<s>
In	O
scientific	O
research	O
,	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
(	O
often	O
denoted	O
H0	O
)	O
is	O
the	O
claim	O
that	O
no	O
relationship	O
exists	O
between	O
two	O
sets	O
of	O
data	O
or	O
variables	O
being	O
analyzed	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
that	O
any	O
experimentally	O
observed	O
difference	O
is	O
due	O
to	O
chance	O
alone	O
,	O
and	O
an	O
underlying	O
causative	O
relationship	O
does	O
not	O
exist	O
,	O
hence	O
the	O
term	O
"	O
null	O
"	O
.	O
</s>
<s>
In	O
addition	O
to	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
an	O
alternative	B-General_Concept
hypothesis	I-General_Concept
is	O
also	O
developed	O
,	O
which	O
claims	O
that	O
a	O
relationship	O
does	O
exist	O
between	O
two	O
variables	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
and	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
are	O
types	O
of	O
conjectures	O
used	O
in	O
statistical	O
tests	O
,	O
which	O
are	O
formal	O
methods	O
of	O
reaching	O
conclusions	O
or	O
making	O
decisions	O
on	O
the	O
basis	O
of	O
data	O
.	O
</s>
<s>
"	O
The	O
statement	O
being	O
tested	O
in	O
a	O
test	O
of	O
statistical	B-General_Concept
significance	I-General_Concept
is	O
called	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
The	O
test	O
of	O
significance	O
is	O
designed	O
to	O
assess	O
the	O
strength	O
of	O
the	O
evidence	O
against	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
Usually	O
,	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
a	O
statement	O
of	O
'	O
no	O
effect	O
 '	O
or	O
'	O
no	O
difference	O
 '	O
.	O
"	O
</s>
<s>
The	O
statement	O
that	O
is	O
being	O
tested	O
against	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
Statistical	B-General_Concept
significance	I-General_Concept
test	O
:	O
"	O
Very	O
roughly	O
,	O
the	O
procedure	O
for	O
deciding	O
goes	O
like	O
this	O
:	O
Take	O
a	O
random	O
sample	O
from	O
the	O
population	O
.	O
</s>
<s>
If	O
the	O
sample	O
data	O
are	O
consistent	O
with	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
then	O
do	O
not	O
reject	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
;	O
if	O
the	O
sample	O
data	O
are	O
inconsistent	O
with	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
then	O
reject	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
and	O
conclude	O
that	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
is	O
true.	O
"	O
</s>
<s>
A	O
possible	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
that	O
the	O
mean	O
male	O
score	O
is	O
the	O
same	O
as	O
the	O
mean	O
female	O
score	O
:	O
</s>
<s>
H0	O
=	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
</s>
<s>
A	O
stronger	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
that	O
the	O
two	O
samples	O
are	O
drawn	O
from	O
the	O
same	O
population	O
,	O
such	O
that	O
the	O
variances	O
and	O
shapes	O
of	O
the	O
distributions	O
are	O
also	O
equal	O
.	O
</s>
<s>
Fisher	O
required	O
an	O
exact	O
null	B-General_Concept
hypothesis	I-General_Concept
for	O
testing	O
(	O
see	O
the	O
quotations	O
below	O
)	O
.	O
</s>
<s>
A	O
one-tailed	B-General_Concept
hypothesis	I-General_Concept
(	O
tested	O
using	O
a	O
one-sided	B-General_Concept
test	I-General_Concept
)	O
is	O
an	O
inexact	O
hypothesis	O
in	O
which	O
the	O
value	O
of	O
a	O
parameter	O
is	O
specified	O
as	O
being	O
either	O
