<s>
Omnibus	B-General_Concept
tests	I-General_Concept
are	O
a	O
kind	O
of	O
statistical	O
test	O
.	O
</s>
<s>
They	O
test	O
whether	O
the	O
explained	O
variance	O
in	O
a	O
set	O
of	O
data	O
is	O
significantly	B-General_Concept
greater	O
than	O
the	O
unexplained	O
variance	O
,	O
overall	O
.	O
</s>
<s>
One	O
example	O
is	O
the	O
F-test	B-General_Concept
in	O
the	O
analysis	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
.	O
</s>
<s>
There	O
can	O
be	O
legitimate	O
significant	O
effects	O
within	O
a	O
model	O
even	O
if	O
the	O
omnibus	B-General_Concept
test	I-General_Concept
is	O
not	O
significant	O
.	O
</s>
<s>
For	O
instance	O
,	O
in	O
a	O
model	O
with	O
two	O
independent	O
variables	O
,	O
if	O
only	O
one	O
variable	O
exerts	O
a	O
significant	O
effect	O
on	O
the	O
dependent	O
variable	O
and	O
the	O
other	O
does	O
not	O
,	O
then	O
the	O
omnibus	B-General_Concept
test	I-General_Concept
may	O
be	O
non-significant	O
.	O
</s>
<s>
In	O
order	O
to	O
test	O
effects	O
within	O
an	O
omnibus	B-General_Concept
test	I-General_Concept
,	O
researchers	O
often	O
use	O
contrasts	O
.	O
</s>
<s>
Omnibus	B-General_Concept
test	I-General_Concept
,	O
as	O
a	O
general	O
name	O
,	O
refers	O
to	O
an	O
overall	O
or	O
a	O
global	O
test	O
.	O
</s>
<s>
Other	O
names	O
include	O
F-test	B-General_Concept
or	O
Chi-squared	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
Hypotheses	O
regarding	O
equality	O
vs.	O
inequality	O
between	O
k	O
expectancies	O
vs.	O
at	O
least	O
one	O
pair	O
,	O
where	O
and	O
,	O
in	O
Analysis	B-General_Concept
Of	I-General_Concept
Variance	I-General_Concept
(	O
ANOVA	B-General_Concept
)	O
;	O
</s>
<s>
or	O
regarding	O
equality	O
between	O
k	O
standard	O
deviations	O
vs.	O
at	O
least	O
one	O
pair	O
in	O
testing	O
equality	O
of	O
variances	O
in	O
ANOVA	B-General_Concept
;	O
</s>
<s>
Omnibus	B-General_Concept
test	I-General_Concept
commonly	O
refers	O
to	O
either	O
one	O
of	O
those	O
statistical	O
tests	O
:	O
</s>
<s>
ANOVA	B-General_Concept
F	B-General_Concept
test	I-General_Concept
to	O
test	O
significance	O
between	O
all	O
factor	O
means	O
and/or	O
between	O
their	O
variances	O
equality	O
in	O
Analysis	B-General_Concept
of	I-General_Concept
Variance	I-General_Concept
procedure	O
;	O
</s>
<s>
The	O
omnibus	O
multivariate	O
F	B-General_Concept
Test	I-General_Concept
in	O
ANOVA	B-General_Concept
with	O
repeated	O
measures	O
;	O
</s>
<s>
F	B-General_Concept
test	I-General_Concept
for	O
equality/inequality	O
of	O
the	O
regression	O
coefficients	O
in	O
multiple	O
regression	O
;	O
</s>
<s>
Chi-Square	B-General_Concept
test	I-General_Concept
for	O
exploring	O
significance	O
differences	O
between	O
blocks	O
of	O
independent	O
explanatory	O
variables	O
or	O
their	O
coefficients	O
in	O
a	O
logistic	O
regression	O
.	O
</s>
<s>
These	O
omnibus	B-General_Concept
tests	I-General_Concept
are	O
usually	O
conducted	O
whenever	O
one	O
tends	O
to	O
test	O
an	O
overall	O
hypothesis	O
on	O
a	O
quadratic	O
statistic	O
(	O
like	O
sum	B-General_Concept
of	I-General_Concept
squares	I-General_Concept
or	O
variance	O
or	O
covariance	O
)	O
or	O
rational	O
quadratic	O
statistic	O
(	O
like	O
the	O
ANOVA	B-General_Concept
overall	O
F	B-General_Concept
test	I-General_Concept
in	O
Analysis	B-General_Concept
of	I-General_Concept
Variance	I-General_Concept
or	O
F	B-General_Concept
Test	I-General_Concept
in	O
Analysis	B-General_Concept
of	I-General_Concept
covariance	I-General_Concept
or	O
the	O
