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e
attr
ib
u
ted
to
th
e
tr
ea
tm
en
t
[
3
]
,
[
6
]
.
Desp
ite
th
is
p
r
ac
tical
ad
v
an
tag
e,
th
e
b
asic
R
D
d
esig
n
h
as
s
ev
er
al
l
im
itatio
n
s
th
at
ca
n
r
ed
u
ce
its
u
tili
ty
.
T
h
e
b
asic
R
D
d
esig
n
is
less
ef
f
icien
t
th
a
n
a
co
m
p
ar
ab
le
R
C
T
d
u
e
to
th
e
h
ig
h
c
o
r
r
elatio
n
b
etwe
en
th
e
ass
ig
n
m
en
t
v
ar
ia
b
le
an
d
th
e
b
in
a
r
y
tr
ea
tm
en
t
in
d
icato
r
,
th
u
s
r
eq
u
ir
i
n
g
m
o
r
e
ca
s
es
f
o
r
th
e
s
am
e
s
tatis
t
ical
p
o
wer
[
7
]
.
Ad
d
itio
n
ally
,
in
th
e
b
asic
R
D
d
esig
n
,
ca
u
s
al
in
f
er
en
ce
is
lim
ited
to
th
e
cu
to
f
f
as
tr
ea
tm
en
t
an
d
c
o
n
tr
o
l
ca
s
es
d
o
n
o
t
o
v
er
lap
b
e
y
o
n
d
th
e
cu
t
o
f
f
v
al
u
e
[
8
]
.
C
o
n
s
eq
u
e
n
tly
,
f
o
r
th
o
s
e
in
ter
ested
in
ass
es
s
in
g
p
r
o
g
r
am
ef
f
ec
tiv
en
ess
at
o
th
er
p
o
in
ts
in
th
e
ass
ig
n
m
en
t
v
ar
iab
le
d
is
tr
ib
u
tio
n
,
th
e
lo
ca
l
im
p
ac
t
esti
m
ate
m
ay
h
av
e
s
o
m
ewh
at
l
im
ited
v
alu
e.
T
h
e
b
asic
R
D
d
esig
n
h
as
e
v
o
lv
ed
in
to
m
u
ltip
le
d
esig
n
v
ar
ian
ts
to
ad
d
r
ess
th
e
co
m
p
lex
ity
o
f
ev
alu
atio
n
co
n
tex
ts
i
n
th
e
f
iel
d
o
f
ed
u
ca
tio
n
.
On
e
co
m
m
o
n
v
ar
iatio
n
is
t
h
e
u
tili
za
tio
n
o
f
m
u
ltip
le
cu
to
f
f
s
in
R
D
d
esig
n
.
T
h
e
m
u
ltip
le
-
cu
to
f
f
r
eg
r
ess
io
n
d
is
co
n
tin
u
ity
(
M
C
R
D)
d
esig
n
ar
is
es
f
r
o
m
v
ar
iatio
n
s
in
th
e
cu
to
f
f
s
u
s
ed
to
ass
ig
n
in
d
iv
id
u
als
o
r
u
n
its
to
co
n
d
itio
n
s
[
9
]
–
[
1
2
]
.
Fo
r
ex
am
p
le,
s
ch
o
o
l
d
is
tr
ict
s
m
ay
u
s
e
d
if
f
er
en
t
r
ea
d
in
g
ass
ess
m
en
t
s
co
r
e
cu
to
f
f
s
as
th
e
elig
ib
ilit
y
cr
iter
ia
f
o
r
in
v
itin
g
s
tu
d
en
ts
to
s
u
m
m
er
s
ch
o
o
l,
o
r
u
n
iv
er
s
ities
m
ay
u
s
e
d
if
f
e
r
en
t
in
co
m
e
elig
ib
ilit
y
th
r
esh
o
ld
s
f
o
r
d
eter
m
i
n
in
g
f
i
n
an
cial
aid
r
e
cip
ien
ts
.
T
o
d
ate,
th
e
m
o
s
t
co
m
m
o
n
a
n
aly
tic
m
eth
o
d
f
o
r
th
e
MCR
D
d
esig
n
is
esti
m
atin
g
an
av
er
ag
e
R
D
tr
ea
tm
en
t
ef
f
ec
t
b
y
p
o
o
lin
g
tr
ea
tm
en
t
esti
m
ates
ac
r
o
s
s
cu
to
f
f
s
(
i.e
.
,
th
e
ce
n
ter
in
g
-
an
d
-
p
o
l
lin
g
ap
p
r
o
ac
h
)
[
9
]
,
[
1
0
]
.
T
h
e
p
o
o
led
R
D
esti
m
ate
p
r
o
v
id
es
a
s
u
m
m
ar
y
o
f
th
e
a
v
er
ag
e
t
r
ea
tm
en
t
e
f
f
ec
t
ac
r
o
s
s
cu
to
f
f
s
.
Ho
wev
er
,
th
e
u
s
e
o
f
th
e
p
o
o
lin
g
m
eth
o
d
m
ay
ig
n
o
r
e
h
ete
r
o
g
e
n
eity
in
th
e
tr
ea
tm
en
t
ef
f
ec
t
esti
m
at
es
at
d
if
f
er
en
t
cu
to
f
f
lo
ca
tio
n
s
[
9
]
.
W
h
en
tr
ea
tm
e
n
t
ef
f
ec
ts
v
ar
y
ac
r
o
s
s
cu
to
f
f
s
,
s
im
p
ly
av
er
ag
in
g
th
ese
ef
f
ec
ts
ca
n
o
b
s
cu
r
e
ev
id
en
ce
th
at
th
e
in
ter
v
e
n
tio
n
was m
o
r
e
o
r
less
ef
f
ec
tiv
e
f
o
r
p
ar
ticip
an
ts
at
d
if
f
er
e
n
t
cu
t p
o
in
ts
.
As
a
r
esu
lt,
th
e
p
u
r
p
o
s
e
o
f
th
is
p
ap
er
is
to
d
em
o
n
s
tr
ate
m
o
d
elin
g
ap
p
r
o
ac
h
es
th
at
allo
w
f
o
r
s
im
u
l
t
a
n
e
ou
s
esti
m
atio
n
o
f
th
e
av
er
ag
e
MCR
D
tr
ea
tm
en
t
ef
f
ec
t
an
d
th
e
p
o
ten
tial
h
eter
o
g
en
eity
in
e
f
f
ec
ts
ac
r
o
s
s
in
ter
v
en
tio
n
s
ites
.
Usi
n
g
d
ata
f
r
o
m
a
k
in
d
e
r
g
ar
ten
m
ath
em
atics
in
ter
v
en
tio
n
tar
g
etin
g
lo
w
ac
h
iev
in
g
s
tu
d
en
ts
at
-
r
is
k
f
o
r
d
ev
el
o
p
in
g
a
lear
n
in
g
d
is
ab
ilit
y
,
we
illu
s
tr
ate
th
e
ap
p
licatio
n
o
f
MC
R
D
u
s
in
g
p
ar
am
etr
ic
an
d
n
o
n
p
ar
am
etr
ic
m
o
d
elin
g
[
3
]
,
[1
3
]
a
n
d
esti
m
ate
an
d
m
o
d
el
in
ter
v
en
tio
n
ef
f
ec
t
h
eter
o
g
en
eity
ac
r
o
s
s
cu
to
f
f
s
.
T
h
e
cu
r
r
en
t
d
em
o
n
s
tr
atio
n
u
tili
ze
s
s
m
all
with
in
-
cu
to
f
f
u
n
it
s
am
p
les,
wh
ic
h
m
ir
r
o
r
r
ea
l
-
wo
r
ld
ev
alu
atio
n
co
n
tex
ts
well
[1
4
]
.
Ho
wev
er
,
s
m
all
s
am
p
les
r
ed
u
ce
th
e
s
tatis
tical
p
o
wer
o
f
t
h
e
R
D
es
tim
ates
a
t
ea
ch
lo
ca
l
cu
t
o
f
f
[
7
]
.
T
h
er
e
f
o
r
e,
wh
ile
we
u
s
e
b
o
th
p
ar
am
etr
ic
an
d
n
o
n
p
a
r
am
etr
ic
m
et
h
o
d
s
to
d
em
o
n
s
tr
ate
th
e
MCR
D
d
esig
n
an
d
an
aly
s
is
,
we
o
n
ly
im
p
lem
en
t
th
e
p
ar
a
m
etr
ic
m
eth
o
d
to
e
x
p
lo
r
e
h
eter
o
g
en
eity
i
n
im
p
ac
ts
ac
r
o
s
s
tr
ea
tm
en
t
s
ites
a
s
th
e
n
o
n
p
a
r
am
etr
ic
m
eth
o
d
d
o
es
n
o
t
s
u
p
p
o
r
t
th
e
m
o
r
e
co
m
p
lex
m
o
d
el
r
eq
u
ir
ed
f
o
r
s
u
ch
an
aly
s
is
.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
o
f
f
er
s
a
p
r
ac
tical
s
o
l
u
tio
n
f
o
r
e
v
alu
atin
g
ed
u
ca
tio
n
a
l
p
r
o
g
r
am
s
t
h
at
u
s
e
d
if
f
er
en
t
c
u
to
f
f
s
ac
r
o
s
s
m
u
ltip
le
in
ter
v
en
tio
n
u
n
its
o
r
s
ites
,
esp
ec
ially
in
co
n
te
x
ts
with
s
m
all
s
am
p
le
s
izes,
an
d
p
r
o
v
id
es a
v
alu
ab
le
co
n
tr
i
b
u
tio
n
to
r
esear
ch
o
n
ev
alu
ati
o
n
m
eth
o
d
s
in
ed
u
ca
tio
n
.
2.
M
E
T
H
O
D
2
.
1
.
Da
t
a
s
o
urce
Ma
th
em
atics
in
ter
v
en
tio
n
d
ata
wer
e
co
llected
f
r
o
m
2
0
1
2
to
2
0
1
5
in
c
o
n
ju
n
ctio
n
with
a
u
n
iv
er
s
ity
–
s
ch
o
o
l
d
is
tr
ict
co
llab
o
r
atio
n
d
esig
n
ed
to
ev
alu
ate
th
e
im
p
ac
t
o
f
a
s
m
all
-
g
r
o
u
p
,
tier
2
[1
5
]
k
in
d
er
g
ar
te
n
m
ath
em
atics
in
ter
v
en
tio
n
,
R
OOT
S
.
I
n
t
h
e
f
i
r
s
t
two
y
e
ar
s
o
f
th
e
p
r
o
ject,
s
tu
d
y
p
ar
ticip
an
ts
atten
d
ed
k
in
d
er
g
a
r
ten
in
o
n
e
o
f
f
o
u
r
s
ch
o
o
l
d
is
tr
icts
in
Or
eg
o
n
,
U
n
ited
S
tates
:
o
n
e
s
ch
o
o
l
d
i
s
tr
ict
lo
ca
ted
in
th
e
Po
r
tlan
d
m
etr
o
p
o
litan
ar
ea
an
d
th
r
ee
lo
ca
ted
in
s
u
b
u
r
b
an
a
n
d
r
u
r
al
ar
ea
s
o
f
wester
n
Or
e
g
o
n
(
5
1
class
r
o
o
m
s
f
r
o
m
1
3
s
ch
o
o
ls
in
to
tal)
.
I
n
y
ea
r
s
two
an
d
th
r
ee
,
two
s
ch
o
o
l
d
is
tr
icts
f
r
o
m
th
e
m
etr
o
p
o
litan
ar
ea
o
f
B
o
s
to
n
,
Ma
s
s
ac
h
u
s
etts
,
Un
ited
State
s
,
also
p
ar
ticip
ated
(
5
5
class
r
o
o
m
s
f
r
o
m
9
s
ch
o
o
ls
in
to
tal)
.
2
.
2
.
RO
O
T
S inte
rv
ent
io
n
R
OOT
S
is
a
5
0
-
less
o
n
,
tier
2
k
in
d
er
g
a
r
ten
m
ath
em
atics
in
ter
v
en
tio
n
tar
g
etin
g
s
tu
d
en
t
s
with
o
r
at
-
r
is
k
f
o
r
m
ath
lear
n
in
g
d
is
ab
ilit
ies.
Dir
ec
t
m
ath
in
s
tr
u
ctio
n
was
d
eliv
er
ed
to
s
tu
d
en
ts
in
s
m
all
g
r
o
u
p
s
(
m
ax
im
u
m
o
f
f
iv
e
s
tu
d
en
ts
)
a
cr
o
s
s
1
0
6
class
r
o
o
m
s
.
E
ac
h
s
ess
io
n
last
ed
2
0
m
in
u
tes an
d
to
o
k
p
lace
f
iv
e
d
a
y
s
a
wee
k
o
v
er
a
1
0
-
wee
k
p
er
i
o
d
.