:	O
</s>
<s>
A	O
one-tailed	B-General_Concept
hypothesis	I-General_Concept
is	O
said	O
to	O
have	O
directionality	O
.	O
</s>
<s>
Fisher	O
's	O
original	O
(	O
lady	O
tasting	O
tea	O
)	O
example	O
was	O
a	O
one-tailed	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
was	O
asymmetric	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
a	O
default	O
hypothesis	O
that	O
a	O
quantity	O
to	O
be	O
measured	O
is	O
zero	O
(	O
null	O
)	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
states	O
that	O
a	O
quantity	O
(	O
of	O
interest	O
)	O
is	O
larger	O
or	O
equal	O
to	O
zero	O
and	O
smaller	O
or	O
equal	O
to	O
zero	O
.	O
</s>
<s>
If	O
either	O
requirement	O
can	O
be	O
positively	O
overturned	O
,	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
"	O
excluded	O
from	O
the	O
realm	O
of	O
possibilities	O
"	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
generally	O
assumed	O
to	O
remain	O
possibly	O
true	O
.	O
</s>
<s>
having	O
a	O
high	O
confidence	O
level	O
,	O
thus	O
demonstrating	O
a	O
statistically	B-General_Concept
significant	I-General_Concept
difference	O
.	O
</s>
<s>
Failure	O
to	O
exclude	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
(	O
with	O
any	O
confidence	O
)	O
does	O
not	O
logically	O
confirm	O
or	O
support	O
the	O
(	O
unprovable	O
)	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
Confirming	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
two-sided	O
would	O
amount	O
to	O
positively	O
proving	O
it	O
is	O
bigger	O
or	O
equal	O
than	O
0	O
and	O
to	O
positively	O
proving	O
it	O
is	O
smaller	O
or	O
equal	O
than	O
0	O
;	O
this	O
is	O
something	O
for	O
which	O
infinite	O
accuracy	O
is	O
needed	O
as	O
well	O
as	O
exactly	O
zero	O
effect	O
,	O
neither	O
of	O
which	O
normally	O
are	O
realistic	O
.	O
</s>
<s>
So	O
failure	O
of	O
an	O
exclusion	O
of	O
a	O
null	B-General_Concept
hypothesis	I-General_Concept
amounts	O
to	O
a	O
"	O
do	O
n't	O
know	O
"	O
at	O
the	O
specified	O
confidence	O
level	O
;	O
it	O
does	O
not	O
immediately	O
imply	O
null	O
somehow	O
,	O
as	O
the	O
data	O
may	O
already	O
show	O
a	O
(	O
less	O
strong	O
)	O
indication	O
for	O
a	O
non-null	O
.	O
</s>
<s>
A	O
non-null	O
hypothesis	O
can	O
have	O
the	O
following	O
meanings	O
,	O
depending	O
on	O
the	O
author	O
a	O
)	O
a	O
value	O
other	O
than	O
zero	O
is	O
used	O
,	O
b	O
)	O
some	O
margin	O
other	O
than	O
zero	O
is	O
used	O
and	O
c	O
)	O
the	O
"	B-General_Concept
alternative	I-General_Concept
"	I-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
Testing	O
(	O
excluding	O
or	O
failing	O
to	O
exclude	O
)	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
provides	O
evidence	O
that	O
there	O
are	O
(	O
or	O
are	O
not	O
)	O
statistically	O
sufficient	O
grounds	O
to	O
believe	O
there	O
is	O
a	O
relationship	O
between	O
two	O
phenomena	O
(	O
e.g.	O
,	O
that	O
a	O
potential	O
treatment	O
has	O
a	O
non-zero	O
effect	O
,	O
either	O
way	O
)	O
.	O
</s>
<s>
Testing	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
a	O
central	O
task	O
in	O
statistical	O
hypothesis	O
testing	O
in	O
the	O
modern	O
practice	O
of	O
science	O
.	O
</s>
<s>
There	O
are	O
precise	O
criteria	O
for	O
excluding	O
or	O
not	O
excluding	O
a	O
null	B-General_Concept
hypothesis	I-General_Concept
at	O
a	O
certain	O
confidence	O
level	O
.	O
</s>
<s>
The	O
confidence	O
