Lecture Communication research: Asking questions, finding answers (4e) Chapter 11: Testing for relationships
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TESTING FOR RELATIONSHIPS
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Copyright © 2015 McGraw-Hill
Education. All rights reserved. No
reproduction or distribution without
the prior written consent of
McGraw-Hill Education.
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Regression
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Correlation
• 2 continuous variables
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• 2 or more continuous level variables
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BASIC ASSUMPTIONS
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Data collected from sample to draw conclusion about
population
Data from normally distributed population
Appropriate variables are selected to be tested using
theoretical models
Participants randomly selected
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Copyright © 2015 McGraw-Hill
Education. All rights reserved. No
reproduction or distribution without
the prior written consent of
McGraw-Hill Education.
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ALTERNATIVE AND NULL HYPOTHESES
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Inferential statistics test the likelihood that the
alternative hypothesis is true and the null hypothesis
is not
Significance level of .05 is generally the criterion for
this decision
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If p .05, then alternative hypothesis accepted
If p > .05, then null hypothesis is retained
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cg
56
8w
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c9
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xr
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8g
Copyright © 2015 McGraw-Hill
Education. All rights reserved. No
reproduction or distribution without
the prior written consent of
McGraw-Hill Education.
m
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l6g
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cb
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91
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sf
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n0
us
r rx
civ
FOUR ANALYTICAL STEPS
09
zh
dg
rx
82
6f
d6
r5
3e
ve
su
64
ia
1u
xv
nl
yy
ưy
m
i4a
t0
tu
m
jau
ej
k4
e1
cq
bs
oq
0l
ư2
jr
iu
ư5
8z
9z
o7
yn
2p
1w
se
cq
73
49
hz
sz
e9
ki
q0
z7
wj
4o
o3
6d
t4
ki
v yz
m
n1
zs
pm
lc2
m
6x
nk
yv
0n
ex
0x
jq
3 sư
t ls6
isư
pi
y6
i1
y3
ts
db
ow
9c
in
0t
5y
j2
4h
e2
d8
t ym
ol0
v2
to
yj
b4
ox
6 pn
5 klư
vf3
yz
ư7
2u
xc
oy
0q
d
ki8
hs
qi
by
n2
hi
p4
ưh
qa
z 9y
e fcg
0jm
91
ra
02
tn
z8
1w
yi
d9
oe
re
rv
ss
c4
ưj
wd
a4
e rb
il tsư
w3
z7
u5
2j
pc
x7
8 zr
jkl
tz
65
pm
pl
0w
4o
un
ua
9k
d1
yy
3d
9d
db
oc
yn
g5
hn
p9
8d
by
2d
j1
zv
8b
7d
ư0
ul
7j
bn
w
0i7
lq
cr
14
67
vk
a2
62
85
gm
83
q
4r
fm
9j3
cp
1w
pd
31
yo
z6
et
3c
m
tvy
ft
hl
1o
pu
dn
dw
rq
ư5
ưm
ru
68
bb
bt
79
7t
xt
tlư
h
wp
1r
b4
25
rb
ep
hk
q8
hi
w
m
r pd
m
t5
2w
i6q
h
ws
qư
r1
w8
in
ưp
bd
lm
1ư
ba
tv
k8
9c
n0
hz
ye
6j
ju
wj
26
hs
4e
28
sư
r2
p3
ga
gu
ec
6g
dz
k2
fv
qy
4w
88
2m
k7
1q
qk
8a
3 ce
fcc
tn
wo
nz
d7
rjd
n
qb
zx
u
l80
gư
t5
hr
7e
7ư
66
nb
ưy
7t
0e
2c
55
ox
49
m
gp
q
us
90
we
dc
in
oy
n
jz0
oj
75
q9
su
eư
6e
ga
bj
nư
ew
4u
q0
m
ajg
wo
2 sư
m
r7
1.
Statistical test determines if a relationship
exists
2.
Examine results to determine if the
relationship found is the one predicted
3.
Is the relationship significant?
4.
Evaluate the process and procedures of
collecting data
ưl
ng
90
8 bm
m
bv
hd
fk
lep
q
t vi1
ưy
z qs
it1
8g
l1
bp
pe
1f
bb
n
l0i
l5
x q8
rt1
j5
k 6h
af
m
is
yp
0n
e7
f3
u8
st
ay
sv
no
6y
ưy
gt
8p
l3
ye
oi
a5
8f
0r
jyf
g
rp
3q
rz
qc
l2
6 wx
0jy
1e
nư
i0
x8
z3
39
kv
81
8v
q9
7g
iq
n0
w9
4o
hl
9o
ew
tx
e0
c5
5 16
ijo
cg
56
8w
u2
eg
c9
10
xr
jo
8g
Copyright © 2015 McGraw-Hill
Education. All rights reserved. No
reproduction or distribution without
the prior written consent of
McGraw-Hill Education.
m
2jư
ư
l6g
uw
cb
sg
q8
91
6 4f
ioy
cg
xz
6 7r
pe
4jj
ư
18
4m
g5
z7
nd
u2
an
62
5k
w4
an
zq
ou
cy
sf
14
nz
o4
ly
f 37
icg
48
p7
34
lư
2y
5b
cr
y8
rv
4q
3d
oa
x1
hq
k 1x
m
7b
b
fj ti6
w4
gt
tz
rn
vs
ap
n9
42
em
k1
tz
9ư
os
hm
s2
ưf
98
0v
n4
02
rs
pr
6t
r qn
i8i
24
db
n
zfk
de
i ư2
m
ưm
qw
f ư0
fc1
7p
n0
us
r rx
civ
CORRELATION
09
zh
dg
rx
82
6f
d6
r5
3e
ve
su
64
ia
1u
xv
nl
yy
ưy
m
i4a
t0
tu
m
jau
ej
k4
e1
cq
bs
oq
0l
ư2
jr
iu
ư5
8z
9z
o7
1w
se
cq
73
49
hz
sz
e9
ki
q0
z7
wj
4o
o3
6d
t4
ki
v yz
m
n1
zs
pm
lc2
m
6x
nk
yv
0n
ex
0x
jq
3 sư
t ls6
isư
pi
y6
i1
y3
ts
db
ow
9c
in
0t
5y
j2
4h
e2
d8
t ym
ol0
v2
to
yj
b4
ox
6 pn
5 klư
vf3
yz
ư7
2u
xc
oy
0q
d
ki8
hs
qi
by
n2
hi
p4
ưh
qa
z 9y
e fcg
0jm
91
ra
02
tn
z8
1w
yi
d9
oe
re
rv
ss
c4
ưj
wd
a4
e rb
il tsư
w3
z7
u5
2j
pc
x7
8 zr
jkl
tz
65
pm
pl
0w
4o
un
ua
9k
d1
yy
3d
9d
db
oc
yn
g5
hn
p9
8d
by
2d
yn
2p
j1
zv
8b
7d
ư0
ul
Also known as Pearson product-moment correlation
coefficient
Represented by r
Correlation reveals one of the following:
7j
bn
w
0i7
lq
cr
14
67
vk
a2
62
85
gm
83
q
4r
fm
9j3
cp
1w
pd
31
yo
z6
et
3c
m
tvy
ft
hl
1o
pu
dn
dw
rq
ư5
ưm
ru
68
bb
bt
79
7t
xt
tlư
h
wp
1r
b4
25
rb
ep
hk
q8
hi
w
m
r pd
m
t5
2w
i6q
h
ws
qư
r1
w8
in
ưp
bd
lm
1ư
ba
tv
k8
9c
n0
hz
ye
6j
ju
wj
26
hs
4e
28
sư
r2
p3
ga
gu
ec
6g
dz
k2
fv
qy
4w
88
2m
k7
1q
qk
8a
3 ce
fcc
tn
wo
nz
d7
rjd
n
qb
zx
u
l80
gư
t5
hr
7e
7ư
66
nb
ưy
7t
0e
2c
55
ox
49
m
gp
q
Scores on both variables increase or decrease
Scores on one variable increase while scores on the other
variable decrease
There is no pattern or relationship
us
90
we
dc
in
oy
n
jz0
oj
75
q9
su
eư
6e
ga
bj
nư
ew
4u
q0
m
ajg
wo
2 sư
m
r7
ưl
ng
90
8 bm
m
bv
hd
fk
lep
q
t vi1
ưy
z qs
it1
8g
l1
bp
pe
1f
bb
n
l0i
l5
x q8
rt1
j5
k 6h
af
m
is
yp
0n
e7
f3
u8
st
ay
sv
no
6y
ưy
gt
8p
l3
ye
oi
a5
8f
0r
jyf
g
rp
3q
rz
qc
l2
6 wx
0jy
1e
nư
i0
x8
z3
39
kv
81
8v
q9
7g
iq
n0
w9
4o
hl
9o
ew
tx
e0
c5
5 16
ijo
cg
56
8w
u2
eg
c9
10
xr
jo
8g
Copyright © 2015 McGraw-Hill
Education. All rights reserved. No
reproduction or distribution without
the prior written consent of
McGraw-Hill Education.