F	B-General_Concept
Test	I-General_Concept
in	O
Linear	O
Regression	O
,	O
or	O
Chi-Square	B-General_Concept
in	O
Logistic	O
Regression	O
)	O
.	O
</s>
<s>
While	O
significance	O
is	O
founded	O
on	O
the	O
omnibus	B-General_Concept
test	I-General_Concept
,	O
it	O
does	O
n't	O
specify	O
exactly	O
where	O
the	O
difference	O
is	O
occurred	O
,	O
meaning	O
,	O
it	O
does	O
n't	O
bring	O
specification	O
on	O
which	O
parameter	O
is	O
significantly	B-General_Concept
different	O
from	O
the	O
other	O
,	O
but	O
it	O
statistically	O
determines	O
that	O
there	O
is	O
a	O
difference	O
,	O
so	O
at	O
least	O
two	O
of	O
the	O
tested	O
parameters	O
are	O
statistically	O
different	O
.	O
</s>
<s>
If	O
significance	O
was	O
met	O
,	O
none	O
of	O
those	O
tests	O
will	O
tell	O
specifically	O
which	O
mean	O
differs	O
from	O
the	O
others	O
(	O
in	O
ANOVA	B-General_Concept
)	O
,	O
which	O
coefficient	O
differs	O
from	O
the	O
others	O
(	O
in	O
regression	O
)	O
etc	O
.	O
</s>
<s>
The	O
F-test	B-General_Concept
in	O
ANOVA	B-General_Concept
is	O
an	O
example	O
of	O
an	O
omnibus	B-General_Concept
test	I-General_Concept
,	O
which	O
tests	O
the	O
overall	O
significance	O
of	O
the	O
model	O
.	O
</s>
<s>
A	O
significant	O
F	B-General_Concept
test	I-General_Concept
means	O
that	O
among	O
the	O
tested	O
means	O
,	O
at	O
least	O
two	O
of	O
the	O
means	O
are	O
significantly	B-General_Concept
different	O
,	O
but	O
this	O
result	O
does	O
n't	O
specify	O
exactly	O
which	O
means	O
are	O
different	O
one	O
from	O
the	O
other	O
.	O
</s>
<s>
Actually	O
,	O
testing	O
means	O
 '	O
differences	O
is	O
done	O
by	O
the	O
quadratic	O
rational	O
F	B-General_Concept
statistic	I-General_Concept
(	O
F	O
=	O
MSB/MSW	O
)	O
.	O
</s>
<s>
In	O
order	O
to	O
determine	O
which	O
mean	O
differs	O
from	O
another	O
mean	O
or	O
which	O
contrast	O
of	O
means	O
are	O
significantly	B-General_Concept
different	O
,	O
Post	O
Hoc	O
tests	O
(	O
Multiple	O
Comparison	O
tests	O
)	O
or	O
planned	O
tests	O
should	O
be	O
conducted	O
after	O
obtaining	O
a	O
significant	O
omnibus	O
F	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
It	O
may	O
be	O
considered	O
to	O
use	O
the	O
simple	O
Bonferroni	B-General_Concept
correction	I-General_Concept
or	O
another	O
suitable	O
correction	O
.	O
</s>
<s>
Another	O
omnibus	B-General_Concept
test	I-General_Concept
we	O
can	O
find	O
in	O
ANOVA	B-General_Concept
is	O
the	O
F	B-General_Concept
test	I-General_Concept
for	O
testing	O
one	O
of	O
the	O
ANOVA	B-General_Concept
assumptions	O
:	O
the	O
equality	O
of	O
variance	O
between	O
groups	O
.	O
</s>
<s>
In	O
One-Way	O
ANOVA	B-General_Concept
,	O
for	O
example	O
,	O
the	O
hypotheses	O
tested	O
by	O
omnibus	O
F	B-General_Concept
test	I-General_Concept
are	O
:	O
</s>
<s>
The	O
F	B-General_Concept
statistics	I-General_Concept
of	O
the	O
omnibus	B-General_Concept
test	I-General_Concept
is	O
:	O
</s>
<s>
The	O
F	B-General_Concept
statistic	I-General_Concept
is	O
distributed	O
F(k-1,n-k )	O
,	O
( α	O
)	O
under	O
assumption	O
of	O
null	O
hypothesis	O
and	O
normality	O
assumption	O
.	O
</s>
<s>
F	B-General_Concept
test	I-General_Concept
is	O
considered	O
robust	O
in	O
some	O
situations	O
,	O
even	O
when	O
the	O
normality	O
assumption	O
is	O
n't	O
met	O
.	O
</s>
<s>
Although	O
the	O
LSD	O
(	O
Fisher	O
's	O
Least	O
Significant	B-General_Concept
Difference	I-General_Concept
)	O
is	O
a	O
very	O
strong	O
test	O
in	O
detecting	O
pairs	O
of	O
means	O
differences	O
,	O
it	O
is	O
applied	O
only	O
when	O