R
OOT
S
u
s
es
ev
id
en
ce
-
b
ased
p
r
ac
tices
to
en
h
a
n
ce
n
u
m
b
er
s
en
s
e
an
d
wh
o
le
-
n
u
m
b
er
c
o
n
ce
p
ts
,
c
o
v
e
r
in
g
co
u
n
tin
g
an
d
ca
r
d
in
ality
,
n
u
m
b
er
o
p
e
r
atio
n
s
,
an
d
b
ase
t
en
/p
lace
v
alu
e.
T
h
e
in
ter
v
en
tio
n
in
co
r
p
o
r
ates
f
o
u
r
v
alid
ated
,
e
x
p
licit,
an
d
s
y
s
tem
atic
in
s
tr
u
ctio
n
al
p
r
ac
tices:
teac
h
er
m
o
d
elin
g
,
d
elib
er
ate
p
r
ac
tice,
v
is
u
al
r
e
p
r
esen
tatio
n
s
o
f
m
ath
em
atics,
an
d
ac
ad
em
ic
f
ee
d
b
ac
k
.
A
d
d
itio
n
ally
,
R
OOT
S
aim
s
to
p
r
o
m
o
te
s
tu
d
en
t e
n
g
ag
em
en
t b
y
p
r
o
v
id
in
g
s
tr
u
ct
u
r
ed
o
p
p
o
r
tu
n
ities
f
o
r
s
tu
d
en
t r
esp
o
n
s
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
Mu
ltip
le
-
cu
to
ff reg
r
ess
io
n
d
is
co
n
tin
u
ity
d
esig
n
s
in
e
d
u
ca
tio
n
a
l e
va
lu
a
tio
n
(
Hye
o
n
Jin
Yo
o
n
)
1599
2
.
3
.
M
ea
s
ures
2
.
3
.
1
.
Ass
ess
i
ng
s
t
ud
ent
pro
f
iciency
in ea
rly
nu
m
ber
s
ens
e
(
ASPENS)
Ass
es
s
in
g
s
tu
d
en
t
p
r
o
f
icien
cy
in
ea
r
ly
n
u
m
b
e
r
s
en
s
e
(
ASPE
NS)
was
o
n
e
o
f
two
s
cr
ee
n
in
g
m
ea
s
u
r
es
th
at
co
m
p
r
is
ed
th
e
ass
ig
n
m
en
t
v
ar
iab
le
u
s
ed
to
i
d
en
tify
s
tu
d
en
ts
f
o
r
in
clu
s
io
n
in
th
e
R
OOT
S
in
ter
v
en
tio
n
.
ASPENS
wa
s
d
esig
n
ed
to
s
cr
ee
n
an
d
m
o
n
ito
r
th
e
p
r
o
g
r
e
s
s
o
f
s
tu
d
en
ts
wh
o
ar
e
at
r
is
k
f
o
r
m
ath
em
atics
d
if
f
icu
lty
in
Gr
a
d
es
K
th
r
o
u
g
h
1
[1
6
]
.
T
h
e
k
i
n
d
er
g
a
r
ten
A
SP
E
NS
as
s
es
s
m
en
t
co
m
p
r
is
es
th
r
ee
cu
r
r
icu
lu
m
-
b
ased
m
ea
s
u
r
es:
n
u
m
b
e
r
id
en
t
if
icatio
n
(
1
1
2
item
s
)
,
m
ag
n
itu
d
e
co
m
p
a
r
is
o
n
(
5
6
item
s
)
,
an
d
m
is
s
in
g
n
u
m
b
e
r
s
(
4
2
item
s
)
,
ea
ch
i
n
d
iv
id
u
ally
ad
m
in
is
ter
ed
f
o
r
o
n
e
m
i
n
u
te.
C
h
ild
r
en
n
am
e
n
u
m
b
er
s
q
u
ic
k
ly
,
id
e
n
tify
g
r
ea
ter
n
u
m
b
er
s
,
a
n
d
d
ete
r
m
in
e
m
is
s
in
g
n
u
m
b
er
s
f
r
o
m
s
tr
in
g
s
.
E
a
ch
s
u
b
test
s
co
r
es
co
r
r
ec
t
o
r
in
co
r
r
ec
t
r
esp
o
n
s
es,
with
a
co
m
p
o
s
ite
s
co
r
e
d
e
r
iv
ed
f
r
o
m
weig
h
ted
s
u
b
test
s
co
r
es
b
ased
o
n
s
tan
d
a
r
d
d
e
v
iatio
n
(
SD)
o
f
th
e
r
aw
s
co
r
es
[1
6
]
.
Fo
r
th
e
cu
r
r
e
n
t
d
ata,
th
e
p
r
etest
AS
PENS
co
m
p
o
s
ite
r
an
g
ed
f
r
o
m
0
to
2
5
3
.
9
(
M=
5
7
.
0
1
,
SD=4
7
.
6
8
)
,
with
ac
ce
p
tab
le
te
s
t
–
r
etest r
eliab
ilit
ies (
r
=.
7
4
-
.
8
5
)
.
2
.
3
.
2
.
Num
ber
s
ens
e
brief
(
N
SB
)
T
h
e
n
u
m
b
e
r
s
en
s
e
b
r
ief
(
NSB
)
,
th
e
s
ec
o
n
d
s
cr
ee
n
in
g
m
ea
s
u
r
e
u
s
ed
to
co
n
s
tr
u
ct
th
e
ass
ig
n
m
en
t
v
ar
iab
le
[1
7
]
,
id
en
tifie
s
s
tu
d
en
ts
at
r
is
k
f
o
r
later
d
if
f
icu
lties
in
ad
v
an
ce
d
m
ath
em
atics
co
n
ce
p
ts
.
Stu
d
en
ts
’
n
u
m
er
ical
c
o
m
p
eten
cies,
in
c
lu
d
in
g
co
u
n
tin
g
k
n
o
wled
g
e,
n
u
m
b
er
r
ec
o
g
n
itio
n
,
co
m
p
ar
is
o
n
s
,
n
o
n
-
v
er
b
al
ca
lcu
latio
n
,
an
d
s
to
r
y
p
r
o
b
le
m
s
ar
e
ass
ess
ed
.
Ad
m
in
is
ter
ed
in
d
iv
i
d
u
ally
a
n
d
u
n
tim
ed
,
it
co
m
p
r
is
es
3
3
p
o
s
s
ib
le
item
s
s
co
r
ed
as
co
r
r
ec
t
o
r
in
co
r
r
ec
t,
y
ield
in
g
a
to
ta
l
s
co
r
e
r
an
g
e
o
f
0
to
3
3
.
T
est
–
r
etest
r
eliab
ilit
ies
r
an
g
ed
f
r
o
m
.
7
8
t
o
.
8
6
[1
8
]
.
P
r
ed
ictiv
e
v
alid
ity
,
ass
ess
ed
b
y
th
e
co
r
r
elatio
n
b
etwe
en
NSB
s
co
r
es
in
Gr
ad
es
K
th
r
o
u
g
h
1
a
n
d
Gr
a
d
e
3
W
o
o
d
c
o
ck
–
J
o
h
n
s
o
n
Ach
iev
em
e
n
t T
e
s
t sco
r
es,
r
an
g
ed
f
r
o
m
.
6
2
to
.
6
4
[
1
8
].
2
.
3
.
3
.
Sta
nfo
rd
ea
rly
s
cho
o
l
a
chiev
em
ent
t
est
2
m
a
t
hem
a
t
ics
(
SE
SA
T
2
)
T
h
e
Stan
f
o
r
d
ea
r
l
y
s
ch
o
o
l
ac
h
iev
em
en
t
test
2
(
SESAT
2
)
m
ath
em
atics
is
th
e
k
in
d
e
r
g
ar
ten
v
er
s
io
n
o
f
th
e
Stan
f
o
r
d
ac
h
ie
v
em
en
t te
s
t
1
0
th
ed
itio
n
s
er
ies (
SAT
-
10
)
[
19
]
.
T
h
e
SESAT
2
s
er
v
e
d
as th
e
p
o
s
ttes
t m
ea
s
u
r
e
in
th
e
c
u
r
r
en
t
s
tu
d
y
.
T
h
e
SESAT
2
m
ea
s
u
r
es
ea
r
ly
m
at
h
em
atica
l
s
k
ills
,
in
clu
d
in
g
n
u
m
b
er
r
ec
o
g
n
itio
n
,
co
u
n
tin
g
,
an
d
b
asic
o
p
er
atio
n
s
s
u
ch
as
s
im
p
le
ad
d
itio
n
an
d
s
u
b
tr
ac
tio
n
.
T
h
e
in
ter
n
al
co
n
s
is
ten
cy
o
f
SESAT
2
m
ath
em
atics
was r
ep
o
r
ted
as .
8
8
in
o
n
e
s
tu
d
y
[2
0
]
.
2
.
4
.
O
rig
ina
l r
esea
rc
h desi
g
n:
RCT
Stu
d
en
ts
wer
e
f
ir
s
t
co
n
s
id
er
ed
elig
ib
le
f
o
r
th
e
R
OOT
S
in
ter
v
en
tio
n
if
th
ey
s
co
r
e
d
2
0
o
r
less
o
n
th
e
NSB
an
d
h
ad
a
co
m
p
o
s
ite
ASPENS
s
co
r
e
th
at
p
lace
d
th
e
m
in
th
e
s
tr
ateg
ic
o
r
in
ten
s
iv
e
r
a
n
g
e.
T
h
e
ASPENS
an
d
NSB
s
co
r
es o
f
R
OOT
S
-
el
ig
ib
le
s
tu
d
en
ts
wer
e
th
en
s
ep
ar
ately
co
n
v
er
te
d
in
to
s
tan
d
ar
d
s
co
r
es,
an
d
th
e
two
s
tan
d
ar
d
s
co
r
es
wer
e
s
u
m
m
ed
to
co
m
p
u
te
an
o
v
e
r
all
co
m
p
o
s
ite
s
co
r
e.
T
h
e
co
m
p
o
s
ite
s
tan
d
ar
d
s
co
r
es
o
f
R
OOT
S
-
elig
ib
le
s
tu
d
en
ts
wer
e
r
an
k
-
o
r
d
er
ed
with
in
ea
c
h
cl
ass
r
o
o
m
,
an
d
th
e
lo
west
s
co
r
i
n
g
10
s
tu
d
en
ts
wer
e
th
en
r
an
d
o
m
ly
ass
ig
n
ed
t
o
o
n
e
o
f
two
co
n
d
itio
n
s
:
a
R
OOT
S
g
r
o
u
p
[2
1
]
o
r
a
n
o
-
t
r
ea
tm
en
t
b
u
s
in
ess
-
as
-
u
s
u
al
(
B
AU)
co
n
tr
o
l c
o
n
d
itio
n
(
i.e
.
,
r
an
d
o
m
ass
ig
n
m
en
t a
t stu
d
en
t
-
lev
el
with
in
ea
ch
class
r
o
o
m
)
.
2
.
5
.
Curre
nt
re
s
ea
rc
h desi
g
n:
M
CRD
R
an
k
o
r
d
er
in
g
o
f
th
e
co
m
p
o
s
ite
s
tan
d
ar
d
s
co
r
es
in
ea
ch
class
r
o
o
m
to
id
en
tify
th
e
10
lo
west
-
p
er
f
o
r
m
in
g
s
tu
d
en
ts
r
esu
lted
i
n
1
0
6
u
n
iq
u
e
c
u
to
f
f
s
co
r
es
(
o
n
e
f
r
o
m
ea
ch
class
r
o
o
m
)
,
en
a
b
lin
g
t
h
e
cr
ea
tio
n
o
f
th
e
cu
r
r
en
t
s
y
n
th
etic
MCR
D
d
esig
n
[
8
]
.
Sp
ec
i
f
ically
,
f
r
o
m
th
e
R
C
T
d
ataset,
a
s
in
g
le
c
u
to
f
f
b
ased
o
n
th
e
ass
ig
n
m
en
t
v
ar
iab
le
co
n
tin
u
u
m
an
d
th
e
t
r
ea
tm
en
t
ass
ig
n
m
e
n
t
r
u
le
wer
e
d
ete
r
m
in
ed
,
d
iv
id
in
g
th
e
o
b
s
er
v
atio
n
s
in
to
eith
er
th
e
tr
ea
tm
en
t
o
r
co
n
tr
o
l
co
n
d
itio
n
.
T
h
en
,
an
R
D
tr
ea
tm
en
t
(
R
D
-
T
)
g
r
o
u
p
was
cr
ea
ted
b
y
ex
clu
d
in
g
all
co
n
tr
o
l
g
r
o
u
p
o
b
s
er
v
atio
n
s
in
th
e
tr
ea
ted
s
id
e
(
e.
g
.