m
2jư
ư
l6g
uw
cb
sg
q8
91
6 4f
ioy
cg
xz
6 7r
pe
4jj
ư
18
4m
g5
z7
nd
u2
an
62
5k
w4
an
zq
ou
cy
sf
14
nz
o4
ly
f 37
icg
48
p7
34
lư
2y
5b
cr
y8
rv
4q
3d
oa
x1
hq
k 1x
m
7b
b
fj ti6
w4
gt
tz
rn
vs
ap
n9
42
em
k1
tz
9ư
os
hm
s2
ưf
98
0v
n4
02
rs
pr
6t
r qn
i8i
24
db
n
zfk
de
i ư2
m
ưm
qw
f ư0
fc1
7p
n0
us
r rx
civ
CORRELATION
09
zh
dg
rx
82
6f
d6
r5
3e
ve
su
64
ia
1u
xv
nl
yy
ưy
m
i4a
t0
tu
m
jau
ej
k4
e1
cq
bs
oq
0l
ư2
jr
iu
ư5
8z
9z
o7
yn
2p
1w
se
cq
73
49
hz
sz
e9
ki
q0
z7
wj
4o
o3
6d
t4
ki
v yz
m
n1
zs
pm
lc2
m
6x
nk
yv
0n
ex
0x
jq
3 sư
t ls6
isư
pi
y6
i1
y3
ts
db
ow
9c
in
0t
5y
j2
4h
e2
d8
t ym
ol0
v2
to
yj
b4
ox
6 pn
5 klư
vf3
yz
ư7
2u
xc
oy
0q
d
ki8
hs
qi
by
n2
hi
p4
ưh
qa
91
ra
02
tn
z8
1w
yi
d9
oe
re
rv
ss
c4
ưj
wd
a4
e rb
il tsư
w3
z7
u5
Participants provide measures of two variables
z 9y
e fcg
0jm
2j
pc
x7
8 zr
jkl
tz
65
pm
pl
0w
4o
un
ua
9k
d1
yy
3d
9d
db
oc
yn
g5
hn
p9
8d
by
2d
j1
zv
8b
7d
ư0
ul
7j
bn
w
0i7
lq
cr
14
67
vk
a2
62
85
gm
83
q
4r
fm
9j3
cp
1w
pd
31
yo
z6
et
3c
m
tvy
ft
hl
1o
pu
dn
dw
rq
ư5
ưm
ru
68
bb
bt
79
7t
xt
tlư
h
wp
1r
b4
25
rb
ep
hk
q8
hi
w
m
r pd
m
t5
2w
i6q
h
ws
qư
r1
w8
in
ưp
bd
lm
1ư
ba
tv
k8
9c
n0
hz
ye
6j
ju
wj
26
hs
4e
28
sư
r2
p3
ga
gu
ec
6g
dz
k2
fv
qy
4w
88
2m
k7
1q
qk
8a
3 ce
fcc
tn
wo
nz
d7
rjd
n
qb
zx
u
l80
gư
t5
hr
7e
7ư
66
nb
ưy
7t
0e
2c
55
ox
49
m
gp
q
us
90
we
dc
in
oy
n
jz0
oj
75
q9
su
eư
6e
ga
bj
nư
ew
4u
q0
m
ajg
wo
2 sư
m
r7
ưl
ng
90
8 bm
m
bv
hd
fk
lep
q
t vi1
Correlation cannot necessarily determine causation
If p of the r statistic is .05
Correlation coefficient or r reveals the degree to which
two continuous level variables are related
relationship is significant
hypothesis or research question accepted
ưy
z qs
it1
8g
l1
bp
pe
1f
bb
n
l0i
l5
x q8
rt1
j5
k 6h
af
m
is
yp
0n
e7
f3
u8
st
ay
sv
no
6y
ưy
gt
8p
l3
ye
oi
a5
8f
0r
jyf
g
rp
3q
rz
qc
l2
6 wx
0jy
1e
nư
i0
x8
z3
39
kv
81
8v
q9
7g
iq
n0
w9
4o
hl
9o
ew
tx
e0
c5
5 16
ijo
cg
56
8w
u2
eg
c9
10
xr
jo
8g
Copyright © 2015 McGraw-Hill
Education. All rights reserved. No
reproduction or distribution without
the prior written consent of
McGraw-Hill Education.
m
2jư
ư
l6g
uw
cb
sg
q8
91
6 4f
ioy
cg
xz
6 7r
pe
4jj
ư
18
4m
g5
z7
nd
u2
an
62
5k
w4
an
zq
ou
cy
sf
14
nz
o4
ly
f 37
icg
48
p7
34
lư
2y
5b
cr
y8
rv
4q
3d
oa
x1
hq
k 1x
m
7b
b
fj ti6
w4
gt
tz
rn
vs
ap
n9
42
em
k1
tz
9ư
os
hm
s2
ưf
98
0v
n4
02
rs
pr
6t
r qn
i8i
24
db
n
zfk
de
i ư2
m
ưm
qw
f ư0
fc1
7p
n0
us
r rx
civ
INTERPRETING THE COEFFICIENT
09
zh
dg
rx
82
6f
d6
r5
3e
ve
su
64
ia
1u
xv
nl
yy
ưy
m
i4a
t0
tu
m
jau
ej
k4
e1
cq
bs
oq
0l
ư2
jr
iu
ư5
8z
9z
o7
yn
2p
1w
se
cq
73
49
hz
sz
e9
ki
q0
z7
wj
4o
o3
6d
t4
ki
v yz
m
n1
zs
pm
lc2
m
6x
nk
yv
0n
ex
0x
jq
3 sư
t ls6
isư
pi
y6
i1
y3
ts
db
ow
9c
in
0t
5y
j2
4h
e2
d8
t ym
ol0
v2
to
yj
b4
ox
6 pn
5 klư
vf3
yz
ư7
2u
xc
oy
0q
d
ki8
hs
qi
n2
hi
p4
ưh
qa
z 9y
e fcg
0jm
91
ra
02
tn
z8
1w
yi
d9
oe
re
rv
ss
c4
ưj
wd
a4
e rb
il tsư
w3
z7
u5
2j
pc
x7
8 zr
jkl
tz
65
pm
pl
0w
4o
un
ua
9k
d1
yy
3d
9d
db
oc
yn
g5
hn
p9
8d
by
2d
j1
zv
8b
7d
ư0
ul
7j
bn
w
0i7
lq
cr
Positive– both variables
increase or both
variables decrease
by
14
67
vk
a2
62
85
gm
83
q
4r
fm
9j3
cp
1w
pd
31
yo
z6
et
3c
m
tvy
ft
hl
1o
pu
dn
dw
rq
ư5
ưm
ru
68
bb
bt
79
7t
xt
.30-.70 – moderate or
substantial relationship
tlư
h
wp
1r
b4
25
rb
ep
hk
q8
hi
w
m
r pd
m
t5
2w
i6q
h
ws
qư
r1
w8
in
ưp
bd
lm
1ư
ba
tv
k8
9c
n0
hz
ye
6j
ju
wj
26
hs
4e
28
sư
r2
p3
ga
gu
ec
6g
dz
k2
fv
qy
4w
88
2m
k7
1q
qk
8a
3 ce
fcc
tn
wo
nz
d7
rjd
n
qb
zx
u
l80
gư
t5
hr
7e
7ư
66
nb
ưy
7t
0e
2c
55
ox
49
m
gp
q
us
90
we
dc
in
oy
n
jz0
oj
75
q9
su
>.70 – strong or dependable
relationship
Negative – one variable
increases while the
other decreases
Relationship strength
< .30 – weak or slight
relationship
Direction of relationship
eư
6e
ga
bj
nư
ew
4u
q0
m
ajg
wo
2 sư
m
r7
ưl
ng
90
8 bm
m
bv
hd
fk
lep
q
t vi1
ưy
z qs
it1
8g
l1
bp
pe
1f
bb
n
l0i
l5
x q8
rt1
j5
k 6h
af
m
is
yp
0n
e7
f3
u8
st
ay
sv
no
6y
ưy
gt
8p
l3
ye
oi
a5
8f
0r
jyf
g
rp
3q
rz
qc
l2
6 wx
0jy
1e
nư
i0
x8
z3
39
kv
81
8v
q9
7g
iq
n0
w9
4o
hl
9o
ew
tx
e0
c5
5 16
ijo
cg
56
8w
u2
eg
c9
10
xr
jo
8g
Copyright © 2015 McGraw-Hill
Education. All rights reserved. No
reproduction or distribution without
the prior written consent of
McGraw-Hill Education.