the	O
F	B-General_Concept
test	I-General_Concept
is	O
significant	O
,	O
and	O
it	O
is	O
mostly	O
less	O
preferable	O
since	O
its	O
method	O
fails	O
in	O
protecting	O
low	O
error	O
rate	O
.	O
</s>
<s>
Bonferroni	B-General_Concept
test	I-General_Concept
is	O
a	O
good	O
choice	O
due	O
to	O
its	O
correction	O
suggested	O
by	O
his	O
method	O
.	O
</s>
<s>
On	O
small	O
sample	O
sizes	O
,	O
when	O
the	O
assumption	O
of	O
normality	O
is	O
not	O
met	O
,	O
a	O
nonparametric	O
analysis	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
can	O
be	O
made	O
by	O
the	O
Kruskal-Wallis	O
test	O
.	O
</s>
<s>
An	O
alternative	O
option	O
is	O
to	O
use	O
bootstrap	B-Application
methods	I-Application
to	O
assess	O
whether	O
the	O
group	O
means	O
are	O
different	O
.	O
</s>
<s>
Bootstrap	B-Application
methods	I-Application
do	O
not	O
have	O
any	O
specific	O
distributional	O
assumptions	O
and	O
may	O
be	O
an	O
appropriate	O
tool	O
to	O
use	O
like	O
using	O
re-sampling	O
,	O
which	O
is	O
one	O
of	O
the	O
simplest	O
bootstrap	B-Application
methods	I-Application
.	O
</s>
<s>
A	O
person	O
can	O
extend	O
the	O
idea	O
to	O
the	O
case	O
of	O
multiple	O
groups	O
and	O
estimate	O
p-values	B-General_Concept
.	O
</s>
<s>
Assuming	O
none	O
of	O
the	O
customers	O
called	O
twice	O
and	O
none	O
of	O
them	O
have	O
customer	O
relations	O
among	O
each	O
other	O
,	O
One	O
Way	O
ANOVA	B-General_Concept
was	O
run	O
on	O
SPSS	B-Algorithm
to	O
find	O
significant	B-General_Concept
differences	I-General_Concept
between	O
the	O
days	O
time-wait	O
:	O
</s>
<s>
Source	O
Sum	B-General_Concept
of	I-General_Concept
Squares	I-General_Concept
df	O
Mean	O
Square	O
F	O
Sig	O
.	O
</s>
<s>
The	O
omnibus	O
F	O
ANOVA	B-General_Concept
test	O
results	O
above	O
indicate	O
significant	B-General_Concept
differences	I-General_Concept
between	O
the	O
days	O
time-wait	O
(	O
P-Value	B-General_Concept
=	O
0.000	O
<	O
0.05	O
,	O
α	O
=	O
0.05	O
)	O
.	O
</s>
<s>
The	O
other	O
omnibus	O
tested	O
was	O
the	O
assumption	O
of	O
Equality	O
of	O
Variances	O
,	O
tested	O
by	O
the	O
Levene	O
F	B-General_Concept
test	I-General_Concept
:	O
</s>
<s>
A	O
significant	O
omnibus	O
F	B-General_Concept
test	I-General_Concept
in	O
ANOVA	B-General_Concept
procedure	O
,	O
is	O
an	O
in	O
advance	O
requirement	O
before	O
conducting	O
the	O
Post	O
Hoc	O
comparison	O
,	O
otherwise	O
those	O
comparisons	O
are	O
not	O
required	O
.	O
</s>
<s>
If	O
the	O
omnibus	B-General_Concept
test	I-General_Concept
fails	O
to	O
find	O
significant	B-General_Concept
differences	I-General_Concept
between	O
all	O
means	O
,	O
it	O
means	O
that	O
no	O
difference	O
has	O
been	O
found	O
between	O
any	O
combinations	O
of	O
the	O
tested	O
means	O
.	O
</s>
<s>
In	O
such	O
,	O
it	O
protects	O
family-wise	O
Type	O
I	O
error	O
,	O
which	O
may	O
be	O
increased	O
if	O
overlooking	O
the	O
omnibus	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
Some	O
debates	O
have	O
occurred	O
about	O
the	O
efficiency	O
of	O
the	O
omnibus	O
F	B-General_Concept
Test	I-General_Concept
in	O
ANOVA	B-General_Concept
.	O
</s>
<s>
William	O
B	O
.	O
Ware	O
(	O
1997	O
)	O
claims	O
that	O
the	O
omnibus	B-General_Concept
test	I-General_Concept
significance	O
is	O
required	O
depending	O
on	O
the	O
Post	O
Hoc	O
test	O
is	O
conducted	O
or	O
planned	O
:	O
"	O
...	O
Tukey	O
's	O
HSD	O
and	O
Scheffé	O
's	O
procedure	O
are	O
one-step	O
procedures	O
and	O
can	O
be	O
done	O
without	O
the	O
omnibus	O
F	O
having	O
to	O
be	O
significant	O