level	O
should	O
indicate	O
the	O
likelihood	O
that	O
much	O
more	O
and	O
better	O
data	O
would	O
still	O
be	O
able	O
to	O
exclude	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
on	O
the	O
same	O
side	O
.	O
</s>
<s>
The	O
concept	O
of	O
a	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
used	O
differently	O
in	O
two	O
approaches	O
to	O
statistical	O
inference	O
.	O
</s>
<s>
In	O
the	O
significance	O
testing	O
approach	O
of	O
Ronald	O
Fisher	O
,	O
a	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
rejected	O
if	O
the	O
observed	O
data	O
are	O
significantly	B-General_Concept
unlikely	O
to	O
have	O
occurred	O
if	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
were	O
true	O
.	O
</s>
<s>
In	O
this	O
case	O
,	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
rejected	O
and	O
an	O
alternative	B-General_Concept
hypothesis	I-General_Concept
is	O
accepted	O
in	O
its	O
place	O
.	O
</s>
<s>
If	O
the	O
data	O
are	O
consistent	O
with	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
statistically	O
possibly	O
true	O
,	O
then	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
not	O
rejected	O
.	O
</s>
<s>
In	O
neither	O
case	O
is	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
or	O
its	O
alternative	O
proven	O
;	O
with	O
better	O
or	O
more	O
data	O
,	O
the	O
null	O
may	O
still	O
be	O
rejected	O
.	O
</s>
<s>
This	O
is	O
analogous	O
to	O
the	O
legal	O
principle	O
of	O
presumption	O
of	O
innocence	O
,	O
in	O
which	O
a	O
suspect	O
or	O
defendant	O
is	O
assumed	O
to	O
be	O
innocent	O
(	O
null	O
is	O
not	O
rejected	O
)	O
until	O
proven	O
guilty	O
(	O
null	O
is	O
rejected	O
)	O
beyond	O
a	O
reasonable	O
doubt	O
(	O
to	O
a	O
statistically	B-General_Concept
significant	I-General_Concept
degree	O
)	O
.	O
</s>
<s>
In	O
the	O
hypothesis	O
testing	O
approach	O
of	O
Jerzy	O
Neyman	O
and	O
Egon	O
Pearson	O
,	O
a	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
contrasted	O
with	O
an	O
alternative	B-General_Concept
hypothesis	I-General_Concept
,	O
and	O
the	O
two	O
hypotheses	O
are	O
distinguished	O
on	O
the	O
basis	O
of	O
data	O
,	O
with	O
certain	O
error	O
rates	O
.	O
</s>
<s>
Statistical	O
inference	O
can	O
be	O
done	O
without	O
a	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
by	O
specifying	O
a	O
statistical	O
model	O
corresponding	O
to	O
each	O
candidate	O
hypothesis	O
,	O
and	O
by	O
using	O
model	O
selection	O
techniques	O
to	O
choose	O
the	O
most	O
appropriate	O
model	O
.	O
</s>
<s>
(	O
The	O
most	O
common	O
selection	O
techniques	O
are	O
based	O
on	O
either	O
Akaike	O
information	O
criterion	O
or	O
Bayes	B-General_Concept
factor	I-General_Concept
)	O
.	O
</s>
<s>
The	O
hypothesis	O
that	O
chance	O
alone	O
is	O
responsible	O
for	O
the	O
results	O
is	O
called	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
The	O
model	O
of	O
the	O
result	O
of	O
the	O
random	O
process	O
is	O
called	O
the	O
distribution	O
under	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
The	O
obtained	O
results	O
are	O
compared	O
with	O
the	O
distribution	O
under	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
and	O
the	O
likelihood	O
of	O
finding	O
the	O
obtained	O
results	O
is	O
thereby	O
determined	O
.	O
</s>
<s>
Hypothesis	O
testing	O
works	O
by	O
collecting	O
data	O
and	O
measuring	O
how	O
likely	O
the	O
particular	O