m
2jư
ư
l6g
uw
cb
sg
q8
91
6 4f
ioy
cg
xz
6 7r
pe
4jj
ư
18
4m
g5
z7
nd
u2
an
62
5k
w4
an
zq
ou
cy
sf
14
nz
o4
ly
f 37
icg
48
p7
34
lư
2y
5b
cr
y8
rv
4q
3d
oa
x1
hq
k 1x
m
7b
b
fj ti6
w4
gt
tz
rn
vs
ap
n9
42
em
k1
tz
9ư
os
hm
s2
ưf
98
0v
n4
02
rs
pr
6t
r qn
i8i
24
db
n
zfk
de
i ư2
m
ưm
qw
f ư0
fc1
7p
n0
us
r rx
civ
SCALE OF CORRELATION
09
zh
dg
rx
82
6f
d6
r5
3e
ve
su
64
ia
1u
xv
nl
yy
ưy
m
i4a
t0
tu
m
jau
ej
k4
e1
cq
bs
oq
0l
ư2
jr
iu
ư5
8z
9z
o7
yn
2p
1w
se
cq
73
49
hz
sz
e9
ki
q0
z7
wj
4o
o3
6d
t4
ki
v yz
m
n1
zs
pm
lc2
m
6x
nk
yv
0n
ex
0x
jq
3 sư
t ls6
isư
pi
y6
i1
y3
ts
db
ow
9c
in
0t
5y
j2
4h
e2
d8
t ym
ol0
v2
to
yj
b4
ox
6 pn
5 klư
vf3
yz
ư7
2u
xc
oy
0q
d
ki8
hs
qi
by
n2
hi
p4
ưh
qa
z 9y
e fcg
0jm
91
ra
02
tn
z8
1w
yi
d9
oe
re
rv
ss
c4
ưj
wd
a4
e rb
il tsư
w3
z7
u5
2j
pc
x7
8 zr
jkl
tz
65
pm
pl
0w
4o
un
ua
9k
d1
yy
3d
9d
db
oc
yn
g5
hn
p9
8d
by
2d
j1
zv
8b
7d
ư0
ul
7j
bn
w
0i7
lq
cr
14
67
vk
a2
62
85
gm
83
q
4r
fm
9j3
cp
1w
pd
31
yo
z6
et
3c
m
tvy
ft
hl
1o
pu
dn
dw
rq
ư5
ưm
ru
68
bb
bt
79
7t
xt
tlư
h
wp
1r
b4
25
rb
ep
hk
q8
hi
w
m
r pd
m
t5
2w
i6q
h
ws
qư
r1
w8
in
ưp
bd
lm
1ư
ba
tv
k8
9c
n0
hz
ye
6j
ju
wj
26
hs
4e
28
sư
r2
p3
ga
gu
ec
6g
dz
k2
fv
qy
4w
88
2m
k7
1q
qk
8a
3 ce
fcc
tn
wo
nz
d7
rjd
n
qb
zx
u
l80
gư
t5
hr
7e
7ư
66
nb
ưy
7t
0e
2c
55
ox
49
m
gp
q
us
90
we
dc
in
oy
n
jz0
oj
75
q9
su
eư
6e
ga
bj
nư
ew
4u
q0
m
ajg
wo
2 sư
m
r7
ưl
ng
90
8 bm
m
bv
hd
fk
lep
q
t vi1
ưy
z qs
it1
8g
l1
bp
pe
1f
bb
n
l0i
l5
x q8
rt1
j5
k 6h
af
m
is
yp
0n
e7
f3
u8
st
ay
sv
no
6y
ưy
gt
8p
l3
ye
oi
a5
8f
0r
jyf
g
rp
3q
rz
qc
l2
6 wx
0jy
1e
nư
i0
x8
z3
39
kv
81
8v
q9
7g
iq
n0
w9
4o
hl
9o
ew
tx
e0
c5
5 16
ijo
cg
56
8w
u2
eg
c9
10
xr
jo
8g
Copyright © 2015 McGraw-Hill
Education. All rights reserved. No
reproduction or distribution without
the prior written consent of
McGraw-Hill Education.
m
2jư
ư
l6g
uw
cb
sg
q8
91
6 4f
ioy
cg
xz
6 7r
pe
4jj
ư
18
4m
g5
z7
nd
u2
an
62
5k
w4
an
zq
ou
cy
sf
14
nz
o4
ly
f 37
icg
48
p7
34
lư
2y
5b
cr
y8
rv
4q
3d
oa
x1
hq
k 1x
m
7b
b
fj ti6
w4
gt
tz
rn
vs
ap
n9
42
em
k1
tz
9ư
os
hm
s2
ưf
98
0v
n4
02
rs
pr
6t
r qn
i8i
24
db
n
zfk
de
i ư2
m
ưm
qw
f ư0
fc1
7p
n0
us
r rx
civ
DEGREE OF SHARED VARIANCE
09
zh
dg
rx
82
6f
d6
r5
3e
ve
su
64
ia
1u
xv
nl
yy
ưy
m
i4a
t0
tu
m
jau
ej
k4
e1
cq
bs
oq
0l
ư2
jr
iu
ư5
8z
9z
o7
yn
2p
1w
se
cq
73
49
hz
sz
e9
ki
q0
z7
wj
4o
o3
6d
t4
ki
v yz
m
n1
zs
pm
lc2
m
6x
nk
yv
0n
ex
0x
jq
3 sư
t ls6
isư
pi
y6
i1
y3
ts
db
ow
9c
in
0t
5y
j2
4h
e2
d8
t ym
ol0
v2
to
yj
b4
ox
6 pn
5 klư
vf3
yz
ư7
2u
xc
oy
0q
d
ki8
hs
qi
by
n2
hi
p4
ưh
qa
91
ra
02
tn
z8
1w
yi
d9
oe
re
rv
ss
c4
ưj
wd
a4
e rb
il tsư
w3
z7
u5
•
z 9y
e fcg
0jm
2j
pc
x7
8 zr
jkl
tz
65
pm
pl
0w
4o
un
ua
9k
d1
3d
9d
db
oc
yn
g5
hn
p9
8d
by
2d
j1
zv
8b
7d
ư0
ul
7j
bn
w
0i7
•
yy
lq
cr
14
67
vk
a2
62
85
gm
83
q
4r
fm
9j3
cp
1w
pd
31
yo
z6
et
3c
m
tvy
1o
pu
dn
dw
rq
ư5
ưm
ru
68
bb
bt
79
7t
xt
tlư
h
wp
1r
b4
25
rb
ep
hk
q8
hi
w
m
r pd
m
t5
2w
i6q
h
ws
qư
r1
w8
in
ưp
bd
lm
1ư
ba
tv
k8
9c
n0
hz
ye
6j
ju
wj
26
•
ft
hl
hs
4e
28
sư
r2
p3
ga
gu
ec
6g
dz
k2
fv
qy
4w
88
2m
k7
1q
qk
8a
3 ce
fcc
tn
wo
nz
d7
rjd
n
qb
zx
u
l80
gư
t5
hr
7e
7ư
66
nb
ưy
7t
0e
2c
55
ox
49
m
gp
q
us
90
we
dc
in
oy
n
jz0
oj
75
q9
su
eư
6e
ga
bj
nư
ew
4u
q0
m
ajg
wo
2 sư
m
r7
•
Found by squaring r
•
•
Known as coefficient of
determination
•
ưl
ng
90
8 bm
m
bv
.2 or -.2 = .04 r2
.3 or -.3 = .09 r2
.4 or -.4 = .16 r2
.5 or -.5 = .25 r2
.6 or -.6 = .36 r2
.7 or -.7 = .49 r2
.8 or -.8 = .64 r2
.9 or -.9 = .81 r2
•
– represents the
percentage of variance
two variables have in
common
r2
hd
fk
lep
q
t vi1
ưy
z qs
it1
8g
l1
bp
pe
1f
bb
n
l0i
l5
x q8
rt1
j5
k 6h
af
m
is
yp
0n
e7
f3
u8
st
ay
sv
no
6y
ưy
gt
8p
l3
ye
oi
a5
8f
0r
jyf
g
rp
3q
rz
qc
l2
6 wx
0jy
1e
nư
i0
x8
z3
39
kv
81
8v
q9
7g
iq
n0
w9
4o
hl
9o
ew
tx
e0
c5
5 16
ijo
cg
56
8w
u2
eg
c9
10
xr
jo
8g
Copyright © 2015 McGraw-Hill
Education. All rights reserved. No
reproduction or distribution without
the prior written consent of
McGraw-Hill Education.