,
b
e
lo
w
th
e
c
u
to
f
f
)
,
a
n
d
an
R
D
co
n
tr
o
l
g
r
o
u
p
was
cr
ea
ted
b
y
e
x
clu
d
in
g
all
tr
ea
ted
o
b
s
er
v
atio
n
s
in
th
e
co
n
tr
o
l
s
id
e
(
e
.
g
.
,
ab
o
v
e
t
h
e
c
u
to
f
f
)
.
Fo
llo
win
g
t
h
is
ap
p
r
o
ac
h
,
th
e
MCR
D
d
ata
w
er
e
co
n
s
tr
u
cted
f
r
o
m
th
e
R
C
T
d
ataset
f
o
r
ea
ch
class
r
o
o
m
.
Sp
ec
if
ically
,
we
cr
ea
ted
an
R
D
tr
ea
tm
en
t
(
R
D
-
T
)
g
r
o
u
p
b
y
ex
clu
d
in
g
all
co
n
tr
o
l
g
r
o
u
p
o
b
s
er
v
atio
n
s
b
elo
w
th
e
cu
to
f
f
i
n
ea
ch
class
r
o
o
m
wh
ile
th
e
R
D
co
n
tr
o
l
(
R
D
-
C
)
g
r
o
u
p
in
ea
ch
c
lass
r
o
o
m
co
m
p
r
is
ed
s
tu
d
e
n
ts
wh
o
s
e
ass
ig
n
m
e
n
t
v
ar
iab
le
s
co
r
es
f
ell
ab
o
v
e
th
e
class
r
o
o
m
c
u
to
f
f
.
I
n
to
tal,
1
0
6
u
n
iq
u
e
cu
to
f
f
s
co
r
es
(
o
n
e
f
o
r
ea
c
h
class
r
o
o
m
)
wer
e
id
en
tifie
d
,
r
a
n
g
in
g
f
r
o
m
-
2
.
1
7
to
0
.
2
4
(
M=
-
.
7
5
,
SD=.
4
2
)
.
T
h
e
m
ajo
r
ity
o
f
th
e
class
r
o
o
m
c
u
to
f
f
v
alu
es
wer
e
b
elo
w
0
,
in
d
icatin
g
th
at
th
e
R
OOT
S
clas
s
r
o
o
m
s
wer
e
ty
p
ically
b
elo
w
th
e
m
ea
n
v
alu
e
o
n
th
e
co
m
p
o
s
ite
s
cr
ee
n
in
g
m
ea
s
u
r
e.
T
h
e
R
D
-
T
g
r
o
u
p
(
n
=
6
4
0
)
an
d
t
h
e
R
D
-
C
g
r
o
u
p
(
n
=1
,
2
6
0
)
co
n
s
is
ted
o
f
s
im
ilar
p
r
o
p
o
r
tio
n
s
o
f
f
em
ale
an
d
eth
n
ic
m
in
o
r
ity
s
tu
d
en
ts
.
T
h
e
R
D
-
T
g
r
o
u
p
in
clu
d
ed
m
o
r
e
E
n
g
lis
h
lan
g
u
ag
e
lear
n
er
s
an
d
m
o
r
e
s
tu
d
en
ts
r
ec
eiv
in
g
s
p
ec
ial
e
d
u
ca
tio
n
s
er
v
ices
th
a
n
th
e
R
D
-
C
g
r
o
u
p
.
As
ex
p
ec
ted
g
iv
en
th
e
u
s
e
o
f
a
cu
to
f
f
-
b
ased
tr
ea
tm
en
t
ass
ig
n
m
en
t
r
u
le,
b
o
th
ass
ig
n
m
en
t
v
a
r
iab
le
an
d
p
o
s
ttes
t
s
co
r
es
wer
e
lo
wer
in
th
e
R
D
-
T
g
r
o
u
p
th
an
i
n
th
e
R
D
-
C
g
r
o
u
p
.
T
ab
le
1
p
r
esen
ts
co
u
n
ts
an
d
d
em
o
g
r
a
p
h
ic
in
f
o
r
m
atio
n
f
o
r
t
h
e
two
R
D
g
r
o
u
p
s
id
en
tifie
d
in
th
is
s
tu
d
y
(
N=
1
,
9
0
0
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
14
,
No
.
3
,
J
u
n
e
20
25
:
1
59
7
-
1
60
7
1600
T
ab
le
1
.
Stu
d
e
n
t
ch
ar
ac
ter
is
tics
an
d
m
ea
n
a
n
d
SD
o
f
ass
ig
n
m
en
t sco
r
es b
y
tr
ea
tm
e
n
t a
s
s
ig
n
m
en
t c
o
n
d
itio
n
in
th
e
MCR
D
d
esig
n
V
a
r
i
a
b
l
e
s
RD
-
T
(
n
=
6
4
0
)
RD
-
C
(
n
=
1
,
2
5
6
)
F
e
m
a
l
e
n
(
%
)
3
3
4
(
5
2
.
2
)
6
2
7
(
4
9
.
9
2
)
E
t
h
n
i
c
m
i
n
o
r
i
t
y
n
(
%
)
7
0
(
1
1
.
0
)
1
5
3
(
1
2
.
2
)
E
n
g
l
i
s
h
l
a
n
g
u
a
g
e
l
e
a
r
n
e
r
n
(
%
)
1
2
4
(
1
9
.
4
)
1
2
7
(
1
0
.
1
)
S
t
u
d
e
n
t
w
i
t
h
d
i
s
a
b
i
l
i
t
i
e
s
n
(
%
)
4
7
(
7
.
3
)
3
7
(
2
.
9
5
)
A
g
e
i
n
y
e
a
r
s
M
(
SD
)
5
.
2
7
(
0
.
4
4
)
5
.
4
1
(
0
.
4
9
)
A
S
P
E
N
S
c
o
m
p
o
s
i
t
e
s
c
o
r
e
s
M
(
SD
)
2
1
.
8
7
(
1
7
.
5
0
)
7
4
.
7
9
(
3
7
.
3
7
)
N
S
B
t
o
t
a
l
r
a
w
s
c
o
r
e
s
M
(
SD
)
1
2
.
2
2
(
3
.
7
5
)
1
9
.
8
8
(
4
.
8
0
)
C
o
m
p
o
s
i
t
e
s
t
a
n
d
a
r
d
s
c
o
r
e
s
*
M
(
SD
)
-
1
.
5
2
(
0
.
7
3
)
1
.
2
7
(
1
.
4
0
)
S
p
r
i
n
g
S
E
S
A
T
2
m
a
t
h
e
m
a
t
i
c
s
s
c
o
r
e
s
M
(
SD
)
4
6
0
.
2
2
(
3
5
.
4
3
)
4
9
4
.
3
8
(
3
7
.
8
7
)
N
o
t
e
.
T
o
t
a
l
M
C
R
D
s
a
m
p
l
e
a
c
r
o
s
s
o
n
c
o
n
d
i
t
i
o
n
s
,
N
=
1
,
9
0
0
.
*
C
o
m
p
o
s
i
t
e
s
t
a
n
d
a
r
d
s
c
o
r
e
s
=
c
o
m
p
o
s
i
t
e
s
t
a
n
d
a
r
d
s
c
o
r
e
s
c
r
e
a
t
e
d
f
r
o
m
c
o
m
b
i
n
i
n
g
s
t
a
n
d
a
r
d
A
S
P
E
N
S
E
a
n
d
N
S
B
s
c
o
r
e
s
2
.
6
.
Ana
ly
t
ic
pro
ce
du
re
s
Pri
o
r
t
o
c
o
n
d
u
cti
n
g
t
h
e
MCR
D
a
n
al
y
s
es
,
th
e
ass
i
g
n
m
en
t
v
a
r
ia
b
l
e
f
o
r
ea
ch
class
r
o
o
m
was
ce
n
te
r
e
d
a
t
th
e
c
lass
r
o
o
m
c
u
t
o
f
f
,
s
o
th
at
all
cl
ass
r
o
o
m
s
h
a
d
a
ze
r
o
-
cu
t
o
f
f
v
al
u
e
.
Ob
s
er
v
ati
o
n
s
f
r
o
m
all
cl
ass
r
o
o
m
s
w
er
e
th
e
n
m
er
g
ed
i
n
t
o
a
s
i
n
g
l
e
d
a
ta
s
et,
r
es
u
lti
n
g
in
a
s
i
n
g
le
c
en
te
r
ed
z
er
o
-
c
u
t
o
f
f
(
C
)
ac
r
o
s
s
c
lass
r
o
o
m
s
.
T
h
is
p
o
o
l
ed
d
at
ase
t w
as
u
s
ed
f
o
r
all
s
u
b
s
e
q
u
e
n
t
MCR
D
a
n
al
y
s
es.
All
a
n
al
y
s
es
f
o
r
th
is
s
t
u
d
y
we
r
e
im
p
l
e
m
e
n
te
d
i
n
R
[2
2
]
.
2
.
6
.
1
.
M
o
del a
s
s
um
ptio
ns
T
o
ex
am
in
e
th
e
in
ter
n
al
v
alid
i
ty
o
f
th
e
p
o
o
led
R
D
esti
m
ate,
th
e
p
r
im
ar
y
R
D
m
o
d
el
ass
u
m
p
tio
n
s
f
o
r
th
e
MCR
D
d
esig
n
wer
e
test
ed
at
th
e
ce
n
ter
e
d
cu
to
f
f
(
C
)
[
6
]
,
[
9
]
,
[2
3
]
.
First,
we
ch
ec
k
ed
wh
eth
er
th
e
d
is
tr
ib
u
tio
n
o
f
k
e
y
s
tu
d
en
t
ch
ar
ac
ter
is
tics
(
co
v
ar
iates)
,
s
u
ch
as
g
en
d
er
,
ag
e,
E
n
g
lis
h
-
lan
g
u
ag
e
lear
n
er
s
tatu
s
,
an
d
s
p
ec
ial
ed
u
ca
tio
n
s
tatu
s
was
b
alan
ce
d
at
th
e
cu
to
f
f
.
T
h
e
ex
am
in
atio
n
was
co
n
d
u
cted
b
y
r
eg
r
ess
in
g
th
e
b
aselin
e
co
v
ar
iates
o
n
th
e
ass
ig
n
m
en
t
v
ar
iab
le
an
d
th
e
tr
ea
t
m
en
t
in
d
icato
r
with
in
an
o
p
ti
m
al
b
an
d
wid
th
th
at
m
in
im
izes
m
ea
n
-
s
q
u
ar
e
er
r
o
r
(
MSE
)
.
Seco
n
d
,
to
d
eter
m
in
e
if
th
er
e
was
m
an
ip
u
latio
n
o
f
th
e
ass
ig
n
m
en
t
s
co
r
es
at
th
e
cu
to
f
f
,
we
ass
ess
ed
th
e
d
is
co
n
tin
u
ity
in
th
e
p
r
o
b
a
b
ilit
y
d
en
s
ity
f
u
n
ctio
n
u
s
in
g
th
e
Mc
C
r
ar
y
test
[2
4
]
with
th
e
r
d
d
en
s
ity
v
e
r
s
io
n
2
.
3
p
ac
k
ag
e
in
R
[2
5
]
.
2
.
6
.
2
.
P
o
o
led pa
ra
m
et
ric
m
ultiple
-
cut
o
f
f
re
g
re
s
s
io
n dis
co
ntinuity
m
o
del
I
n
th
e
MCR
D
d
esig
n
,
th
e
p
o
o
led
tr
ea
tm
en
t
ef
f
ec
t
r
ep
r
ese
n
ts
th
e
av
er
a
g
e
tr
ea
tm
e
n
t
ef
f
ec
t
ac
r
o
s
s
d
if
f
er
en
t
cu
t
p
o
in
ts
in
th
e
ass
ig
n
m
en
t
v
a
r
iab
le
c
o
n
tin
u
u
m
[
9
]
.
Usi
n
g
th
e
c
o
m
b
in
e
d
(
p
o
o
led
)
d
ataset,
we
co
n
d
u
cte
d
a
s
tan
d
a
r
d
R
D
an
al
y
s
is
at
th
e
ce
n
ter
ed
cu
to
f
f
(
C
)
to
esti
m
ate
th
is
ef
f
ec
t.
W
e
u
s
ed
a
2
-
lev
el
lin
ea
r
m
ix
ed
m
o
d
el
(
i.e
.