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
Fisher	O
's	O
Least	O
Significant	B-General_Concept
Difference	I-General_Concept
test	O
is	O
a	O
two-step	O
procedure	O
.	O
</s>
<s>
William	O
B	O
.	O
Ware	O
(	O
1997	O
)	O
argued	O
that	O
there	O
are	O
a	O
number	O
of	O
problems	O
associated	O
with	O
the	O
requirement	O
of	O
an	O
omnibus	B-General_Concept
test	I-General_Concept
rejection	O
prior	O
to	O
conducting	O
multiple	O
comparisons	O
.	O
</s>
<s>
Hancock	O
agrees	O
with	O
that	O
approach	O
and	O
sees	O
the	O
omnibus	O
requirement	O
in	O
ANOVA	B-General_Concept
in	O
performing	O
planned	O
tests	O
an	O
unnecessary	O
test	O
and	O
potentially	O
detrimental	O
,	O
hurdle	O
unless	O
it	O
is	O
related	O
to	O
Fisher	O
's	O
LSD	O
,	O
which	O
is	O
a	O
viable	O
option	O
for	O
k	O
=3	O
groups	O
.	O
</s>
<s>
Other	O
reason	O
for	O
relating	O
to	O
the	O
omnibus	B-General_Concept
test	I-General_Concept
significance	O
when	O
it	O
is	O
concerned	O
to	O
protect	O
family-wise	O
Type	O
I	O
error	O
.	O
</s>
<s>
The	O
publication	O
"	O
Review	O
of	O
Educational	O
Research	O
"	O
discusses	O
four	O
problems	O
in	O
the	O
omnibus	O
F	B-General_Concept
test	I-General_Concept
requirement	O
:	O
</s>
<s>
First	O
,	O
in	O
a	O
well	O
planned	O
study	O
,	O
the	O
researcher	O
's	O
questions	O
involve	O
specific	O
contrasts	O
of	O
group	O
means	O
 '	O
while	O
the	O
omnibus	B-General_Concept
test	I-General_Concept
,	O
addresses	O
each	O
question	O
only	O
tangentially	O
and	O
it	O
is	O
rather	O
used	O
to	O
facilitate	O
control	O
over	O
the	O
rate	O
of	O
Type	O
I	O
error	O
.	O
</s>
<s>
Secondly	O
,	O
this	O
issue	O
of	O
control	O
is	O
related	O
to	O
the	O
second	O
point	O
:	O
the	O
belief	O
that	O
an	O
omnibus	B-General_Concept
test	I-General_Concept
offers	O
protection	O
is	O
not	O
completely	O
accurate	O
.	O
</s>
<s>
When	O
the	O
complete	O
null	O
hypothesis	O
is	O
true	O
,	O
weak	O
family-wise	O
Type	O
I	O
error	O
control	O
is	O
facilitated	O
by	O
the	O
omnibus	B-General_Concept
test	I-General_Concept
;	O
but	O
,	O
when	O
the	O
complete	O
null	O
is	O
false	O
and	O
partial	O
nulls	O
exist	O
,	O
the	O
F-test	B-General_Concept
does	O
not	O
maintain	O
strong	O
control	O
over	O
the	O
family-wise	O
error	O
rate	O
.	O
</s>
<s>
A	O
third	O
point	O
,	O
which	O
Games	O
(	O
1971	O
)	O
demonstrated	O
in	O
his	O
study	O
,	O
is	O
that	O
the	O
F-test	B-General_Concept
may	O
not	O
be	O
completely	O
consistent	O
with	O
the	O
results	O
of	O
a	O
pairwise	O
comparison	O
approach	O
.	O
</s>
<s>
Consider	O
,	O
for	O
example	O
,	O
a	O
researcher	O
who	O
is	O
instructed	O
to	O
conduct	O
Tukey	O
's	O
test	O
only	O
if	O
an	O
alpha-level	O
F-test	B-General_Concept
rejects	O
the	O
complete	O
null	O
.	O
</s>
<s>
It	O
is	O
possible	O
for	O
the	O
complete	O
null	O
to	O
be	O
rejected	O
but	O
for	O
the	O
widest	O
ranging	O
means	O
not	O
to	O
differ	O
significantly	B-General_Concept
.	O
</s>
<s>
One	O
wonders	O
if	O
,	O
in	O
fact	O
,	O
a	O
practitioner	O
in	O
this	O
situation	O
would	O
simply	O
conduct	O
the	O
MCP	O
contrary	O
to	O
the	O
omnibus	B-General_Concept
test	I-General_Concept
's	O
recommendation	O
.	O
</s>
<s>
The	O
fourth	O
argument	O
against	O
the	O
traditional	O
implementation	O
of	O
an	O
initial	O
omnibus	O
F-test	B-General_Concept
stems	O
from	O
the	O
fact	O
that	O
its	O
well-intentioned	O
but	O
unnecessary	O
protection	O
contributes	O
to	O
a	O
decrease	O
in	O
power	O
.	O
</s>
<s>
The	O
first	O
test	O
in	O
a	O