m
2jư
ư
l6g
uw
cb
sg
q8
91
6 4f
ioy
cg
xz
6 7r
pe
4jj
ư
18
4m
g5
z7
nd
u2
an
62
5k
w4
an
zq
ou
cy
sf
14
nz
o4
ly
f 37
icg
48
p7
34
lư
2y
5b
cr
y8
rv
4q
3d
oa
x1
hq
k 1x
m
7b
b
fj ti6
w4
gt
tz
rn
vs
ap
n9
42
em
k1
tz
9ư
os
hm
s2
ưf
98
0v
n4
02
rs
pr
6t
r qn
i8i
24
db
n
zfk
de
i ư2
m
ưm
qw
f ư0
fc1
7p
n0
us
r rx
civ
CORRELATION MATRIX
09
zh
dg
rx
82
6f
d6
r5
3e
ve
su
64
ia
1u
xv
nl
yy
ưy
m
i4a
t0
tu
m
jau
ej
k4
e1
cq
bs
oq
0l
ư2
jr
iu
ư5
8z
9z
o7
yn
2p
1w
se
cq
73
49
hz
sz
e9
ki
q0
z7
wj
4o
o3
6d
t4
ki
v yz
m
n1
zs
pm
lc2
m
6x
nk
yv
0n
ex
0x
jq
3 sư
t ls6
isư
pi
y6
i1
y3
ts
db
ow
9c
in
0t
5y
j2
4h
e2
d8
t ym
ol0
v2
to
yj
b4
ox
6 pn
5 klư
vf3
yz
ư7
2u
xc
oy
0q
d
ki8
hs
qi
by
n2
hi
p4
ưh
qa
z 9y
e fcg
0jm
91
ra
02
tn
z8
1w
yi
d9
oe
re
rv
ss
c4
ưj
wd
a4
e rb
il tsư
w3
z7
u5
2j
pc
x7
8 zr
jkl
tz
65
pm
pl
0w
4o
un
ua
9k
d1
yy
3d
9d
db
oc
yn
g5
hn
p9
8d
by
2d
j1
zv
8b
7d
ư0
ul
7j
bn
w
0i7
lq
cr
14
67
vk
a2
62
85
gm
83
q
4r
fm
9j3
cp
1w
pd
31
yo
z6
et
3c
m
tvy
ft
hl
1o
pu
dn
dw
rq
ư5
ưm
ru
68
bb
bt
79
7t
xt
tlư
h
wp
1r
b4
25
rb
ep
hk
q8
hi
w
m
r pd
m
t5
2w
i6q
h
ws
qư
r1
w8
in
ưp
bd
lm
1ư
ba
tv
k8
9c
n0
hz
ye
6j
ju
wj
26
hs
4e
28
sư
r2
p3
ga
gu
ec
6g
dz
k2
fv
qy
4w
88
2m
k7
1q
qk
8a
3 ce
fcc
tn
wo
nz
d7
rjd
n
qb
zx
u
l80
gư
t5
hr
7e
7ư
66
nb
ưy
7t
0e
2c
55
ox
49
m
gp
q
us
90
we
dc
in
oy
n
jz0
oj
75
q9
su
eư
6e
ga
bj
nư
ew
4u
q0
m
ajg
wo
2 sư
m
r7
ưl
ng
90
8 bm
m
bv
hd
fk
lep
q
t vi1
ưy
z qs
it1
8g
l1
bp
pe
1f
bb
n
l0i
l5
x q8
rt1
j5
k 6h
af
m
is
yp
0n
e7
f3
u8
st
ay
sv
no
6y
ưy
gt
8p
l3
ye
oi
a5
8f
0r
jyf
g
rp
3q
rz
qc
l2
6 wx
0jy
1e
nư
i0
x8
z3
39
kv
81
8v
q9
7g
iq
n0
w9
4o
hl
9o
ew
tx
e0
c5
5 16
ijo
cg
56
8w
u2
eg
c9
10
xr
jo
8g
Copyright © 2015 McGraw-Hill
Education. All rights reserved. No
reproduction or distribution without
the prior written consent of
McGraw-Hill Education.