,
m
u
ltil
ev
e
l
m
o
d
elin
g
)
[2
6
]
with
a
r
an
d
o
m
in
ter
ce
p
t
a
n
d
f
ix
e
d
s
lo
p
es
to
esti
m
ate
th
e
tr
ea
tm
en
t
ef
f
ec
t
ac
r
o
s
s
class
r
o
o
m
s
.
T
h
e
m
u
ltil
ev
el
m
o
d
el
was
u
s
ed
to
ad
d
r
ess
th
e
p
o
te
n
tial
d
ep
en
d
e
n
cies
th
at
ar
is
e
f
r
o
m
s
tu
d
en
ts
(
L
ev
el
1
)
n
ested
with
in
clas
s
r
o
o
m
s
(
L
ev
el
2
)
.
Po
s
ttes
t
s
tu
d
en
t
SES
AT
2
Ma
th
em
atics
s
co
r
es
(
L
ev
el
1
)
wer
e
r
e
g
r
ess
ed
o
n
lin
ea
r
,
q
u
ad
r
atic,
an
d
cu
b
ic
ter
m
s
o
f
th
e
ce
n
ter
ed
ass
ig
n
m
en
t
v
ar
ia
b
le,
th
e
tr
ea
tm
en
t
in
d
icato
r
,
a
n
d
in
ter
a
ctio
n
ter
m
s
b
etwe
en
th
e
tr
ea
t
m
en
t
in
d
icato
r
a
n
d
ce
n
ter
e
d
a
s
s
ig
n
m
en
t
v
ar
iab
le
.
No
p
r
ed
icto
r
s
wer
e
in
clu
d
e
d
at
th
e
class
r
o
o
m
lev
el
(
L
ev
el
2
)
.
P
r
ed
icto
r
s
n
o
t
s
tatis
tically
ass
o
ciate
d
with
th
e
o
u
tco
m
e
wer
e
r
em
o
v
ed
iter
ativ
el
y,
s
tar
tin
g
with
h
ig
h
er
-
o
r
d
er
ter
m
s
,
u
n
til
th
e
m
o
s
t
p
ar
s
im
o
n
i
o
u
s
a
n
d
b
est
-
f
itti
n
g
m
o
d
el
was
id
en
tif
ied
.
W
e
u
s
ed
F
-
s
tatis
tics
an
d
th
e
Ak
aik
e
in
f
o
r
m
atio
n
cr
iter
i
o
n
(
AI
C
)
v
alu
e
to
d
eter
m
in
e
if
a
m
o
r
e
co
m
p
lex
m
o
d
el
y
ield
ed
s
tatis
tically
s
ig
n
if
ican
t
im
p
r
o
v
em
en
ts
.
T
h
e
g
en
er
al
f
o
r
m
o
f
th
e
p
ar
am
etr
ic
p
o
o
led
MCR
D
m
o
d
el
is
s
p
ec
if
ied
in
(
1
)
:
=
γ
00
+
γ
10
(
−
)
+
γ
20
(
−
)
2
+
γ
30
(
−
)
3
+
γ
40
+
γ
50
(
−
)
+
γ
60
(
−
)
2
+
γ
70
(
−
)
3
+
u
0
+
r
(
1
)
W
h
er
e,
Y
ij
is
th
e
SESAT
2
m
ath
em
atics
s
co
r
e
o
f
s
tu
d
en
t
i
in
class
r
o
o
m
j
;
x
ij
is
th
e
ass
ig
n
m
en
t
s
co
r
e
f
o
r
s
tu
d
en
t
i
in
class
r
o
o
m
j
;
c
is
th
e
cu
to
f
f
f
o
r
class
r
o
o
m
j
;
Z
ij
is
th
e
d
ich
o
t
o
m
o
u
s
R
OOT
S
in
ter
v
en
tio
n
in
d
icato
r
f
o
r
s
tu
d
en
t
i
in
class
r
o
o
m
j
(
0
=c
o
n
tr
o
l,
1
=tr
ea
tm
en
t)
;
(
x
ij
-
c
)Z
ij
is
th
e
in
ter
ac
tio
n
b
etwe
en
ass
ig
n
m
en
t
s
co
r
e
an
d
th
e
R
OOT
S
in
ter
v
en
tio
n
i
n
d
icato
r
f
o
r
s
tu
d
en
t
i
in
class
r
o
o
m
j
;
00
is
th
e
m
ea
n
SESAT
m
ath
em
atics
s
co
r
e
f
o
r
t
h
e
c
o
n
tr
o
l
g
r
o
u
p
;
10
is
th
e
s
lo
p
e
r
elatin
g
th
e
ass
ig
n
m
en
t
s
co
r
e
to
th
e
p
o
s
ttes
t
SESAT
m
ath
em
atics
s
co
r
e
;
20
is
th
e
s
lo
p
e
r
elatin
g
th
e
q
u
a
d
r
atic
ter
m
o
f
th
e
ass
ig
n
m
en
t
s
co
r
e
to
t
h
e
p
o
s
ttes
t
SESAT
m
ath
em
atics
s
co
r
e
;
30
is
th
e
s
lo
p
e
r
elatin
g
th
e
cu
b
ic
ter
m
o
f
th
e
ass
ig
n
m
en
t
s
co
r
e
to
th
e
p
o
s
ttes
t
SESAT
m
ath
em
atics
s
co
r
e
;
40
is
th
e
d
if
f
e
r
en
ce
i
n
th
e
lin
e
ar
s
lo
p
e
b
etwe
en
th
e
two
co
n
d
itio
n
s
(
0
=c
o
n
tr
o
l,
1
=tr
ea
tm
e
n
t)
;
50
is
th
e
s
lo
p
e
f
o
r
th
e
in
ter
ac
tio
n
b
etwe
en
th
e
ass
ig
n
m
en
t
s
co
r
e
an
d
th
e
R
OOT
S
in
ter
v
en
tio
n
in
d
icato
r
;
60
is
th
e
s
lo
p
e
f
o
r
th
e
in
ter
ac
tio
n
b
etwe
en
th
e
q
u
ad
r
atic
ter
m
o
f
th
e
ass
ig
n
m
e
n
t
s
co
r
e
an
d
th
e
R
OOT
S
in
te
r
v
en
tio
n
in
d
icato
r
;
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
Mu
ltip
le
-
cu
to
ff reg
r
ess
io
n
d
is
co
n
tin
u
ity
d
esig
n
s
in
e
d
u
ca
tio
n
a
l e
va
lu
a
tio
n
(
Hye
o
n
Jin
Yo
o
n
)
1601
70
is
th
e
s
lo
p
e
f
o
r
th
e
in
ter
ac
tio
n
b
etwe
en
th
e
cu
b
ic
te
r
m
o
f
th
e
ass
ig
n
m
en
t
s
co
r
e
an
d
th
e
R
OOT
S
in
ter
v
en
tio
n
in
d
icato
r
;
an
d
r
ij
i
s
th
e
s
tu
d
en
t
-
lev
el
r
esid
u
al
ter
m
.
At
th
e
class
r
o
o
m
lev
el
(
L
ev
el
2
)
,
th
e
in
ter
ce
p
t
(
0j
)
was a
llo
wed
to
v
ar
y
b
etwe
en
class
r
o
o
m
s
,
wh
ile
all
s
lo
p
es we
r
e
f
ix
ed
to
b
e
co
n
s
tan
t a
cr
o
s
s
class
r
o
o
m
s
.
2
.
6
.
3
.
P
o
o
led no
np
a
ra
m
et
ric
m
ultiple
-
cut
o
f
f
re
g
re
s
s
io
n dis
co
ntinuity
m
o
del
A
n
o
n
p
ar
am
etr
ic
an
al
y
s
is
was
co
n
d
u
cted
u
s
in
g
lo
ca
l
lin
ea
r
r
eg
r
ess
io
n
(
L
L
R
)
[1
3
]
to
s
u
p
p
l
em
en
t
th
e
p
ar
am
etr
ic
r
esu
lts
.
First,
we
id
en
tifie
d
an
MSE
-
o
p
tim
al
b
an
d
wid
th
(
h
)
ar
o
u
n
d
th
e
cu
to
f
f
u
s
in
g
th
e
I
m
b
en
s
-
Kaly
an
a
r
am
an
(
I
K)
p
r
o
ce
d
u
r
e
[2
7
]
.
T
h
en
,
we
ap
p
lied
a
lin
ea
r
r
eg
r
ess
io
n
with
tr
ian
g
u
lar
k
e
r
n
el
weig
h
ts
with
in
th
e
o
p
tim
al
b
a
n
d
wid
th
(
h
)
.
T
h
e
n
o
n
p
ar
a
m
etr
ic
p
o
o
led
R
D
m
o
d
el
is
d
ef
in
ed
in
(
2
)
:
Y
ij
=
0
+
1
(
x
ij
-
c
j
)+
2
Z
ij
with
tr
ian
g
le
k
er
n
el
weig
h
ts
(
)
=
(
−
|
|
)
{
|
|
≤
}
(
2
)
W
h
er
e,
x
ij
is
th
e
as
s
ig
n
m
en
t
s
co
r
e
f
o
r
s
tu
d
e
n
t
i
in
class
r
o
o
m
j
;
c
j
is
th
e
cu
to
f
f
s
co
r
e
f
o
r
c
lass
r
o
o
m
j
;
an
d
Z
ij
is
th
e
R
OOT
S
in
ter
v
en
tio
n
in
d
icato
r
f
o
r
s
tu
d
en
t
i
in
class
r
o
o
m
j
(
0
=c
o
n
tr
o
l,
1
=tr
ea
tm
en
t)
.
T
h
e
ter
m
2
r
ep
r
esen
ts
th
e
m
ag
n
itu
d
e
o
f
t
h
e
tr
ea
tm
en
t
e
f
f
ec
t
at
th
e
ce
n
ter
ed
cu
t
o
f
f
C
.
T
o
ch
ec
k
th
e
s
en
s
itiv
ity
o
f
th
e
r
esu
lts
to
th
e
ch
o
ice
o
f
b
a
n
d
w
id
th
,
we
r
ep
ea
te
d
th
e
a
n
aly
s
is
u
s
in
g
b
an
d
wid
th
s
h
alf
a
n
d
twi
ce
th
e
o
p
tim
al
s
ize
f
o
r
co
m
p
ar
is
o
n
.
Stan
d
ar
d
er
r
o
r
s
f
o
r
th
e
n
o
n
p
ar
am
etr
ic
esti
m
ates
wer
e
ca
lcu
lated
u
s
in
g
b
o
o
ts
tr
ap
p
in
g
tech
n
iq
u
es,
with
1
,
0
0
0
r
ep
etiti
o
n
s
.
2
.
6
.
4
.
M
ultiple
-
cut
o
f
f
re
g
re
s
s
io
n dis
co
nti
nu
it
y
het
er
o
g
eneit
y
mo
del
A
2
-
lev
el
lin
ea
r
m
ix
ed
m
o
d
el
was
u
s
ed
to
ex
am
i
n
e
p
o
te
n
tial
h
eter
o
g
en
eity
i
n
th
e
ef
f
ec
t
o
f
th
e
R
OOT
S
in
ter
v
en
tio
n
ac
r
o
s
s
class
r
o
o
m
s
.
Fo
llo
win
g
th
e
b
est
-
f
itti
n
g
p
ar
am
etr
ic
p
o
o
led
m
o
d
el,
th
e
b
as
e
co
n
d
itio
n
al
MCR
D
m
o
d
el
was d
ef
in
ed
as in
(
3
)
.
Y
ij
=
00
+
10
(
x
ij
-
c
j
)+
20
(
x
ij
-
c
j
)
2
+
30
Z
ij
+
31
c
j
Z
ij
+
0j
+
3
j
+
r
ij
(
3
)
W
h
er
e
,
Y
ij
is
th
e
p
o
s
ttes
t
SES
AT
m
ath
em
atics
s
co
r
e
f
o
r
s
tu
d
en
t
i
in
class
r
o
o
m
j
;
x
ij
is
th
e
a
s
s
ig
n
m
en
t
s
co
r
e
f
o
r
s
tu
d
en
t
i
in
clas
s
r
o
o
m
j
;
c
j
is
th
e
cu
to
f
f
s
co
r
e
f
o
r
class
r
o
o
m
j
;
Z
ij
i
s
th
e
R
OOT
S
in
ter
v
en
tio
n
in
d
icato
r
f
o
r
s
tu
d
en
t
i
in
class
r
o
o
m
j
(
0
=c
o
n
tr
o
l,
1
=tr
ea
tm
en
t
)
;
00
is
th
e
class
r
o
o
m
m
ea
n
SESAT
m
at
h
em
atics
s
co
r
e
f
o
r
th
e
co
n
tr
o
l
g
r
o
u
p
;
10
is
th
e
s
lo
p
e
r
elatin
g
th
e
ass
ig
n
m
en
t
s
co
r
e
to
th
e
p
o
s
ttes
t
SESAT
m
ath
em
atics
s
co
r
e
;
20
is
th
e
s
lo
p
e
r
elatin
g
th
e
q
u
ad
r
atic
ter
m
o
f
th
e
ass
ig
n
m
en
t
s
co
r
e
to
th
e
p
o
s
ttes
t
SES
AT
m
ath
em
atics
s
co
r
e
;
30
r
ep
r
esen
ts
th
e
d
i
f
f
er
en
ce
in
t
h
e
p
o
s
ttes
t
s
co
r
e
b
etwe
en
th
e
tr
ea
tm
en
t
an
d
co
n
tr
o
l
g
r
o
u
p
s
;
0j
is
th
e
r
a
n
d
o
m
in
ter
ce
p
t
ter
m
;
a
n
d
r
ij
is
th
e
s
tu
d
en
t
-
lev
el
r
esid
u
al
te
r
m
.