pairwise	O
MCP	O
,	O
such	O
as	O
that	O
of	O
the	O
most	O
disparate	O
means	O
in	O
Tukey	O
's	O
test	O
,	O
is	O
a	O
form	O
of	O
omnibus	B-General_Concept
test	I-General_Concept
all	O
by	O
itself	O
,	O
controlling	O
the	O
family-wise	O
error	O
rate	O
at	O
the	O
α-level	O
in	O
the	O
weak	O
sense	O
.	O
</s>
<s>
Requiring	O
a	O
preliminary	O
omnibus	O
F-test	B-General_Concept
amount	O
to	O
forcing	O
a	O
researcher	O
to	O
negotiate	O
two	O
hurdles	O
to	O
proclaim	O
the	O
most	O
disparate	O
means	O
significantly	B-General_Concept
different	O
,	O
a	O
task	O
that	O
the	O
range	O
test	O
accomplished	O
at	O
an	O
acceptable	O
α	O
-level	O
all	O
by	O
itself	O
.	O
</s>
<s>
If	O
these	O
two	O
tests	O
were	O
perfectly	O
redundant	O
,	O
the	O
results	O
of	O
both	O
would	O
be	O
identical	O
to	O
the	O
omnibus	B-General_Concept
test	I-General_Concept
;	O
probabilistically	O
speaking	O
,	O
the	O
joint	O
probability	O
of	O
rejecting	O
both	O
would	O
be	O
α	O
when	O
the	O
complete	O
null	O
hypothesis	O
was	O
true	O
.	O
</s>
<s>
For	O
this	O
reason	O
,	O
and	O
those	O
listed	O
before	O
,	O
we	O
agree	O
with	O
Games	O
 '	O
(	O
1971	O
)	O
statement	O
regarding	O
the	O
traditional	O
implementation	O
of	O
a	O
preliminary	O
omnibus	O
F-test	B-General_Concept
:	O
There	O
seems	O
to	O
be	O
little	O
point	O
in	O
applying	O
the	O
overall	O
F	B-General_Concept
test	I-General_Concept
prior	O
to	O
running	O
c	O
contrasts	O
by	O
procedures	O
that	O
set	O
[	O
the	O
family-wise	O
error	O
rate ]	O
α	O
....	O
</s>
<s>
In	O
multiple	O
regression	O
,	O
the	O
omnibus	B-General_Concept
test	I-General_Concept
is	O
an	O
ANOVA	B-General_Concept
F	B-General_Concept
test	I-General_Concept
on	O
all	O
the	O
coefficients	O
,	O
that	O
is	O
equivalent	O
to	O
the	O
multiple	O
correlations	O
R	O
Square	O
F	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
The	O
omnibus	O
F	B-General_Concept
test	I-General_Concept
is	O
an	O
overall	O
test	O
that	O
examines	O
model	O
fit	O
,	O
thus	O
failure	O
to	O
reject	O
the	O
null	O
hypothesis	O
implies	O
that	O
the	O
suggested	O
linear	O
model	O
is	O
not	O
significantly	B-General_Concept
suitable	O
to	O
the	O
data	O
.	O
</s>
<s>
The	O
F	B-General_Concept
statistics	I-General_Concept
of	O
the	O
omnibus	B-General_Concept
test	I-General_Concept
is	O
:	O
</s>
<s>
The	O
F	B-General_Concept
statistic	I-General_Concept
is	O
distributed	O
F	O
(	O
k	O
,	O
n-k-1	O
)	O
,	O
( α	O
)	O
under	O
assuming	O
of	O
null	O
hypothesis	O
and	O
normality	O
assumption	O
.	O
</s>
<s>
Which	O
it	O
's	O
omnibus	O
F	B-General_Concept
test	I-General_Concept
(	O
like	O
Levene	O
F	B-General_Concept
test	I-General_Concept
)	O
.	O
</s>
<s>
The	O
omnibus	B-General_Concept
test	I-General_Concept
examines	O
whether	O
there	O
are	O
any	O
regression	O
coefficients	O
that	O
are	O
significantly	B-General_Concept
non-zero	O
,	O
except	O
for	O
the	O
coefficient	O
β0	O
.	O
</s>
<s>
The	O
null	O
hypothesis	O
is	O
generally	O
thought	O
to	O
be	O
false	O
and	O
is	O
easily	O
rejected	O
with	O
a	O
reasonable	O
amount	O
of	O
data	O
,	O
but	O
in	O
contrary	O
to	O
ANOVA	B-General_Concept
,	O
it	O
is	O
important	O
to	O
do	O
the	O
test	O
anyway	O
.	O
</s>
<s>
The	O
omnibus	B-General_Concept
test	I-General_Concept
comes	O
to	O
be	O
significant	O
mostly	O
if	O
at	O
least	O
one	O
of	O
the	O
independent	O
variables	O
is	O
significant	O
.	O
</s>
<s>
This	O
means	O
that	O
any	O
other	O
variable	O
may	O
enter	O
the	O
model	O
,	O
under	O
the	O
model	O