m
2jư
ư
l6g
uw
cb
sg
q8
91
6 4f
ioy
cg
xz
6 7r
pe
4jj
ư
18
4m
g5
z7
nd
u2
an
62
5k
w4
an
zq
ou
cy
sf
14
nz
o4
ly
f 37
icg
48
p7
34
lư
2y
5b
cr
y8
rv
4q
3d
oa
x1
hq
k 1x
m
7b
b
fj ti6
w4
gt
tz
rn
vs
ap
n9
42
em
k1
tz
9ư
os
hm
s2
ưf
98
0v
n4
02
rs
pr
6t
r qn
i8i
24
db
n
zfk
de
i ư2
m
ưm
qw
f ư0
fc1
7p
n0
us
r rx
civ
LIMITS OF CORRELATION
09
zh
dg
rx
82
6f
d6
r5
3e
ve
su
64
ia
1u
xv
nl
yy
ưy
m
i4a
t0
tu
m
jau
ej
k4
e1
cq
bs
oq
0l
ư2
jr
iu
ư5
8z
9z
o7
yn
2p
1w
se
cq
73
49
hz
sz
e9
ki
q0
z7
wj
4o
o3
6d
t4
ki
v yz
m
n1
zs
pm
lc2
m
6x
nk
yv
0n
ex
0x
jq
3 sư
t ls6
isư
pi
y6
i1
y3
ts
db
ow
9c
in
0t
5y
j2
4h
e2
d8
t ym
ol0
v2
to
yj
b4
ox
6 pn
5 klư
vf3
yz
ư7
2u
xc
oy
0q
d
ki8
hs
qi
by
n2
hi
p4
ưh
qa
z 9y
e fcg
0jm
91
ra
02
tn
z8
1w
yi
d9
oe
re
rv
ss
c4
ưj
wd
a4
e rb
il tsư
w3
z7
u5
2j
pc
x7
8 zr
jkl
tz
65
pm
pl
0w
4o
un
ua
9k
d1
yy
3d
9d
db
oc
yn
g5
hn
p9
8d
by
2d
j1
zv
8b
7d
ư0
ul
7j
bn
w
0i7
lq
cr
14
67
vk
a2
62
85
gm
83
q
4r
fm
9j3
cp
1w
pd
31
yo
z6
et
3c
m
tvy
ft
hl
1o
pu
dn
Examines relationship between only 2 variables
Any relationship is presumed to be linear
Limited in the degree to which inferences can
be made
dw
rq
ư5
ưm
ru
68
bb
bt
79
7t
xt
tlư
h
wp
1r
b4
25
rb
ep
hk
q8
hi
w
m
r pd
m
t5
2w
i6q
h
ws
qư
r1
w8
in
ưp
bd
lm
1ư
ba
tv
k8
9c
n0
hz
ye
6j
ju
wj
26
hs
4e
28
sư
r2
p3
ga
gu
ec
6g
dz
k2
fv
qy
4w
88
2m
k7
1q
qk
8a
3 ce
fcc
tn
wo
nz
d7
rjd
n
qb
zx
u
l80
gư
t5
hr
7e
7ư
66
depends on the logic of relationship
Causation
does not necessarily equal causation
Correlation
nb
ưy
7t
0e
2c
55
ox
49
m
gp
q
us
90
we
dc
in
oy
n
jz0
oj
75
q9
su
eư
6e
ga
bj
nư
ew
4u
q0
m
ajg
wo
2 sư
m
r7
ưl
ng
90
8 bm
m
bv
hd
fk
lep
q
t vi1
ưy
z qs
it1
8g
l1
bp
pe
1f
bb
n
l0i
l5
x q8
rt1
j5
k 6h
af
m
is
yp
0n
e7
f3
u8
st
ay
sv
no
6y
ưy
gt
8p
l3
ye
oi
a5
8f
0r
jyf
g
rp
3q
rz
qc
l2
6 wx
0jy
1e
nư
i0
x8
z3
39
kv
81
8v
q9
7g
iq
n0
w9
4o
hl
9o
ew
tx
e0
c5
5 16
ijo
cg
56
8w
u2
eg
c9
10
xr
jo
8g
Copyright © 2015 McGraw-Hill
Education. All rights reserved. No
reproduction or distribution without
the prior written consent of
McGraw-Hill Education.
m
2jư
ư
l6g
uw
cb
sg
q8
91
6 4f
ioy
cg
xz
6 7r
pe
4jj
ư
18
4m
g5
z7
nd
u2
an
62
5k
w4
an
zq
ou
cy
sf
14
nz
o4
ly
f 37
icg
48
p7
34
lư
2y
5b
cr
y8
rv
4q
3d
oa
x1
hq
k 1x
m
7b
b
fj ti6
w4
gt
tz
rn
vs
ap
n9
42
em
k1
tz
9ư
os
hm
s2
ưf
98
0v
n4
02
rs
pr
6t
r qn
i8i
24
db
n
zfk
de
i ư2
m
ưm
qw
f ư0
fc1
7p
n0
us
r rx
civ
REGRESSION
09
zh
dg
rx
82
6f
d6
r5
3e
ve
su
64
ia
1u
xv
nl
yy
ưy
m
i4a
t0
tu
m
jau
ej
k4
e1
cq
bs
oq
0l
ư2
jr
iu
ư5
8z
9z
o7
yn
2p
1w
se
cq
73
49
hz
sz
e9
ki
q0
z7
wj
4o
o3
6d
t4
ki
v yz
m
n1
zs
pm
lc2
m
6x
nk
yv
0n
ex
0x
jq
3 sư
t ls6
isư
pi
y6
i1
y3
ts
db
ow
9c
in
0t
5y
j2
4h
e2
d8
t ym
ol0
v2
to
yj
b4
ox
6 pn
5 klư
vf3
yz
ư7
2u
xc
oy
0q
d
ki8
hs
qi
by
n2
hi
p4
ưh
qa
z 9y
e fcg
0jm
91
ra
02
tn
z8
1w
yi
d9
oe
re
rv
ss
c4
ưj
wd
a4
e rb
il tsư
w3
z7
u5
2j
pc
x7
8 zr
jkl
tz
65
pm
pl
0w
4o
un
ua
9k
d1
yy
3d
9d
db
oc
yn
g5
hn
p9
8d
by
2d
j1
zv
8b
7d
ư0
ul
7j
bn
w
0i7
lq
cr
14
67
vk
a2
62
85
gm
83
q
4r
fm
9j3
cp
1w
pd
31
yo
z6
et
3c
tvy
ft
hl
1o
pu
dn
dw
rq
ư5
ưm
ru
68
bb
bt
79
7t
xt
tlư
h
wp
1r
b4
25
rb
ep
hk
q8
hi
w
m
r pd
m
t5
2w
i6q
h
ws
qư
r1
w8
in
ưp
bd
lm
1ư
ba
tv
k8
9c
n0
hz
ye
6j
ju
wj
26
hs
4e
28
sư
r2
p3
ga
gu
ec
6g
dz
k2
fv
qy
4w
88
2m
k7
1q
qk
8a
3 ce
fcc
tn
wo
nz
d7
rjd
n
qb
zx
u
l80
gư
t5
hr
7e
7ư
66
nb
ưy
the % of variance in the criterion variable accounted for by
the predictor variable
m
Predicts some variables by knowing others
Assesses influence of several continuous level
predictor, or IVs, on a single continuous criterion, or DV
Used to examine causation without experimentation
“Variance accounted for”
7t
0e
2c
55
ox
49
m
gp
q
us
90
we
dc
in
oy
n
jz0
oj
75
q9
su
eư
6e
ga
bj
nư
ew
4u
q0
m
ajg
wo
2 sư
m
r7
ưl
ng
90
8 bm
m
bv
hd
fk
lep
q
t vi1
ưy
z qs
it1
8g
l1
bp
pe
1f
bb
n
l0i
l5
x q8
rt1
j5
k 6h
af
m
is
yp
0n
e7
f3
u8
st
ay
sv
no
6y
ưy
gt
8p
l3
ye
oi
a5
8f
0r
jyf
g
rp
3q
rz
qc
l2
6 wx
0jy
1e
nư
i0
x8
z3
39
kv
81
8v
q9
7g
iq
n0
w9
4o
hl
9o
ew
tx
e0
c5
5 16
ijo
cg
56
8w
u2
eg
c9
10
xr
jo
8g
Copyright © 2015 McGraw-Hill
Education. All rights reserved. No
reproduction or distribution without
the prior written consent of
McGraw-Hill Education.