T
h
e
tr
ea
tm
en
t
e
f
f
ec
t
was
m
o
d
eled
to
v
a
r
y
ac
r
o
s
s
class
r
o
o
m
s
(
3
j
)
to
ex
am
i
n
e
th
e
p
o
ten
tial
h
eter
o
g
eity
o
f
th
e
esti
m
ated
tr
ea
tm
en
t
ef
f
ec
t
ac
r
o
s
s
class
r
o
o
m
s
.
W
e
also
in
clu
d
ed
th
e
class
r
o
o
m
c
u
to
f
f
v
alu
e
(
c
j
)
as
a
class
r
o
o
m
-
lev
el
p
r
ed
icto
r
to
e
x
p
lo
r
e
wh
eth
er
th
e
class
r
o
o
m
ass
ig
n
m
en
t c
u
to
f
f
v
alu
e
was a
s
s
o
ciate
d
with
am
p
lify
in
g
o
r
a
tten
u
atin
g
th
e
tr
ea
tm
e
n
t e
f
f
ec
t
(
31
)
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
Resul
t
s
3
.
1
.
1
.
Ass
um
ptio
n t
ests
T
a
b
l
e
2
p
r
e
s
e
n
ts
t
h
e
c
o
v
a
r
i
a
t
e
b
a
l
a
n
c
e
s
t
a
t
is
ti
c
s
.
A
t
t
h
e
c
e
n
te
r
e
d
c
u
t
o
f
f
(
C
)
,
t
h
e
r
e
w
a
s
n
o
s
t
a
ti
s
t
i
c
al
l
y
s
i
g
n
i
f
i
c
a
n
t
d
is
c
o
n
t
i
n
u
i
t
y
i
n
an
y
o
f
t
h
e
t
e
s
t
e
d
c
o
v
a
r
i
at
e
s
.
T
h
e
M
c
C
r
a
r
y
t
es
t
al
s
o
r
e
v
e
ale
d
s
t
at
is
t
i
c
al
l
y
non
-
s
i
g
n
i
f
i
c
a
n
t
r
e
s
u
lt
s
,
s
u
g
g
e
s
t
i
n
g
th
e
r
e
w
a
s
n
o
s
y
s
t
e
m
a
t
i
c
m
a
n
i
p
u
l
a
t
i
o
n
o
f
t
h
e
as
s
i
g
n
m
e
n
t
s
c
o
r
es
a
r
o
u
n
d
t
h
e
c
u
t
o
f
f
.
T
ab
le
2
.
C
o
v
ar
iate
b
alan
ce
s
tatis
tics
C
o
v
a
r
i
a
t
e
s
∆
D
i
f
f
e
r
e
n
c
e
SE
p
V
a
r
i
a
n
c
e
r
a
t
i
o
F
e
mal
e
-
.
0
4
.
0
4
.
3
1
1
.
0
1
S
t
u
d
e
n
t
a
g
e
-
.
0
5
.
0
3
.
1
4
.
9
2
Li
mi
t
e
d
En
g
l
i
s
h
p
r
o
f
i
c
i
e
n
c
y
.
0
3
.
0
3
.
3
9
1
.
1
0
S
p
e
c
i
a
l
e
d
u
c
a
t
i
o
n
.
0
1
.
0
2
.
6
7
1
.
1
4
N
o
t
e
.
∆
d
i
f
f
e
r
e
n
c
e
=
w
e
i
g
h
t
e
d
m
e
a
n
d
i
f
f
e
r
e
n
c
e
i
n
t
h
e
c
o
v
a
r
i
a
t
e
d
i
st
r
i
b
u
t
i
o
n
a
t
t
h
e
c
e
n
t
e
r
e
d
c
u
t
o
f
f
;
v
a
r
i
a
n
c
e
r
a
t
i
o
=
mea
n
r
a
t
i
o
o
f
t
h
e
v
a
r
i
a
n
c
e
o
f
a
d
e
m
o
g
r
a
p
h
i
c
v
a
r
i
a
b
l
e
i
n
t
h
e
t
r
e
a
t
m
e
n
t
g
r
o
u
p
t
o
t
h
e
v
a
r
i
a
n
c
e
o
f
t
h
e
v
a
r
i
a
b
l
e
i
n
t
h
e
c
o
m
p
a
r
i
s
o
n
g
r
o
u
p
3
.
1
.
2
.
M
ultiple
-
cut
o
f
f
re
g
re
s
s
io
n dis
co
nti
nu
it
y
p
a
ra
m
et
ri
c
m
o
del
T
ab
le
3
r
ep
o
r
ts
th
e
esti
m
ates
f
o
r
th
e
p
ar
am
et
r
ic
MCR
D
m
o
d
els.
T
h
e
in
tr
ac
lass
co
r
r
elatio
n
co
ef
f
icien
t
(
I
C
C
)
in
d
icate
d
th
at
4
0
%
o
f
th
e
v
a
r
iatio
n
in
s
tu
d
en
t
p
o
s
ttes
t
SESAT
m
ath
em
atics
s
co
r
es
was
attr
ib
u
tab
le
to
class
r
o
o
m
-
to
-
c
lass
r
o
o
m
d
if
f
er
e
n
ce
s
.
T
h
e
b
e
s
t
-
f
itti
n
g
m
o
d
el
(
Mo
d
el
1
)
in
clu
d
ed
a
lin
ea
r
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
14
,
No
.
3
,
J
u
n
e
20
25
:
1
59
7
-
1
60
7
1602
q
u
ad
r
atic
ter
m
f
o
r
th
e
ass
ig
n
m
en
t
v
a
r
iab
le.
T
h
e
m
o
d
el
r
esu
lts
in
d
icate
d
a
p
o
s
itiv
e
r
e
latio
n
s
h
ip
b
etwe
en
ass
ig
n
m
en
t
s
co
r
es
an
d
p
o
s
ttes
t
SESAT
m
ath
em
atics
s
co
r
es
(
γ
10
=
1
5
.
2
9
,
SE=
.
8
9
)
,
m
ea
n
in
g
th
at
an
in
cr
ea
s
e
in
ass
ig
n
m
en
t
s
co
r
es
p
r
e
d
icted
a
co
r
r
esp
o
n
d
in
g
i
n
cr
ea
s
e
in
th
e
p
o
s
ttes
t
SESAT
m
ath
em
atic
s
s
co
r
es.
Ho
wev
er
,
as
ass
ig
n
m
en
t
s
co
r
es
co
n
tin
u
ed
to
in
cr
ea
s
e,
th
e
r
ate
o
f
im
p
r
o
v
em
en
t
in
p
o
s
ttes
t
SESAT
m
ath
em
atics
s
co
r
es
d
ec
eler
ated
(
γ
20
=
-
.
5
2
,
SE=
.
1
7
)
.
T
h
e
R
D
tr
ea
tm
en
t
e
f
f
ec
t
esti
m
ate
was
s
tatis
t
ically
s
i
g
n
if
ican
t
(
γ
30
=5
.
3
0
,
SE=
2
.
3
2
),
d
em
o
n
s
tr
atin
g
t
h
at
ac
r
o
s
s
th
e
r
an
g
e
o
f
cu
to
f
f
v
al
u
es,
s
tu
d
en
ts
ass
ig
n
ed
to
th
e
tr
ea
tm
en
t
co
n
d
itio
n
o
u
tp
er
f
o
r
m
ed
th
o
s
e
ass
ig
n
ed
to
th
e
co
n
tr
o
l
co
n
d
itio
n
o
n
av
er
ag
e.
Alth
o
u
g
h
th
e
ad
d
itio
n
o
f
a
r
an
d
o
m
ef
f
ec
t
ter
m
f
o
r
th
e
tr
ea
tm
en
t
s
tatu
s
in
d
icato
r
(
u
3j
)
d
id
n
o
t
s
tatis
tical
ly
im
p
r
o
v
e
th
e
m
o
d
el
(
Mo
d
el
2
)
,
th
e
ter
m
was
r
etain
ed
in
o
r
d
er
to
ex
p
lo
r
e
w
h
eth
er
tr
ea
tm
en
t
ef
f
ec
ts
v
ar
ied
b
y
th
e
cu
ts
co
r
e
t
h
at
was
u
s
ed
to
ass
ig
n
s
tu
d
en
ts
to
th
e
tr
ea
tm
en
t
o
r
co
n
tr
o
l c
o
n
d
itio
n
ac
r
o
s
s
class
r
o
o
m
u
n
its
(
Mo
d
el
3
)
.
T
ab
le
3
.
Mu
ltil
ev
el
SESAT
m
ath
em
atics o
u
tco
m
e
m
o
d
els (
N
=1
,
9
0
0
)
Ef
f
e
c
t
M
o
d
e
l
1
M
o
d
e
l
2
M
o
d
e
l
3
Est
i
m
a
t
e
SE
Est
i
m
a
t
e
SE
Est
i
m
a
t
e
SE
F
i
x
e
d
e
f
f
e
c
t
I
n
t
e
r
c
e
p
t
,
γ
00
4
6
8
.
2
7
***
2
.
4
9
4
6
8
.
1
7
***
2
.
4
9
4
7
8
.
1
4
***
4
.
2
4
I
n
t
e
r
-
st
u
d
e
n
t
p
r
e
d
i
c
t
o
r
s
A
ssi
g
n
me
n
t
sc
o
r
e
,
γ
10
1
5
.
2
9
***
.
8
9
1
5
.
3
6
***
.
9
0
1
5
.
9
2
***
.
9
1
A
ssi
g
n
me
n
t
sc
o
r
e
sq
u
a
r
e
d
,
γ
20
-
.
5
2
**
.
1
7
-
.
5
3
**
.
1
7
-
.
6
4
***
.
1
7
Tr
e
a
t
me
n
t
,
γ
30
5
.
3
0
*
2
.
3
2
5
.
4
8
*
2
.
3
7
1
2
.
6
5
***
3
.
6
0
I
n
t
e
r
-
c
l
a
ssr
o
o
m
p
r
e
d
i
c
t
o
r
s
C
u
t
-
p
o
i
n
t
,
γ
01
1
5
.
3
0
**
5
.
0
3
C
u
t
-
p
o
i
n
t
,
γ
31
8
.
8
8
*
3
.
4
1
R
a
n
d
o
m
e
f
f
e
c
t
VC
SD
VC
SD
VC
SD
S
t
u
d
e
n
t
(
l
e
v
e
l
1
)
,
r
ij
6
9
7
.
4
0
2
1
.
4
5
6
9
2
.
0
5
2
6
.
2
3
6
9
2
.
4
5
2
6
.
3
1
M
e
a
n
S
ESA
T
s
c
o
r
e
,
u
0j
4
6
0
.
1
0
2
6
.
4
1
4
5
9
.
4
3
2
1
.
6
0
4
1
9
.
6
4
2
0
.
4
9
Tr
e
a
t
me
n
t
e
f
f
e
c
t
,
u
3j
2
3
.
6
2
5
.
3
5
1
3
.
2
9
3
.
6
5
N
o
t
e
:
S
E
=
S
t
a
n
d
a
r
d
e
r
r
o
r
,
V
C
=
V
a
r
i
a
n
c
e
c
o
m
p
o
n
e
n
t
s,
S
D
=
S
t
a
n
d
a
r
d
d
e
v
i
a
t
i
o
n
*
p
<
.
0
5
,
*
*
p
<
.
0
1
,
*
*
*
p
<
.
0
0
1
3
.
1
.
3
.
No
np
a
ra
m
e
t
ric
mo
del
L
o
ca
l
lin
ea
r
r
eg
r
ess
io
n
was
im
p
lem
en
ted
with
in
t
h
e
MSE
-
o
p
tim
al
b
an
d
wid
th
(
two
p
o
in
t
s
)
ar
o
u
n
d
th
e
cu
to
f
f
,
as
d
ete
r
m
in
ed
b
y
th
e
I
K
p
r
o
ce
d
u
r
e.
