydifference * ASA 7 0.005 2.549 0.015 0.077 213 0.002 275