m
2jư
ư
l6g
uw
cb
sg
q8
91
6 4f
ioy
cg
xz
6 7r
pe
4jj
ư
18
4m
g5
z7
nd
u2
an
62
5k
w4
an
zq
ou
cy
sf
14
nz
o4
ly
f 37
icg
48
p7
34
lư
2y
5b
cr
y8
rv
4q
3d
oa
x1
hq
k 1x
m
7b
b
fj ti6
w4
gt
tz
rn
vs
ap
n9
42
em
k1
tz
9ư
os
hm
s2
ưf
98
0v
n4
02
rs
pr
6t
r qn
i8i
24
db
n
zfk
de
i ư2
m
ưm
qw
f ư0
fc1
7p
n0
us
r rx
civ
LINEAR REGRESSION
09
zh
dg
rx
82
6f
d6
r5
3e
ve
su
64
ia
1u
xv
nl
yy
ưy
m
i4a
t0
tu
m
jau
ej
k4
e1
cq
bs
oq
0l
ư2
jr
iu
ư5
8z
9z
o7
yn
2p
1w
se
cq
73
49
hz
sz
e9
ki
q0
z7
wj
4o
o3
6d
t4
ki
v yz
m
n1
zs
pm
lc2
m
6x
nk
yv
0n
ex
0x
jq
3 sư
t ls6
isư
pi
y6
i1
y3
ts
db
ow
9c
in
0t
5y
j2
4h
e2
d8
t ym
ol0
v2
to
yj
b4
ox
6 pn
5 klư
vf3
yz
ư7
2u
xc
oy
0q
d
ki8
hs
qi
by
n2
hi
p4
ưh
qa
z 9y
e fcg
0jm
91
ra
02
tn
z8
1w
yi
d9
oe
re
rv
ss
c4
ưj
wd
a4
e rb
il tsư
w3
z7
u5
2j
pc
x7
8 zr
jkl
tz
65
pm
pl
0w
4o
un
ua
9k
d1
yy
3d
9d
db
oc
yn
g5
hn
p9
8d
by
2d
j1
zv
8b
ư0
ul
7j
bn
w
0i7
lq
cr
14
67
vk
a2
62
85
gm
83
q
4r
fm
9j3
cp
1w
pd
31
yo
z6
et
3c
m
tvy
better the fit of the line, the higher R
The
7d
ft
hl
1o
pu
dn
dw
rq
ư5
ưm
ru
68
bb
bt
79
7t
xt
tlư
h
wp
1r
b4
25
rb
ep
hk
q8
hi
w
m
r pd
m
t5
2w
i6q
h
ws
qư
r1
w8
in
ưp
bd
lm
1ư
ba
tv
k8
9c
n0
hz
ye
6j
ju
wj
26
hs
4e
28
sư
r2
p3
ga
gu
ec
6g
dz
k2
fv
qy
4w
88
2m
k7
1q
qk
8a
3 ce
fcc
tn
wo
nz
d7
rjd
n
qb
zx
u
l80
gư
t5
hr
7e
7ư
66
nb
ưy
7t
0e
2c
55
Adjusted R2– the proportion of variance
explained or accounted for on the DV by the IV
Regression line – line drawn through the data
points that best summarizes the relationship
between the IV and DV
ox
49
m
gp
q
us
90
we
dc
in
oy
n
jz0
oj
75
q9
su
eư
6e
ga
bj
nư
ew
4u
q0
m
ajg
wo
2 sư
m
r7
ưl
ng
90
8 bm
m
bv
hd
fk
lep
q
t vi1
ưy
z qs
it1
8g
l1
bp
pe
1f
bb
n
l0i
l5
x q8
rt1
j5
k 6h
af
m
is
yp
0n
e7
f3
u8
st
ay
sv
no
6y
ưy
gt
8p
l3
ye
oi
a5
8f
0r
jyf
g
rp
3q
rz
qc
l2
6 wx
0jy
1e
nư
i0
x8
z3
39
kv
81
8v
q9
7g
iq
n0
w9
4o
hl
9o
ew
tx
e0
c5
5 16
ijo
cg
56
8w
u2
eg
c9
10
xr
jo
8g
Copyright © 2015 McGraw-Hill
Education. All rights reserved. No
reproduction or distribution without
the prior written consent of
McGraw-Hill Education.
m
2jư
ư
l6g
uw
cb
sg
q8
91
6 4f
ioy
cg
xz
6 7r
pe
4jj
ư
18
4m
g5
z7
nd
u2
an
62
5k
w4
an
zq
ou
cy
sf
14
nz
o4
ly
f 37
icg
48
p7
34
lư
2y
5b
cr
y8
rv
4q
3d
oa
x1
hq
k 1x
m
7b
b
fj ti6
w4
gt
tz
rn
vs
ap
n9
42
em
k1
tz
9ư
os
hm
s2
ưf
98
0v
n4
02
rs
pr
6t
r qn
i8i
24
db
n
zfk
de
i ư2
m
ưm
qw
f ư0
fc1
7p
n0
us
r rx
civ
BETA WEIGHTS
09
zh
dg
rx
82
6f
d6
r5
3e
ve
su
64
ia
1u
xv
nl
yy
ưy
m
i4a
t0
tu
m
jau
ej
k4
e1
cq
bs
oq
0l
ư2
jr
iu
ư5
8z
9z
o7
yn
2p
1w
se
cq
73
49
hz
sz
e9
ki
q0
z7
wj
4o
o3
6d
t4
ki
v yz
m
n1
zs
pm
lc2
m
6x
nk
yv
0n
ex
0x
jq
3 sư
t ls6
isư
pi
y6
i1
y3
ts
db
ow
9c
in
0t
5y
j2
4h
e2
d8
t ym
ol0
v2
to
yj
b4
ox
6 pn
5 klư
vf3
yz
ư7
2u
xc
oy
0q
d
ki8
hs
qi
by
n2
hi
p4
ưh
qa
z 9y
e fcg
0jm
91
ra
02
tn
z8
1w
yi
d9
oe
re
rv
ss
c4
ưj
wd
a4
e rb
il tsư
w3
z7
u5
2j
pc
x7
8 zr
jkl
tz
65
pm
pl
0w
4o
un
ua
9k
d1
yy
3d
9d
db
oc
yn
g5
hn
p9
8d
by
2d
j1
zv
8b
7d
ư0
ul
7j
bn
w
0i7
lq
cr
14
67
vk
a2
62
85
gm
83
q
4r
fm
9j3
cp
1w
pd
31
yo
z6
et
3c
m
tvy
ft
hl
1o
pu
dn
dw
rq
ư5
ưm
ru
68
bb
bt
79
7t
xt
tlư
h
wp
1r
b4
25
rb
ep
hk
q8
hi
w
m
r pd
m
t5
2w
i6q
h
ws
qư
r1
w8
in
ưp
bd
lm
1ư
ba
tv
k8
9c
n0
hz
ye
6j
ju
wj
26
hs
4e
Also known as beta coefficients
Represented by β
Allows comparison among variables of different
measuring units
Range from +1.00 to –1.00
28
sư
r2
p3
ga
gu
ec
6g
dz
k2
fv
qy
4w
88
2m
k7
1q
qk
8a
3 ce
fcc
tn
wo
nz
d7
rjd
n
qb
zx
u
l80
gư
t5
hr
7e
7ư
66
nb
ưy
7t
0e
2c
55
ox
49
m
gp
q
us
90
we
dc
in
oy
n
jz0
oj
75
q9
su
eư
6e
ga
bj
nư
ew
4u
q0
m
ajg
wo
2 sư
m
r7
ưl
ng
90
8 bm
m
bv
hd
fk
lep
q
t vi1
ưy
z qs
it1
8g
l1
bp
pe
1f
bb
n
l0i
l5
x q8
rt1
j5
k 6h
af
m
is
yp
0n
e7
f3
u8
st
ay
sv
no
6y
ưy
gt
8p
l3
ye
oi
a5
8f
0r
jyf
g
rp
3q
rz
qc
l2
6 wx
0jy
1e
nư
i0
x8
z3
39
kv
81
8v
q9
7g
iq
n0
w9
4o
hl
9o
ew
tx
e0
c5
5 16
ijo
cg
56
8w
u2
eg
c9
10
xr
jo
8g
Copyright © 2015 McGraw-Hill
Education. All rights reserved. No
reproduction or distribution without
the prior written consent of
McGraw-Hill Education.