B
y
r
estrictin
g
th
e
an
aly
s
is
to
o
b
s
er
v
atio
n
s
with
in
th
is
b
an
d
wid
th
,
th
e
l
o
ca
l lin
ea
r
an
aly
s
is
u
s
ed
3
9
.
4
% o
f
th
e
s
tu
d
e
n
t o
b
s
er
v
atio
n
s
.
T
ab
le
4
r
ev
ea
ls
th
at
th
e
tr
ea
tm
en
t
ef
f
ec
t
with
in
th
e
o
p
tim
al
b
a
n
d
wid
th
was
s
tatis
t
ically
s
ig
n
if
ican
t
(
β
2
=6
.
6
3
)
.
T
h
is
r
esu
lt
in
d
icate
d
th
at,
o
n
av
er
ag
e,
s
tu
d
en
ts
in
th
e
tr
ea
t
m
en
t
co
n
d
itio
n
h
ad
h
ig
h
er
p
o
s
ttes
t
SE
SAT
m
ath
em
atics
s
c
o
r
es
th
an
t
h
o
s
e
in
t
h
e
co
n
tr
o
l
co
n
d
itio
n
ac
r
o
s
s
all
c
u
to
f
f
v
alu
es.
T
h
e
r
esu
lts
o
f
th
e
s
en
s
itiv
ity
an
aly
s
is
a
ls
o
r
ev
ea
led
th
at
u
s
in
g
th
e
h
alf
o
r
d
o
u
b
le
-
s
ized
b
an
d
wid
th
led
to
p
o
o
led
R
D
esti
m
ates
o
f
8
.
8
1
(
p
<.
0
5
)
an
d
4
.
1
7
p
o
in
ts
(
p
>.
0
5
)
,
r
esp
ec
tiv
ely
,
s
u
g
g
esti
n
g
th
at
t
h
e
n
o
n
p
ar
am
etr
ic
im
p
ac
t
esti
m
ate
was
s
en
s
itiv
e
to
th
e
b
an
d
wid
th
s
ize.
Fig
u
r
e
1
d
is
p
lay
s
th
e
n
o
n
p
ar
a
m
etr
ic
lo
ca
l
lin
ea
r
r
e
g
r
ess
io
n
p
lo
t
o
f
th
e
ass
ig
n
m
en
t
a
n
d
o
u
tco
m
e
v
ar
iab
le
r
elatio
n
s
h
ip
,
wh
er
eb
y
th
e
6
-
p
o
in
t d
is
co
n
tin
u
ity
at
th
e
p
o
o
led
c
u
t
p
o
in
t c
a
n
b
e
s
ee
n
.
T
ab
le
4
.
No
n
p
ar
am
etr
ic
p
o
o
le
d
R
D
esti
m
ates o
f
SESAT
m
at
h
em
atics o
u
tco
m
e
Ef
f
e
c
t
H
a
l
f
b
a
n
d
w
i
d
t
h
O
p
t
i
mal
b
a
n
d
w
i
d
t
h
D
o
u
b
l
e
b
a
n
d
w
i
d
t
h
Est
i
m
a
t
e
t
Est
i
m
a
t
e
t
Est
i
m
a
t
e
t
I
n
t
e
r
c
e
p
t
,
β
0
4
6
5
.
2
1
(
2
.
7
5
)
1
6
9
.
0
8
***
4
6
6
.
2
2
(
1
.
9
6
)
2
3
7
.
6
7
***
4
6
7
.
5
5
(
1
.
6
7
)
2
8
0
.
4
0
***
A
ssi
g
n
me
n
t
sc
o
r
e
,
β
1
2
0
.
4
3
(
5
.
2
6
)
3
.
8
9
*
**
1
5
.
7
2
(
2
.
0
3
)
7
.
7
4
*
**
1
3
.
6
3
(
1
.
0
5
)
1
3
.
0
1
***
Tr
e
a
t
me
n
t
,
β
2
8
.
8
1
(
5
.
4
9
)
2
.
3
0
*
6
.
6
3
(
3
.
8
6
)
2
.
2
4
*
4
.
1
7
(
2
.
8
9
)
1
.
6
3
N
o
t
e
.
N
o
n
p
a
r
a
me
t
r
i
c
p
o
o
l
e
d
R
D
e
st
i
mat
e
s
a
r
e
sh
o
w
n
w
i
t
h
st
a
n
d
a
r
d
e
r
r
o
r
s
i
n
p
a
r
e
n
t
h
e
si
s.
N
o
n
p
a
r
a
me
t
r
i
c
e
s
t
i
m
a
t
e
s h
a
v
e
b
o
o
t
st
r
a
p
p
e
d
st
a
n
d
a
r
d
e
r
r
o
r
s
(
r
e
p
e
t
i
t
i
o
n
=
1
,
0
0
0
)
*
p
<
.
0
5
,
**
p
<
.
0
1
,
***
p
<
.
0
0
1
3
.
1
.
4
.
M
ultiple
-
cut
o
f
f
re
g
re
s
s
io
n dis
co
nti
nu
it
y
het
er
o
g
eneit
y
mo
del
W
h
en
th
e
class
r
o
o
m
cu
to
f
f
s
c
o
r
e
was
ad
d
ed
as
a
p
r
ed
icto
r
o
f
th
e
v
ar
ia
n
ce
in
tr
ea
tm
en
t
e
f
f
ec
ts
(
s
ee
Mo
d
el
3
an
d
T
ab
le
3
)
in
t
h
e
p
ar
am
etr
ic
R
D
m
o
d
el,
r
esu
lts
i
n
d
icate
d
a
p
o
s
itiv
e
in
ter
ac
tio
n
b
etwe
en
th
e
cu
to
f
f
s
co
r
e
an
d
th
e
tr
ea
tm
en
t
ef
f
e
ct
p
ar
am
eter
(
γ
31
=8
.
8
8
,
SE
=
3
.
4
1
)
.
T
h
e
m
o
d
er
ated
r
elatio
n
s
h
ip
s
u
g
g
ests
th
at
h
ig
h
er
c
u
to
f
f
s
co
r
es
wer
e
ass
o
ciate
d
with
g
r
ea
ter
tr
ea
tm
en
t
ef
f
ec
t
s
.
No
tab
ly
,
th
e
class
r
o
o
m
cu
tp
o
in
t
was
also
ass
o
ciate
d
with
o
v
er
all
clas
s
r
o
o
m
m
ea
n
p
er
f
o
r
m
a
n
ce
(
γ
01
=
1
5
.
3
0
,
SE=
5
.
0
3
)
,
in
d
icatin
g
t
h
at
class
r
o
o
m
s
with
h
ig
h
er
cu
to
f
f
v
alu
es
h
ad
s
tatis
tically
h
ig
h
er
m
ea
n
p
o
s
ttes
t
s
co
r
es
r
elativ
e
to
th
o
s
e
wi
th
l
o
wer
cu
to
f
f
s
co
r
es.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
Mu
ltip
le
-
cu
to
ff reg
r
ess
io
n
d
is
co
n
tin
u
ity
d
esig
n
s
in
e
d
u
ca
tio
n
a
l e
va
lu
a
tio
n
(
Hye
o
n
Jin
Yo
o
n
)
1603
Fig
u
r
e
2
s
h
o
ws
th
at
th
e
lo
ca
l
R
D
tr
ea
tm
en
t
ef
f
ec
t
esti
m
ate
s
v
ar
ied
wid
ely
d
ep
e
n
d
in
g
o
n
th
e
cu
to
f
f
v
alu
e
u
s
ed
to
s
cr
ee
n
s
tu
d
en
ts
in
to
tr
ea
t
m
en
t
co
n
d
itio
n
s
,
with
an
ap
p
r
o
x
im
ate
r
an
g
e
b
etwe
en
-
5
7
an
d
+6
8
p
o
i
n
ts
.
C
las
s
r
o
o
m
s
with
h
ig
h
er
cu
to
f
f
v
alu
es
g
en
er
ally
ex
h
ib
ited
l
ar
g
er
tr
ea
tm
en
t
ef
f
ec
ts
,
alth
o
u
g
h
th
e
class
r
o
o
m
with
th
e
lo
west
cu
to
f
f
s
co
r
e
al
s
o
d
is
p
lay
ed
a
s
u
b
s
tan
tial
p
o
s
i
tiv
e
ef
f
ec
t.
I
t
is
im
p
o
r
tan
t
to
n
o
te,
h
o
wev
e
r
,
th
at
th
e
co
n
f
i
d
en
ce
in
te
r
v
al
f
o
r
ea
ch
R
D
esti
m
ate
was
lar
g
e
d
u
e
to
th
e
s
m
all
s
am
p
le
s
ize,
s
u
g
g
esti
n
g
th
at
ca
u
tio
n
s
h
o
u
ld
b
e
u
s
ed
wh
en
i
n
ter
p
r
eti
n
g
th
e
in
d
iv
id
u
al
l
o
ca
l RD e
s
ti
m
ates.
Fig
u
r
e
1
.
No
n
p
ar
am
et
r
ic
p
lo
t
o
f
th
e
ass
ig
n
m
en
t a
n
d
o
u
tco
m
e
v
ar
iab
le
r
elatio
n
s
h
i
p
Fig
u
r
e
2
.
L
o
ca
l RD tr
ea
tm
en
t
ef
f
ec
t
esti
m
ates
at
v
ar
io
u
s
class
r
o
o
m
cu
t p
o
in
ts
with
9
5
% c
o
n
f
id
en
ce
in
te
r
v
al
s
3
.
2
.
Dis
cus
s
io
n
T
h
e
R
D
d
esig
n
is
o
f
te
n
co
n
s
id
er
ed
as
a
p
r
ac
tical
alter
n
ativ
e
to
t
h
e
R
C
T
in
f
ield
-
b
ased
s
ettin
g
s
as
it
ca
n
p
r
o
v
i
d
e
an
u
n
b
iased
tr
ea
tm
en
t
ef
f
ec
t
esti
m
ate
wh
en
m
o
d
el
ass
u
m
p
tio
n
s
ar
e
m
et
an
d
th
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
ass
ig
n
m
en
t
a
n
d
o
u
tco
m
e
v
ar
iab
les
is
co
r
r
ec
tly
s
p
ec
if
ied
.
T
h
is
p
ap
e
r
p
r
o
v
i
d
ed
an
o
v
er
v
iew
o
f
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8
8
2
2
I
n
t
J
E
v
al
&
R
es E
d
u
c
,
Vo
l
.
14
,
No
.
3
,
J
u
n
e
20
25
:
1
59
7
-
1
60
7
1604
MCR
D
d
esig
n
,
an
ex
ten
s
io
n
o
f
b
asic
R
D
d
esig
n
u
s
ed
wh
en
m
u
ltip
le
cu
to
f
f
s
ar
e
u
s
ed
p
r
o
g
r
am
o
r
in
ter
v
e
n
tio
n
ass
ig
n
m
en
t
ac
r
o
s
s
d
if
f
er
en
t
u
n
its
o
r
s
ites
.
Pre
v
io
u
s
an
aly
tic
ap
p
r
o
ac
h
es
f
o
r
MCR
D
d
esig
n
s
p
r
im
ar
ily
f
o
cu
s
e
d
o
n
esti
m
atin
g
av
er
ag
e
tr
ea
tm
en
t
ef
f
ec
ts
ac
r
o
s
s
cu
to
f
f
s
,
p
o
ten
tially
o
v
er
lo
o
k
in
g
s
ite
-
o
r
u
n
it
-
s
p
ec
if
ic
d
if
f
er
en
ce
s
in
tr
ea
tm
en
t
ef
f
ec
ts
[
9
]
.
C
o
n
v
er
s
ely
,
th
is
p
ap
er
d
em
o
n
s
tr
ated
a
m
o
d
eli
n
g
ap
p
r
o
ac
h
th
at
s
im
u
ltan
eo
u
s
ly
esti
m
ates
b
o
th
th
e
o
v
er
all
av
er
a
g
e
tr
ea
tm
en
t
ef
f
ec
t
an
d
tr
ea
tm
en
t
ef
f
ec
t
h
eter
o
g
en
eity
ac
r
o
s
s
d
if
f
er
en
t
in
ter
v
en
tio
n
u
n
its
.
Fin
d
in
g
s
in
d
icate
d
th
at
s
tu
d
en
ts
wh
o
r
ec
eiv
ed
th
e
R
OOT
S
in
ter
v
en
tio
n
h
ad
h
ig
h
er
m
ath
em
atics
s
co
r
es
o
n
av
er
ag
e
at
p
o
s
t
-
in
ter
v
e
n
tio
n
co
m
p
ar
ed
to
th
o
s
e
wh
o
d
i
d
n
o
t.