assumption	O
of	O
non-colinearity	O
between	O
independent	O
variables	O
,	O
while	O
the	O
omnibus	B-General_Concept
test	I-General_Concept
still	O
shows	O
significance	O
.	O
</s>
<s>
The	O
omnibus	O
F	B-General_Concept
test	I-General_Concept
in	O
the	O
ANOVA	B-General_Concept
table	O
implies	O
that	O
the	O
model	O
involved	O
these	O
three	O
predictors	O
can	O
fit	O
for	O
predicting	O
"	O
Average	O
cost	O
of	O
claims	O
"	O
,	O
since	O
the	O
null	O
hypothesis	O
is	O
rejected	O
(	O
P-Value	B-General_Concept
=	O
0.000	O
<	O
0.01	O
,	O
α	O
=	O
0.01	O
)	O
.	O
</s>
<s>
This	O
rejection	O
of	O
the	O
omnibus	B-General_Concept
test	I-General_Concept
implies	O
that	O
at	O
least	O
one	O
of	O
the	O
coefficients	O
of	O
the	O
predictors	O
in	O
the	O
model	O
have	O
found	O
to	O
be	O
non-zero	O
.	O
</s>
<s>
Source	O
Sum	B-General_Concept
of	I-General_Concept
Squares	I-General_Concept
df	O
Mean	O
Square	O
F	O
Sig	O
.	O
</s>
<s>
However	O
,	O
only	O
the	O
predictors	O
:	O
"	O
Vehicle	O
age	O
"	O
and	O
"	O
Number	O
of	O
claims	O
"	O
has	O
statistical	O
influence	O
and	O
prediction	O
on	O
the	O
"	O
Average	O
cost	O
of	O
claims	O
"	O
as	O
shown	O
on	O
the	O
following	O
"	O
Coefficients	O
table	O
"	O
,	O
whereas	O
"	O
Policyholder	O
age	O
"	O
is	O
not	O
significant	O
as	O
a	O
predictor	O
(	O
P-Value	B-General_Concept
=	O
0.116>0.05	O
)	O
.	O
</s>
<s>
The	O
last	O
line	O
describes	O
the	O
omnibus	O
F	B-General_Concept
test	I-General_Concept
for	O
model	O
fit	O
.	O
</s>
<s>
Note	O
that	O
the	O
conclusion	O
from	O
Coefficients	O
:	O
table	O
is	O
that	O
only	O
β1	O
is	O
significant	O
(	O
P-Value	B-General_Concept
shown	O
on	O
Pr( 	O
>	O
|t|	O
)	O
column	O
is	O
4.37e-05	O
<<	O
0.001	O
)	O
.	O
</s>
<s>
Thus	O
one	O
step	O
test	O
,	O
like	O
omnibus	O
F	B-General_Concept
test	I-General_Concept
for	O
model	O
fitting	O
is	O
not	O
sufficient	O
to	O
determine	O
model	O
fit	O
for	O
those	O
predictors	O
.	O
</s>
<s>
The	O
omnibus	B-General_Concept
test	I-General_Concept
,	O
among	O
the	O
other	O
parts	O
of	O
the	O
logistic	O
regression	O
procedure	O
,	O
is	O
a	O
likelihood-ratio	B-General_Concept
test	I-General_Concept
based	O
on	O
the	O
maximum	O
likelihood	O
method	O
.	O
</s>
<s>
In	O
general	O
,	O
regarding	O
simple	O
hypotheses	O
on	O
parameter	O
θ	O
(	O
for	O
example	O
)	O
:H0	O
:	O
θ	O
=	O
θ0vs.H1	O
:	O
θ	O
=	O
θ1	O
,	O
the	O
likelihood	B-General_Concept
ratio	I-General_Concept
test	I-General_Concept
statistic	I-General_Concept
can	O
be	O
referred	O
as	O
:	O
</s>
<s>
The	O
likelihood	B-General_Concept
ratio	I-General_Concept
test	I-General_Concept
provides	O
the	O
following	O
decision	O
rule	O
:	O
</s>
<s>
whereas	O
the	O
critical	O
values	O
c	O
,	O
q	O
are	O
usually	O
chosen	O
to	O
obtain	O
a	O
specified	O
significance	B-General_Concept
level	I-General_Concept
α	O
,	O
through	O
:	O
.	O
</s>
<s>
Thus	O
,	O
the	O
likelihood-ratio	B-General_Concept
test	I-General_Concept
rejects	O
the	O
null	O
hypothesis	O
if	O
the	O
value	O
of	O
this	O
statistic	O
is	O
too	O
small	O
.	O
</s>
<s>
The	O
Neyman-Pearson	O
lemma	O
states	O
that	O
this	O
likelihood	B-General_Concept
ratio	I-General_Concept
test	I-General_Concept
is	O
the	O
most	O
powerful	O
among	O
all	O
level-α	O
tests	O
for	O
this	O
problem	O
.	O
</s>
<s>
When	O
assessed	O
upon	O
a	O
chi-square	B-General_Concept
distribution	O
,	O
non-significant	O
chi-square	B-General_Concept
values	O
indicate	O
very	O
little	O
unexplained	O
variance	O
and	O
thus	O
,	O
good	O