m
2jư
ư
l6g
uw
cb
sg
q8
91
6 4f
ioy
cg
xz
6 7r
pe
4jj
ư
18
4m
g5
z7
nd
u2
an
62
5k
w4
an
zq
ou
cy
sf
14
nz
o4
ly
f 37
icg
48
p7
34
lư
2y
5b
cr
y8
rv
4q
3d
oa
x1
hq
k 1x
m
7b
b
fj ti6
w4
gt
tz
rn
vs
ap
n9
42
em
k1
tz
9ư
os
hm
s2
ưf
98
0v
n4
02
rs
pr
6t
r qn
i8i
24
db
n
zfk
de
i ư2
m
ưm
qw
f ư0
fc1
7p
n0
us
r rx
civ
MULTIPLE REGRESSION
09
zh
dg
rx
82
6f
d6
r5
3e
ve
su
64
ia
1u
xv
nl
yy
ưy
m
i4a
t0
tu
m
jau
ej
k4
e1
cq
bs
oq
0l
ư2
jr
iu
ư5
8z
9z
o7
yn
2p
1w
se
cq
73
49
hz
sz
e9
ki
q0
z7
wj
4o
o3
6d
t4
ki
v yz
m
n1
zs
pm
lc2
m
6x
nk
yv
0n
ex
0x
jq
3 sư
t ls6
isư
pi
y6
i1
y3
ts
db
ow
9c
in
0t
5y
j2
4h
e2
d8
t ym
ol0
v2
to
yj
b4
ox
6 pn
5 klư
vf3
yz
ư7
2u
xc
oy
0q
d
ki8
hs
qi
by
n2
hi
p4
ưh
qa
z 9y
e fcg
0jm
91
tn
1w
yi
d9
oe
re
rv
ss
c4
ưj
wd
a4
e rb
il tsư
w3
z7
u5
2j
pc
x7
8 zr
jkl
tz
65
pm
pl
0w
4o
un
ua
9k
d1
yy
3d
9d
db
oc
yn
g5
hn
p9
8d
by
2d
j1
zv
8b
7d
ư0
ul
7j
bn
w
0i7
lq
cr
14
67
vk
a2
62
85
gm
83
q
4r
fm
9j3
cp
1w
pd
31
yo
z6
a group
As
z8
Independently
ra
02
et
3c
m
tvy
ft
hl
1o
pu
dn
dw
rq
ư5
ưm
ru
68
bb
bt
79
7t
xt
tlư
h
wp
1r
b4
25
rb
ep
hk
q8
hi
w
m
r pd
m
t5
2w
i6q
h
ws
qư
r1
w8
in
ưp
bd
lm
1ư
ba
tv
k8
9c
n0
hz
ye
6j
ju
wj
26
hs
4e
28
sư
r2
p3
ga
gu
ec
6g
dz
k2
fv
qy
4w
88
2m
k7
1q
qk
8a
3 ce
fcc
tn
wo
nz
d7
Use beta weights to interpret the relative
contribution of each IV
Tests for significant relationship between one
DV and multiple IVs
rjd
n
qb
zx
u
l80
gư
t5
hr
7e
7ư
66
nb
ưy
7t
0e
2c
55
ox
49
m
gp
q
us
90
we
dc
in
oy
n
jz0
oj
75
q9
su
eư
6e
ga
bj
nư
ew
4u
q0
m
ajg
wo
2 sư
m
r7
ưl
ng
90
8 bm
m
bv
hd
fk
lep
q
t vi1
ưy
z qs
it1
8g
l1
bp
pe
1f
bb
n
l0i
l5
x q8
rt1
j5
k 6h
af
m
is
yp
0n
e7
f3
u8
st
ay
sv
no
6y
ưy
gt
8p
l3
ye
oi
a5
8f
0r
jyf
g
rp
3q
rz
qc
l2
6 wx
0jy
1e
nư
i0
x8
z3
39
kv
81
8v
q9
7g
iq
n0
w9
4o
hl
9o
ew
tx
e0
c5
5 16
ijo
cg
56
8w
u2
eg
c9
10
xr
jo
8g
Copyright © 2015 McGraw-Hill
Education. All rights reserved. No
reproduction or distribution without
the prior written consent of
McGraw-Hill Education.
m
2jư
ư
l6g
uw
cb
sg
q8
91
6 4f
ioy
cg
xz
6 7r
pe
4jj
ư
18
4m
g5
z7
nd
u2
an
62
5k
w4
an
zq
ou
cy
sf
14
nz
o4
ly
f 37
icg
48
p7
34
lư
2y
5b
cr
y8
rv
4q
3d
oa
x1
hq
k 1x
m
7b
b
fj ti6
w4
gt
tz
rn
vs
ap
n9
42
em
k1
tz
9ư
os
hm
s2
ưf
98
0v
n4
02
rs
pr
6t
r qn
i8i
24
db
n
zfk
de
i ư2
m
ưm
qw
f ư0
fc1
7p
n0
us
r rx
civ
STRUCTURAL EQUATION MODELING
09
zh
dg
rx
82
6f
d6
r5
3e
ve
su
64
ia
1u
xv
nl
yy
ưy
m
i4a
t0
tu
m
jau
ej
k4
e1
cq
bs
oq
0l
ư2
ư5
8z
9z
o7
yn
2p
1w
se
cq
73
49
hz
sz
e9
ki
q0
z7
wj
4o
o3
6d
t4
ki
v yz
m
n1
zs
pm
lc2
m
6x
nk
yv
0n
ex
0x
ts
db
ow
9c
in
0t
5y
j2
4h
e2
d8
t ym
ol0
v2
to
yj
b4
ox
6 pn
5 klư
vf3
yz
ư7
2u
xc
oy
0q
d
ki8
hs
qi
by
n2
hi
p4
ưh
qa
z 9y
e fcg
0jm
91
ra
02
tn
z8
1w
yi
d9
oe
re
rv
ss
c4
ưj
wd
a4
e rb
il tsư
w3
z7
u5
2j
pc
x7
8 zr
jkl
tz
65
pm
pl
0w
4o
un
ua
9k
d1
yy
3d
9d
db
oc
yn
g5
hn
p9
8d
by
2d
j1
zv
8b
7d
ư0
ul
7j
bn
w
0i7
lq
cr
14
67
vk
a2
62
85
gm
83
q
4r
fm
9j3
cp
1w
pd
31
yo
z6
et
3c
m
tvy
ft
hl
1o
pu
dn
dw
rq
ư5
ưm
ru
68
bb
bt
79
7t
xt
tlư
h
wp
1r
b4
25
rb
ep
hk
q8
hi
w
m
r pd
m
t5
2w
i6q
h
ws
qư
r1
w8
in
ưp
bd
lm
by another variable in the model
Caused
i1
cause by another variable in the model
Not
y3
1ư
ba
tv
k8
9c
n0
hz
ye
6j
ju
wj
26
hs
4e
28
sư
r2
p3
ga
gu
ec
6g
dz
k2
fv
qy
4w
88
2m
k7
1q
qk
8a
3 ce
fcc
tn
wo
nz
d7
rjd
n
qb
zx
u
l80
gư
t5
hr
7e
7ư
66
nb
ưy
7t
0e
2c
55
ox
49
m
gp
q
us
90
we
dc
in
oy
n
jz0
oj
75
q9
su
eư
6e
ga
bj
nư
ew
4u
q0
m
ajg
wo
2 sư
m
r7
ưl
ng
90
8 bm
m
bv
hd
fk
lep
q
t vi1
ưy
z qs
it1
8g
l1
bp
pe
1f
bb
n
l0i
Is the theoretical model different from associations found in
the data?
Endogenous variable
Exogenous variable
pi
Multiple variables
y6
jq
Also known as SEM
3 sư
t ls6
isư
Tests for a theoretical or hypothesized associations
jr
iu
l5
x q8
rt1
j5
k 6h
af
m
is
yp
0n
e7
f3
u8
st
ay
sv
no
6y
ưy
gt
8p
l3
ye
oi
a5
8f
0r
jyf
g
rp
3q
rz
qc
l2
6 wx
0jy
1e
nư
i0
x8
z3
39
kv
81
8v
q9
7g
iq
n0
w9
4o
hl
9o
ew
tx
e0
c5
5 16
ijo
cg
56
8w
u2
eg
c9
10
xr
jo
8g
Copyright © 2015 McGraw-Hill
Education. All rights reserved. No
reproduction or distribution without
the prior written consent of
McGraw-Hill Education.