Ad
d
itio
n
ally
,
th
e
s
ize
o
f
th
e
in
ter
v
en
tio
n
ef
f
ec
ts
v
ar
ied
ac
r
o
s
s
class
r
o
o
m
s
,
with
g
r
ea
ter
ef
f
ec
ts
g
en
er
ally
o
b
s
er
v
e
d
in
class
r
o
o
m
s
th
at
h
ad
h
ig
h
er
cu
t
o
f
f
s
co
r
es to
s
cr
ee
n
s
tu
d
en
ts
f
o
r
th
e
in
ter
v
en
tio
n
.
3
.
2
.
1
.
M
ultiple
-
cut
o
f
f
re
g
re
s
s
io
n dis
co
nti
nu
it
y
e
s
t
im
a
t
io
n a
nd
s
t
a
t
is
t
ica
l
v
a
lid
it
y
T
h
e
r
esu
lts
r
ev
ea
le
d
th
at
th
e
p
o
o
led
tr
ea
tm
en
t
ef
f
ec
t
esti
m
ate
v
ar
ied
d
ep
e
n
d
in
g
o
n
th
e
esti
m
atio
n
m
eth
o
d
(
p
ar
am
et
r
ic
o
r
n
o
n
p
ar
am
etr
ic)
.
T
h
e
m
a
g
n
itu
d
e
o
f
th
e
R
D
esti
m
ate
was
lar
g
er
wh
en
u
s
in
g
t
h
e
n
o
n
p
a
r
am
etr
ic
m
o
d
el
(
6
.
4
8
,
ef
f
ec
t
s
ize
g
=.
1
9
)
[
28
]
co
m
p
ar
ed
to
th
e
p
ar
am
etr
ic
m
o
d
e
l
(
5
.
1
3
,
e
f
f
ec
t
s
ize
g
=.
1
4
)
.
Alth
o
u
g
h
th
e
ef
f
ec
t
s
izes
ac
r
o
s
s
th
e
m
eth
o
d
s
wer
e
r
elativ
ely
s
im
ilar
,
th
e
o
b
s
er
v
ed
d
if
f
er
en
ce
s
in
th
e
r
aw
tr
ea
tm
en
t
ef
f
ec
t
esti
m
ates
ca
n
b
e
attr
ib
u
ted
to
th
e
m
eth
o
d
s
u
s
ed
in
th
e
esti
m
atio
n
o
f
ea
ch
m
o
d
el.
T
h
e
p
ar
am
etr
ic
m
eth
o
d
u
s
es
all
a
v
ailab
le
o
b
s
er
v
atio
n
s
in
th
e
d
ataset
to
f
it
a
m
o
d
el,
wh
er
ea
s
th
e
n
o
n
p
ar
am
etr
ic
m
eth
o
d
r
elies
o
n
a
s
u
b
s
am
p
le
av
ailab
le
with
in
th
e
o
p
tim
al
b
an
d
wid
th
.
I
n
th
e
p
r
esen
t
d
e
m
o
n
s
tr
atio
n
,
we
d
i
d
n
o
t
ev
alu
ate
th
e
in
ter
n
al
v
alid
i
ty
o
f
t
h
e
d
if
f
er
en
t
tr
ea
tm
e
n
t
ef
f
ec
t
esti
m
ates.
Ho
wev
er
,
we
h
y
p
o
th
esize
th
at
th
e
n
o
n
p
a
r
am
etr
ic
m
eth
o
d
is
lik
ely
to
p
r
o
d
u
ce
a
m
o
r
e
r
o
b
u
s
t
ca
u
s
al
esti
m
ate
th
an
th
e
p
ar
am
etr
ic
m
eth
o
d
,
g
iv
e
n
th
at
it
u
s
es
o
n
ly
o
b
s
er
v
atio
n
s
n
ea
r
th
e
cu
to
f
f
.
An
e
x
am
in
a
tio
n
o
f
t
h
e
s
tan
d
ar
d
er
r
o
r
s
ass
o
ciate
d
with
ea
ch
tr
ea
tm
en
t
ef
f
ec
t
esti
m
ate
r
ev
e
aled
th
at
t
h
e
n
o
n
p
ar
am
etr
ic
m
eth
o
d
p
r
o
d
u
ce
d
h
ig
h
er
s
tan
d
ar
d
er
r
o
r
s
th
an
th
e
p
ar
am
etr
ic
m
eth
o
d
.
T
h
is
f
in
d
in
g
is
n
o
t
s
u
r
p
r
is
in
g
,
g
iv
en
th
at
th
e
n
o
n
p
a
r
am
etr
ic
m
et
h
o
d
u
s
es
a
s
m
aller
n
u
m
b
er
o
f
o
b
s
er
v
atio
n
s
with
in
a
s
m
all
b
an
d
wid
th
to
esti
m
ate
th
e
r
elatio
n
s
h
ip
b
etwe
e
n
th
e
ass
ig
n
m
en
t
v
ar
iab
le
an
d
th
e
o
u
tco
m
e.
T
h
e
ch
o
ice
b
etwe
en
p
ar
am
etr
ic
an
d
n
o
n
p
ar
am
etr
ic
esti
m
atio
n
m
eth
o
d
s
in
p
o
o
le
d
MCR
D
an
aly
s
es
will
b
e
o
f
te
n
co
n
tex
t
-
s
p
ec
if
ic
.
W
h
ile
th
e
n
o
n
p
ar
am
etr
ic
m
o
d
el
m
a
y
y
ield
a
m
o
r
e
r
o
b
u
s
t
R
D
esti
m
ate,
it
g
en
er
ally
h
as
lo
wer
s
tatis
tical
p
o
wer
co
m
p
ar
ed
to
th
e
p
ar
am
etr
ic
m
o
d
el.
T
h
er
ef
o
r
e,
th
e
n
o
n
p
ar
am
etr
ic
m
eth
o
d
is
b
est
s
u
ited
f
o
r
m
u
l
ti
-
s
ite
p
r
o
g
r
am
ev
alu
atio
n
s
with
r
elativ
ely
lar
g
e
with
in
-
u
n
i
t
s
am
p
les.
A
lar
g
e
with
in
-
s
ite
s
am
p
le
will
ty
p
ically
b
e
r
eq
u
ir
e
d
wh
e
n
th
e
u
n
it
-
s
p
ec
if
ic
tr
ea
tm
en
t
ef
f
ec
ts
an
d
R
D
tr
ea
tm
en
t
ef
f
ec
t
h
eter
o
g
en
eity
ar
e
o
f
p
r
im
a
r
y
i
n
ter
est.
Ad
d
itio
n
ally
,
s
in
ce
th
e
n
o
n
p
a
r
am
etr
ic
ap
p
r
o
ac
h
es
s
u
ch
as
lo
ca
l
lin
ea
r
r
eg
r
ess
io
n
u
tili
ze
th
e
s
am
p
les
with
in
th
e
o
p
tim
al
b
an
d
wid
th
ar
o
u
n
d
th
e
cu
to
f
f
,
it is
cr
itical
to
h
av
e
a
s
u
f
f
icien
t
n
u
m
b
er
o
f
o
b
s
er
v
atio
n
s
n
ea
r
th
e
cu
t
o
f
f
(
i.e
.
,
ef
f
ec
tiv
e
s
am
p
le)
to
u
s
e
th
is
m
et
h
o
d
ef
f
ec
tiv
ely
.
I
f
a
lar
g
e
with
in
-
u
n
it
s
am
p
le
o
r
ef
f
ec
ti
v
e
s
am
p
le
is
n
o
t
a
v
ailab
le
-
a
co
m
m
o
n
ch
allen
g
e
in
r
ea
l
-
wo
r
ld
ev
alu
atio
n
s
-
p
ar
am
etr
ic
m
o
d
elin
g
wo
u
ld
b
e
a
v
iab
le
alter
n
ativ
e,
g
iv
en
th
at
it
p
r
o
d
u
ce
s
an
im
p
ac
t
esti
m
ate
with
a
r
elativ
ely
h
ig
h
er
s
tatis
tical
p
o
wer
.
W
e
r
ec
o
m
m
en
d
th
at
r
esear
c
h
er
s
em
p
lo
y
b
o
th
MCR
D
esti
m
ati
o
n
m
eth
o
d
s
,
alo
n
g
with
g
r
ap
h
ical
an
aly
s
is
,
to
ex
am
in
e
th
e
s
en
s
itiv
ity
o
f
tr
ea
t
m
en
t
im
p
ac
t
an
d
p
r
ec
is
io
n
esti
m
ates
p
r
o
v
id
ed
b
y
ea
ch
m
eth
o
d
.
3
.
2
.
2
.
I
nte
rv
ent
io
n
i
m
pa
ct
h
e
t
er
o
g
eneit
y
in
m
ultiple
-
cut
o
f
f
re
g
re
s
s
io
n dis
co
ntin
uity
d
esig
ns
R
esu
lts
f
r
o
m
MCR
D
m
o
d
el
in
d
icate
d
th
at
th
e
R
OOT
S
in
ter
v
en
tio
n
wo
r
k
ed
d
if
f
er
e
n
tly
d
e
p
en
d
in
g
o
n
th
e
cu
to
f
f
v
alu
e
ch
o
s
en
t
o
s
cr
ee
n
s
tu
d
en
ts
in
to
th
e
tr
ea
tm
en
t c
o
n
d
itio
n
in
ea
c
h
class
r
o
o
m
.
Sp
ec
if
ically
,
h
ig
h
e
r
ass
ig
n
m
en
t
s
co
r
e
cu
to
f
f
v
alu
e
s
wer
e
as
s
o
ciate
d
with
g
r
ea
te
r
in
ter
v
en
tio
n
ef
f
ec
ts
o
n
av
er
ag
e
.
T
h
ese
f
in
d
in
g
s
s
u
g
g
est
th
at
th
e
MCR
D
ca
n
b
e
an
in
f
o
r
m
ati
v
e
p
r
o
g
r
a
m
ev
alu
atio
n
d
esig
n
wh
e
n
tr
ea
tm
en
t
ass
ig
n
m
en
t
cu
to
f
f
s
v
ar
y
b
y
in
ter
v
en
tio
n
u
n
it
o
r
s
ite.
B
y
id
en
tify
in
g
th
e
p
o
o
led
tr
ea
tm
en
t
ef
f
ec
t
o
v
er
a
r
an
g
e
o
f
th
e
ass
ig
n
m
en
t
v
ar
iab
le
co
n
tin
u
u
m
an
d
ex
am
in
in
g
wh
eth
er
an
in
ter
v
en
tio
n
ef
f
ec
t
v
ar
ies
at
d
if
f
er
en
t
cu
t
-
p
o
in
ts
,
r
esear
ch
er
s
an
d
ed
u
ca
to
r
s
ca
n
g
ain
a
m
o
r
e
co
m
p
r
eh
e
n
s
iv
e
u
n
d
e
r
s
tan
d
in
g
o
f
p
r
o
g
r
am
p
er
f
o
r
m
a
n
c
e
an
d
th
e
f
ac
to
r
s
in
f
lu
en
cin
g
d
if
f
e
r
en
tial o
u
tco
m
es.
T
h
e
ab
ilit
y
to
d
er
iv
e
a
p
o
o
le
d
im
p
ac
t
esti
m
ate
ac
r
o
s
s
a
wid
er
r
an
g
e
o
f
th
e
ass
ig
n
m
e
n
t
v
ar
iab
le
co
n
tin
u
u
m
n
o
tab
ly
c
o
n
tr
asts
with
th
e
b
asic
R
D
d
esig
n
,
wh
e
r
e
ca
u
s
al
in
f
er
en
ce
is
r
estricte
d
to
a
n
ar
r
o
w
r
e
g
io
n
ar
o
u
n
d
a
s
in
g
le
cu
to
f
f
s
co
r
e.
Fo
r
ed
u
ca
tio
n
al
r
esear
ch
er
s
an
d
p
r
o
g
r
am
ev
al
u
ato
r
s
,
th
e
MCR
D
d
esig
n
m
ay
th
u
s
b
e
u
s
ed
t
o
p
r
o
b
e
wh
e
th
er
a
p
r
o
g
r
am
is
ef
f
ec
tiv
e
o
r
d
if
f
e
r
en
tially
e
f
f
ec
tiv
e
ac
r
o
s
s
a
r
a
n
g
e
o
f
d
iag
n
o
s
tically
im
p
o
r
tan
t
ass
ig
n
m
en
t
s
co
r
e
v
alu
es.