model	O
fit	O
.	O
</s>
<s>
Conversely	O
,	O
a	O
significant	O
chi-square	B-General_Concept
value	O
indicates	O
that	O
a	O
significant	O
amount	O
of	O
the	O
variance	O
is	O
unexplained	O
.	O
</s>
<s>
Therefore	O
,	O
to	O
assess	O
the	O
contribution	O
of	O
a	O
predictor	O
or	O
set	O
of	O
predictors	O
,	O
one	O
can	O
subtract	O
the	O
model	O
deviance	O
from	O
the	O
null	O
deviance	O
and	O
assess	O
the	O
difference	O
on	O
a	O
chi-square	B-General_Concept
distribution	O
with	O
one	O
degree	O
of	O
freedom	O
.	O
</s>
<s>
If	O
the	O
model	O
deviance	O
is	O
significantly	B-General_Concept
smaller	O
than	O
the	O
null	O
deviance	O
then	O
one	O
can	O
conclude	O
that	O
the	O
predictor	O
or	O
set	O
of	O
predictors	O
significantly	B-General_Concept
improved	O
model	O
fit	O
.	O
</s>
<s>
This	O
is	O
analogous	O
to	O
the	O
F-test	B-General_Concept
used	O
in	O
linear	O
regression	O
analysis	O
to	O
assess	O
the	O
significance	O
of	O
prediction	O
.	O
</s>
<s>
A	O
convenient	O
result	O
,	O
attributed	O
to	O
Samuel	O
S	O
.	O
Wilks	O
,	O
says	O
that	O
as	O
the	O
sample	O
size	O
n	O
approaches	O
the	O
test	O
statistic	O
has	O
asymptotically	O
distribution	O
with	O
degrees	O
of	O
freedom	O
equal	O
to	O
the	O
difference	O
in	O
dimensionality	O
of	O
and	O
parameters	O
the	O
β	O
coefficients	O
as	O
mentioned	O
before	O
on	O
the	O
omnibus	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
This	O
means	O
that	O
we	O
can	O
retrieve	O
the	O
critical	O
value	O
C	O
from	O
the	O
chi	O
squared	O
with	O
2	O
degrees	O
of	O
freedom	O
under	O
a	O
specific	O
significance	B-General_Concept
level	I-General_Concept
.	O
</s>
<s>
The	O
Wald	O
statistic	O
is	O
the	O
ratio	O
of	O
the	O
square	O
of	O
the	O
regression	O
coefficient	O
to	O
the	O
square	O
of	O
the	O
standard	O
error	O
of	O
the	O
coefficient	O
and	O
is	O
asymptotically	O
distributed	O
as	O
a	O
chi-square	B-General_Concept
distribution	O
.	O
</s>
<s>
Although	O
several	O
statistical	O
packages	O
(	O
e.g.	O
,	O
SPSS	B-Algorithm
,	O
SAS	O
)	O
report	O
the	O
Wald	O
statistic	O
to	O
assess	O
the	O
contribution	O
of	O
individual	O
predictors	O
,	O
the	O
Wald	O
statistic	O
has	O
some	O
limitations	O
.	O
</s>
<s>
Statistical	O
analysis	O
using	O
logistic	O
regression	O
of	O
Grade	O
on	O
GPA	O
,	O
Tuce	O
and	O
Psi	O
was	O
conducted	O
in	O
SPSS	B-Algorithm
using	O
Stepwise	O
Logistic	O
Regression	O
.	O
</s>
<s>
In	O
the	O
output	O
,	O
the	O
"	O
block	O
"	O
line	O
relates	O
to	O
Chi-Square	B-General_Concept
test	I-General_Concept
on	O
the	O
set	O
of	O
independent	O
variables	O
that	O
are	O
tested	O
and	O
included	O
in	O
the	O
model	O
fitting	O
.	O
</s>
<s>
The	O
"	O
step	O
"	O
line	O
relates	O
to	O
Chi-Square	B-General_Concept
test	I-General_Concept
on	O
the	O
step	O
level	O
while	O
variables	O
included	O
in	O
the	O
model	O
step	O
by	O
step	O
.	O
</s>
<s>
Note	O
that	O
in	O
the	O
output	O
a	O
step	O
chi-square	B-General_Concept
,	O
is	O
the	O
same	O
as	O
the	O
block	O
chi-square	B-General_Concept
since	O
they	O
both	O
are	O
testing	O
the	O
same	O
hypothesis	O
that	O
the	O
tested	O
variables	O
enter	O
on	O
this	O
step	O
are	O
non-zero	O
.	O
</s>
<s>
In	O
the	O
first	O
block	O
,	O
psi	O
alone	O
gets	O
entered	O
,	O
so	O
the	O
block	O
and	O
step	O
Chi	B-General_Concept
Test	I-General_Concept
relates	O
to	O
the	O
hypothesis	O
H0	O
:	O
βPSI	O
=	O
0	O
.	O
</s>
<s>
Results	O
of	O
the	O
omnibus	O
Chi-Square	B-General_Concept
tests	I-General_Concept
implies	O
that	O
PSI	O
is	O