m
2jư
ư
l6g
uw
cb
sg
q8
91
6 4f
ioy
cg
xz
6 7r
pe
4jj
ư
18
4m
g5
z7
nd
u2
an
62
5k
w4
an
zq
ou
cy
sf
14
nz
o4
ly
f 37
icg
48
p7
34
lư
2y
5b
cr
y8
rv
4q
3d
oa
x1
hq
k 1x
m
7b
b
fj ti6
w4
gt
tz
rn
vs
ap
n9
42
em
k1
tz
9ư
os
hm
s2
ưf
98
0v
n4
02
rs
pr
6t
r qn
i8i
24
db
n
zfk
de
i ư2
m
ưm
IDENTIFYING APPROPRIATE
STATISTICAL TEST OF RELATIONSHIP
qw
f ư0
fc1
7p
n0
us
r rx
civ
09
zh
dg
rx
82
6f
d6
r5
3e
ve
su
64
ia
1u
xv
nl
yy
ưy
m
i4a
t0
tu
m
jau
ej
k4
e1
cq
bs
oq
0l
ư2
jr
iu
ư5
8z
9z
o7
yn
2p
1w
se
cq
73
49
hz
sz
e9
ki
q0
z7
wj
4o
o3
6d
t4
ki
v yz
m
n1
zs
pm
lc2
m
6x
nk
yv
0n
ex
0x
jq
3 sư
t ls6
isư
pi
y6
i1
y3
ts
db
ow
9c
in
0t
5y
j2
4h
e2
d8
t ym
ol0
v2
to
yj
b4
ox
6 pn
5 klư
vf3
yz
ư7
2u
xc
oy
0q
d
ki8
hs
qi
by
n2
hi
p4
ưh
qa
z 9y
e fcg
0jm
91
ra
02
tn
z8
1w
yi
d9
oe
re
rv
ss
c4
ưj
wd
a4
e rb
il tsư
w3
z7
u5
2j
pc
x7
8 zr
jkl
tz
65
pm
pl
0w
4o
un
ua
9k
d1
yy
3d
9d
db
oc
yn
g5
hn
p9
8d
by
2d
j1
zv
8b
7d
ư0
ul
7j
bn
w
0i7
lq
cr
14
67
vk
a2
62
85
gm
83
q
4r
fm
9j3
cp
1w
pd
31
yo
z6
et
3c
m
tvy
ft
hl
1o
pu
dn
dw
rq
ư5
ưm
ru
68
bb
bt
79
7t
xt
tlư
h
wp
1r
b4
25
rb
ep
hk
q8
hi
w
m
r pd
m
t5
2w
i6q
h
ws
qư
r1
w8
in
ưp
bd
lm
1ư
ba
tv
k8
9c
n0
hz
ye
6j
ju
wj
26
hs
4e
28
sư
r2
p3
ga
gu
ec
6g
dz
k2
fv
qy
4w
88
2m
k7
1q
qk
8a
3 ce
fcc
tn
wo
nz
d7
rjd
n
qb
zx
u
l80
gư
t5
hr
7e
7ư
66
nb
ưy
7t
0e
2c
55
ox
49
m
gp
q
us
90
we
dc
in
oy
n
jz0
oj
75
q9
su
eư
6e
ga
bj
nư
ew
4u
q0
m
ajg
wo
2 sư
m
r7
ưl
ng
90
8 bm
m
bv
hd
fk
lep
q
t vi1
ưy
z qs
it1
8g
l1
bp
pe
1f
bb
n
l0i
l5
x q8
rt1
j5
k 6h
af
m
is
yp
0n
e7
f3
u8
st
ay
sv
no
6y
ưy
gt
8p
l3
ye
oi
a5
8f
0r
jyf
g
rp
3q
rz
qc
l2
6 wx
0jy
1e
nư
i0
x8
z3
39
kv
81
8v
q9
7g
iq
n0
w9
4o
hl
9o
ew
tx
e0
c5
5 16
ijo
cg
56
8w
u2
eg
c9
10
xr
jo
8g
Copyright © 2015 McGraw-Hill
Education. All rights reserved. No
reproduction or distribution without
the prior written consent of
McGraw-Hill Education.
m
2jư
ư
l6g
uw
cb
sg
q8
91
6 4f
ioy
cg
xz
6 7r
pe
4jj
ư
18
4m
g5
z7
nd
u2
an
62
5k
w4
an
zq
ou
cy
sf
14
nz
o4
ly
f 37
icg
48
p7
34
lư
2y
5b
cr
y8
rv
4q
3d
oa
x1
hq
k 1x
m
7b
b
fj ti6
w4
gt
tz
rn
vs
ap
n9
42
em
k1
tz
9ư
os
hm
s2
ưf
98
0v
n4
02
rs
pr
6t
r qn
i8i
24
db
n
zfk
de
i ư2
m
ưm
qw
f ư0
fc1
7p
n0
us
r rx
civ
CAUTION IN USING STATISTICS
09
zh
dg
rx
82
6f
d6
r5
3e
ve
su
64
ia
1u
xv
nl
yy
ưy
m
i4a
t0
tu
m
jau
ej
k4
e1
cq
bs
oq
0l
ư2
jr
iu
ư5
8z
9z
o7
yn
2p
1w
se
cq
73
49
hz
sz
e9
ki
q0
z7
wj
4o
o3
6d
t4
ki
v yz
m
n1
zs
pm
Use and interpretation of statistical tests is subjective
lc2
m
6x
nk
yv
0n
ex
0x
jq
3 sư
t ls6
isư
pi
y6
i1
y3
ts
db
ow
9c
in
0t
5y
j2
4h
e2
d8
t ym
ol0
v2
to
yj
b4
ox
6 pn
5 klư
vf3
yz
ư7
2u
xc
oy
0q
d
ki8
hs
qi
by
n2
hi
p4
ưh
qa
z 9y
e fcg
0jm
91
ra
02
tn
z8
1w
yi
d9
oe
re
rv
ss
c4
ưj
wd
a4
e rb
il tsư
w3
Many variations of each test
Researcher must interpret statistical result
z7
u5
2j
pc
x7
8 zr
jkl
tz
65
pm
pl
0w
4o
un
ua
9k
d1
yy
3d
9d
db
oc
yn
g5
hn
p9
8d
by
2d
j1
zv
8b
7d
ư0
ul
7j
bn
w
0i7
lq
cr
14
67
vk
a2
62
85
gm
83
q
4r
fm
9j3
cp
1w
pd
31
yo
z6
et
3c
m
tvy
ft
hl
1o
pu
dn
dw
rq
ư5
ưm
ru
68
bb
bt
79
7t
xt
tlư
h
wp
1r
b4
25
rb
ep
hk
q8
hi
w
m
r pd
m
t5
2w
i6q
h
ws
qư
r1
w8
in
ưp
bd
lm
1ư
ba
tv
k8
9c
n0
hz
ye
6j
ju
wj
26
hs
4e
28
sư
r2
p3
ga
gu
ec
6g
dz
k2
fv
qy
4w
88
2m
k7
1q
qk
8a
3 ce
fcc
tn
wo
nz
d7
rjd
n
qb
zx
u
l80
gư
t5
hr
7e
7ư
66
nb
ưy
7t
0e
2c
55
ox
49
m
gp
q
us
90
we
dc
in
oy
Are the results worth interpreting statistically?
Was appropriate statistical test selected and used?
Are the results statistically significant?
Are the results socially significant?
n
jz0
oj
75
q9
su
eư
6e
ga
bj
nư
ew
4u
q0
m
ajg
wo
2 sư
m
r7
ưl
ng
90
8 bm
m
bv
hd
fk
lep
q
t vi1
ưy
z qs
it1
8g
l1
bp
pe
1f
bb
n
l0i
l5
x q8
rt1
j5
k 6h
af
m
is
yp
0n
e7
f3
u8
st
ay
sv
no
6y
ưy
gt
8p
l3
ye
oi
a5
8f
0r
jyf
g
rp
3q
rz
qc
l2
6 wx
0jy
1e
nư
i0
x8
z3
39
kv
81
8v
q9
7g
iq
n0
w9
4o
hl
9o
ew
tx
e0
c5
5 16
ijo
cg
56
8w
u2
eg
c9
10
xr
jo
8g
Copyright © 2015 McGraw-Hill
Education. All rights reserved. No
reproduction or distribution without
the prior written consent of
McGraw-Hill Education.
m
2jư
ư
l6g
uw
cb
sg
q8
91
6 4f
ioy
cg