I
n
ca
s
es
wh
er
e
h
eter
o
g
en
eity
in
th
e
l
o
c
al
tr
ea
tm
en
t
ef
f
ec
ts
is
n
o
t
o
b
s
er
v
ed
,
a
p
o
o
led
R
D
esti
m
ate
s
er
v
es
to
p
r
o
v
id
e
an
ac
cu
r
ate
s
u
m
m
ar
y
o
f
th
e
av
er
ag
e
tr
ea
tm
en
t
ef
f
ec
t
ac
r
o
s
s
all
cu
to
f
f
s
in
clu
d
ed
i
n
t
h
e
d
esig
n
.
T
h
e
r
esear
ch
er
ca
n
th
en
in
f
er
t
h
e
tr
ea
tm
en
t h
a
d
s
im
ilar
im
p
ac
t a
cr
o
s
s
a
s
p
ec
if
ied
ag
e
r
an
g
e
o
r
an
in
co
m
e,
r
ea
d
in
g
s
co
r
e,
o
r
p
r
ep
r
o
g
r
am
p
er
f
o
r
m
an
ce
in
te
r
v
als,
f
o
r
ex
am
p
le.
Ho
wev
er
,
if
th
e
r
esear
ch
er
i
d
en
tifie
s
th
at
th
e
tr
ea
tm
en
t
ef
f
ec
t
v
ar
ies
ac
r
o
s
s
d
if
f
er
e
n
t
p
o
in
ts
alo
n
g
t
h
e
ass
ig
n
m
en
t
v
ar
iab
le
co
n
tin
u
u
m
,
th
en
it
b
ec
o
m
es
p
o
s
s
ib
le
to
in
v
esti
g
ate
wh
eth
er
s
ite
ch
ar
ac
ter
is
tics
(
e.
g
.
,
u
n
it
cu
to
f
f
v
alu
e,
class
s
ize,
f
id
elity
o
f
im
p
lem
en
tatio
n
)
m
o
d
er
ate
th
e
s
ize
o
f
th
e
tr
ea
tm
en
t
im
p
ac
t
o
n
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
E
v
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&
R
es E
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c
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N:
2252
-
8
8
2
2
Mu
ltip
le
-
cu
to
ff reg
r
ess
io
n
d
is
co
n
tin
u
ity
d
esig
n
s
in
e
d
u
ca
tio
n
a
l e
va
lu
a
tio
n
(
Hye
o
n
Jin
Yo
o
n
)
1605
o
u
tco
m
es
o
f
in
ter
est.
T
h
e
r
esear
ch
er
m
ay
th
en
b
e
a
b
le
to
r
ep
o
r
t
th
at
p
r
o
g
r
am
ef
f
ec
ts
v
ar
ied
with
r
esp
ec
t
to
m
o
r
e
o
r
less
m
allea
b
le
p
r
o
g
r
am
ch
ar
ac
ter
is
tics
s
u
ch
as
th
e
lev
el
o
f
a
d
h
er
e
n
ce
to
th
e
p
r
o
g
r
am
m
o
d
el,
th
e
s
ev
er
ity
o
f
n
ee
d
in
th
e
co
m
m
u
n
ity
,
o
r
t
h
e
len
g
th
o
f
p
r
o
g
r
am
o
p
er
atio
n
s
.
T
h
e
ac
q
u
is
itio
n
o
f
m
o
r
e
r
o
b
u
s
t
in
s
ig
h
t
in
to
th
e
R
D
tr
ea
tm
en
t
ef
f
ec
t,
in
cl
u
d
in
g
p
o
s
s
ib
le
h
eter
o
g
en
eity
,
m
ay
e
n
ab
le
e
d
u
ca
tio
n
al
p
r
o
g
r
a
m
d
ev
el
o
p
e
r
s
an
d
ad
m
in
is
tr
ato
r
s
to
r
e
d
e
s
ig
n
o
r
m
o
d
if
y
th
e
d
eliv
er
y
o
f
an
in
ter
v
en
tio
n
to
b
etter
m
ee
t
th
e
n
ee
d
s
o
f
d
iv
er
s
e
p
r
o
g
r
am
p
ar
ticip
an
ts
.
Fo
r
e
x
am
p
le,
if
an
ea
r
ly
ch
ild
h
o
o
d
liter
ac
y
in
ter
v
en
tio
n
is
s
h
o
wn
to
h
a
v
e
a
p
o
s
itiv
e
im
p
ac
t
f
o
r
s
tu
d
en
ts
at
m
o
d
e
r
ate
r
is
k
,
b
u
t
n
o
t
f
o
r
th
o
s
e
m
o
s
t
at
-
r
is
k
,
ed
u
ca
to
r
s
co
u
ld
ch
o
o
s
e
to
r
ec
o
n
s
id
er
th
e
in
ter
v
en
tio
n
’
s
tar
g
et
p
o
p
u
latio
n
,
en
ter
tai
n
ad
o
p
tin
g
a
n
ew
p
r
o
g
r
am
wit
h
a
b
etter
alig
n
ed
c
u
r
r
icu
lu
m
,
o
r
attem
p
t
to
m
o
d
if
y
t
h
e
p
r
o
g
r
am
t
o
p
r
o
v
id
e
a
m
o
r
e
in
ten
s
e
tr
ea
tm
en
t
d
o
s
ag
e
to
th
o
s
e
m
o
s
t
at
-
r
is
k
o
f
n
eg
ativ
e
o
u
tco
m
es.
Similar
ly
,
in
co
lleg
e
r
em
ed
iatio
n
p
r
o
g
r
a
m
s
,
if
a
m
ath
r
em
ed
iat
io
n
co
u
r
s
e
b
e
n
ef
its
s
tu
d
en
ts
with
m
o
d
er
ate
lo
w
s
co
r
es
b
u
t
n
o
t
t
h
o
s
e
with
th
e
lo
west
s
co
r
es,
p
r
o
g
r
am
d
e
v
elo
p
er
s
an
d
ad
m
in
is
tr
ato
r
s
m
ay
ch
o
o
s
e
to
r
ee
v
alu
ate
t
h
e
p
r
o
g
r
am
'
s
tar
g
et
p
o
p
u
latio
n
o
r
e
n
h
an
ce
th
e
p
r
o
g
r
am
'
s
in
ten
s
ity
f
o
r
th
o
s
e
with
th
e
lo
west sco
r
es.
3
.
2
.
3
.
L
im
it
a
t
io
ns
T
h
e
cu
r
r
en
t
s
tu
d
y
h
as
s
ev
er
al
lim
itatio
n
s
to
n
o
te.
First,
we
d
id
n
o
t
ev
alu
ate
th
e
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
MCR
D
es
tim
ate
r
elativ
e
to
t
h
e
b
en
c
h
m
ar
k
R
C
T
ca
u
s
al
esti
m
ate.
T
h
at
is
,
th
e
f
in
d
in
g
s
o
f
th
is
s
tu
d
y
d
o
n
o
t
s
p
ea
k
to
wh
eth
er
t
h
e
MCR
D
d
esig
n
p
r
o
d
u
ce
s
tr
ea
tm
en
t
e
f
f
ec
t
esti
m
ates
th
at
ar
e
co
m
p
ar
ab
le
to
an
R
C
T
b
en
ch
m
ar
k
.
T
h
er
ef
o
r
e,
f
u
tu
r
e
s
tu
d
ies
ar
e
n
ee
d
e
d
to
ev
alu
ate
th
e
v
alid
ity
an
d
ef
f
icien
c
y
o
f
MCR
D
m
eth
o
d
s
in
co
m
p
ar
is
o
n
t
o
R
C
T
esti
m
ates
.
Seco
n
d
,
th
e
d
ataset
u
s
ed
i
n
th
is
s
tu
d
y
h
ad
a
s
m
all
with
in
-
g
r
o
u
p
(
class
r
o
o
m
)
s
am
p
le
s
ize,
th
er
eb
y
lim
itin
g
th
e
r
eliab
ilit
y
o
f
th
e
esti
m
at
io
n
o
f
lo
ca
l
in
ter
v
en
tio
n
ef
f
e
cts
at
ea
ch
cu
to
f
f
.
T
h
ir
d
,
th
is
s
tu
d
y
co
n
s
id
er
e
d
o
n
ly
o
n
e
p
r
e
d
icto
r
o
f
tr
ea
tm
en
t
ef
f
ec
t
h
eter
o
g
en
eity
.
Giv
en
r
ec
en
t
r
esear
c
h
lin
k
in
g
g
r
o
u
p
-
a
n
d
class
r
o
o
m
-
lev
el
f
ac
to
r
s
to
m
ath
d
e
v
elo
p
m
en
t
[
29
]
,
[
3
0
]
,
f
u
tu
r
e
s
tu
d
ies
s
h
o
u
ld
i
n
v
esti
g
ate
h
o
w
v
ar
io
u
s
u
n
it
-
lev
el
f
ac
to
r
s
(
e.
g
.
,
in
s
tr
u
ctio
n
al
s
tr
ateg
y
,
f
id
elity
o
f
im
p
lem
e
n
tatio
n
,
t
ea
ch
er
ex
p
e
r
ien
ce
)
r
elate
to
class
r
o
o
m
d
if
f
e
r
en
ce
s
in
p
r
o
g
r
am
o
u
tco
m
es.
4.
CO
NCLU
SI
O
N
T
h
e
m
o
tiv
atio
n
f
o
r
th
is
s
tu
d
y
was
to
d
em
o
n
s
tr
ate
a
m
eth
o
d
f
o
r
esti
m
atin
g
tr
ea
tm
en
t
ef
f
ec
ts
wh
en
m
u
ltip
le
cu
to
f
f
s
ar
e
u
s
ed
ac
r
o
s
s
d
if
f
er
en
t
in
te
r
v
en
tio
n
u
n
its
an
d
to
m
o
d
el
tr
ea
tm
en
t
e
f
f
ec
t
v
ar
iab
ilit
y
with
in
th
e
R
D
f
r
am
ewo
r
k
f
o
r
ed
u
ca
t
io
n
al
ev
alu
atio
n
.
W
h
ile
f
u
r
th
er
r
esear
ch
is
n
ee
d
ed
,
th
e
cu
r
r
en
t
s
tu
d
y
s
u
g
g
ests
th
at
MCR
D
d
esig
n
s
h
av
e
th
e
p
o
ten
tial
to
id
en
tif
y
th
e
p
o
o
le
d
in
ter
v
en
tio
n
ef
f
ec
t
ac
r
o
s
s
cu
to
f
f
s
an
d
u
n
c
o
v
e
r
th
e
p
r
o
c
ess
es
an
d
m
ec
h
a
n
is
m
s
th
r
o
u
g
h
wh
ich
in
ter
v
e
n
tio
n
s
ar
e
d
if
f
er
en
tially
e
f
f
ec
tiv
e
ac
r
o
s
s
in
d
iv
id
u
als
an
d
co
n
tex
ts
.
W
e
r
ec
o
m
m
en
d
th
a
t
r
esear
ch
er
s
s
tar
t
an
MCR
D
an
aly
s
is
with
a
tr
ad
itio
n
al
p
o
o
lin
g
an
al
y
s
is
to
esti
m
ate
th
e
av
er
ag
e
tr
ea
tm
en
t
ef
f
ec
t
ac
r
o
s
s
cu
to
f
f
s
.
S
u
b
s
eq
u
en
tly
,
th
ey
ca
n
f
u
r
th
e
r
ex
p
lo
r
e
p
o
te
n
tial
h
eter
o
g
en
eity
i
n
tr
ea
tm
en
t
ef
f
ec
ts
at
d
if
f
er
en
t
cu
to
f
f
p
o
in
ts
b
y
ex
am
in
in
g
in
ter
ac
tio
n
e
f
f
ec
ts
o
r
co
n
d
u
ctin
g
s
u
b
g
r
o
u
p
a
n
aly
s
es
b
ased
o
n
r
elev
an
t
th
e
o
r
y
,
th
e
r
esear
ch
c
o
n
tex
t,
a
n
d
p
r
elim
in
a
r
y
an
aly
t
ic
r
esu
lts
(
e.
g
.
,
lo
ca
l
R
D
tr
ea
tm
en
t e
f
f
ec
t e
s
tim
ates)
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
T
h
is
r
esear
ch
was
s
u
p
p
o
r
ted
b
y
th
e
R
OOT
S
Pro
ject
(
Gr
an
t
R
3
2
4
A1
2
0
3
0
4
)
,
f
u
n
d
ed
b
y
th
e
I
n
s
titu
te
o
f
E
d
u
ca
tio
n
Scien
ce
s
,
U.
S.
D
ep
ar
tm
en
t o
f
E
d
u
ca
ti
o
n
.
AUTHO
R
CO
NT
RI
B
UT
I
O
NS ST
A
T
E
M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
t
r
ib
u
to
r
R
o
les
T
a
x
o
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