significant	O
for	O
predicting	O
that	O
GRADE	O
is	O
more	O
likely	O
to	O
be	O
a	O
final	O
grade	O
of	O
A	O
.	O
</s>
<s>
Chi-Square	B-General_Concept
df	O
Sig	O
.	O
</s>
<s>
Chi-Square	B-General_Concept
df	O
Sig	O
.	O
</s>
<s>
The	O
step	O
chi-square	B-General_Concept
,	O
.474	O
,	O
tells	O
you	O
whether	O
the	O
effect	O
of	O
the	O
variable	O
that	O
was	O
entered	O
in	O
the	O
final	O
step	O
,	O
TUCE	O
,	O
significantly	B-General_Concept
differs	O
from	O
zero	O
.	O
</s>
<s>
It	O
is	O
the	O
equivalent	O
of	O
an	O
incremental	O
F	B-General_Concept
test	I-General_Concept
of	O
the	O
parameter	O
,	O
i.e.	O
</s>
<s>
The	O
block	O
chi-square	B-General_Concept
,	O
9.562	O
,	O
tests	O
whether	O
either	O
or	O
both	O
of	O
the	O
variables	O
included	O
in	O
this	O
block	O
(	O
GPA	O
and	O
TUCE	O
)	O
have	O
effects	O
that	O
differ	O
from	O
zero	O
.	O
</s>
<s>
This	O
is	O
the	O
equivalent	O
of	O
an	O
incremental	O
F	B-General_Concept
test	I-General_Concept
,	O
i.e.	O
</s>
<s>
The	O
model	O
chi-square	B-General_Concept
,	O
15.404	O
,	O
tells	O
you	O
whether	O
any	O
of	O
the	O
three	O
Independent	O
Variabls	O
has	O
significant	O
effects	O
.	O
</s>
<s>
It	O
is	O
the	O
equivalent	O
of	O
a	O
global	O
F	B-General_Concept
test	I-General_Concept
,	O
i.e.	O
</s>
<s>
You	O
can	O
,	O
if	O
you	O
want	O
,	O
do	O
an	O
incremental	O
LR	O
chi-square	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
When	O
parameters	O
are	O
tested	O
separately	O
,	O
by	O
controlling	O
the	O
other	O
parameters	O
,	O
we	O
see	O
that	O
the	O
effects	O
of	O
GPA	O
and	O
PSI	O
are	O
statistically	B-General_Concept
significant	I-General_Concept
,	O
but	O
the	O
effect	O
of	O
TUCE	O
is	O
not	O
.	O
</s>
<s>
Logistic	O
regression	O
was	O
applied	O
to	O
the	O
data	O
on	O
SPSS	B-Algorithm
,	O
since	O
the	O
Dependent	O
variable	O
is	O
Categorical	O
(	O
dichotomous	O
)	O
and	O
the	O
researcher	O
examine	O
the	O
odd	O
ratio	O
of	O
potentially	O
being	O
re-arrested	O
vs.	O
not	O
expected	O
to	O
be	O
re-arrested	O
.	O
</s>
<s>
Chi-Square	B-General_Concept
df	O
Sig	O
.	O
</s>
<s>
The	O
table	O
shows	O
the	O
"	O
Omnibus	B-General_Concept
Test	I-General_Concept
of	O
Model	O
Coefficients	O
"	O
based	O
on	O
Chi-Square	B-General_Concept
test	I-General_Concept
,	O
which	O
implies	O
that	O
the	O
overall	O
model	O
is	O
predictive	O
of	O
re-arrest	O
(	O
focus	O
is	O
on	O
row	O
three	O
—	O
"	O
Model	O
"	O
)	O
:	O
(	O
4	O
degrees	O
of	O
freedom	O
)	O
=	O
41.15	O
,	O
p	O
<	O
.001	O
,	O
and	O
the	O
null	O
can	O
be	O
rejected	O
.	O
</s>
<s>
One	O
can	O
also	O
reject	O
the	O
null	O
that	O
the	O
B	O
coefficients	O
for	O
having	O
committed	O
a	O
felony	O
,	O
completing	O
a	O
rehab	O
program	O
,	O
and	O
being	O
employed	O
are	O
equal	O
to	O
zero	O
—	O
they	O
are	O
statistically	B-General_Concept
significant	I-General_Concept
and	O
predictive	O
of	O
re-arrest	O
.	O
</s>
<s>
The	O
statistical	B-General_Concept
significance	I-General_Concept
of	O
each	O
B	O
is	O
tested	O
by	O
the	O
Wald	O
Chi-Square	B-General_Concept
—	O
testing	O
the	O
null	O
that	O
the	O
B	O
coefficient	O
=	O
0	O
(	O
the	O
alternate	O
hypothesis	O
is	O
that	O
it	O
does	O
not	O
=	O
0	O
)	O
.	O
</s>
<s>
p-values	B-General_Concept
lower	O
than	O
alpha	O
are	O
significant	O
,	O
leading	O
to	O
rejection	O
of	O
the	O
null	O
.	O
</s>
<s>
Here	O
,	O
only	O
the	O
independent	O
variables	O
felony	O
,	O
rehab	O
,	O
employment	O
,	O
are	O
significant	O
(	O
P-Value	B-General_Concept
<	O
0.05	O
.	O
</s>