set	O
of	O
data	O
is	O
(	O
assuming	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
)	O
,	O
when	O
the	O
study	O
is	O
on	O
a	O
randomly	O
selected	O
representative	O
sample	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
assumes	O
no	O
relationship	O
between	O
variables	O
in	O
the	O
population	O
from	O
which	O
the	O
sample	O
is	O
selected	O
.	O
</s>
<s>
If	O
the	O
data-set	O
of	O
a	O
randomly	O
selected	O
representative	O
sample	O
is	O
very	O
unlikely	O
relative	O
to	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
(	O
defined	O
as	O
being	O
part	O
of	O
a	O
class	O
of	O
sets	O
of	O
data	O
that	O
only	O
rarely	O
will	O
be	O
observed	O
)	O
,	O
the	O
experimenter	O
rejects	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
concluding	O
it	O
(	O
probably	O
)	O
is	O
false	O
.	O
</s>
<s>
This	O
class	O
of	O
data-sets	O
is	O
usually	O
specified	O
via	O
a	O
test	B-General_Concept
statistic	I-General_Concept
,	O
which	O
is	O
designed	O
to	O
measure	O
the	O
extent	O
of	O
apparent	O
departure	O
from	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
The	O
procedure	O
works	O
by	O
assessing	O
whether	O
the	O
observed	O
departure	O
,	O
measured	O
by	O
the	O
test	B-General_Concept
statistic	I-General_Concept
,	O
is	O
larger	O
than	O
a	O
value	O
defined	O
,	O
so	O
that	O
the	O
probability	O
of	O
occurrence	O
of	O
a	O
more	O
extreme	O
value	O
is	O
small	O
under	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
(	O
usually	O
in	O
less	O
than	O
either	O
5%	O
or	O
1%	O
of	O
similar	O
data-sets	O
in	O
which	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
does	O
hold	O
)	O
.	O
</s>
<s>
If	O
the	O
data	O
do	O
not	O
contradict	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
then	O
only	O
a	O
weak	O
conclusion	O
can	O
be	O
made	O
:	O
namely	O
,	O
that	O
the	O
observed	O
data	O
set	O
provides	O
insufficient	O
evidence	O
against	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
In	O
this	O
case	O
,	O
because	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
could	O
be	O
true	O
or	O
false	O
,	O
in	O
some	O
contexts	O
this	O
is	O
interpreted	O
as	O
meaning	O
that	O
the	O
data	O
give	O
insufficient	O
evidence	O
to	O
make	O
any	O
conclusion	O
,	O
while	O
in	O
other	O
contexts	O
,	O
it	O
is	O
interpreted	O
as	O
meaning	O
that	O
there	O
is	O
not	O
sufficient	O
evidence	O
to	O
support	O
changing	O
from	O
a	O
currently	O
useful	O
regime	O
to	O
a	O
different	O
one	O
.	O
</s>
<s>
Possible	O
null	B-General_Concept
hypotheses	I-General_Concept
are	O
"	O
this	O
drug	O
does	O
not	O
reduce	O
the	O
risk	O
of	O
having	O
a	O
heart	O
attack	O
"	O
or	O
"	O
this	O
drug	O
has	O
no	O
effect	O
on	O
the	O
risk	O
of	O
having	O
a	O
heart	O
attack	O
"	O
.	O
</s>
<s>
If	O
the	O
data	O
show	O
a	O
statistically	B-General_Concept
significant	I-General_Concept
change	O
in	O
the	O
people	O
receiving	O
the	O
drug	O
,	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
rejected	O
.	O
</s>
<s>
There	O
are	O
many	O
types	O
of	O
significance	O
tests	O
for	O
one	O
,	O
two	O
or	O
more	O
samples	O
,	O
for	O
means	O
,	O
variances	O
and	O
proportions	O
,	O
paired	O
or	O
unpaired	O
data	O
,	O
for	O
different	O
distributions	O
,	O
for	O
large	O
and	O
small	O
samples	O
;	O
all	O
have	O
null	B-General_Concept
hypotheses	I-General_Concept
.	O
</s>
<s>
There	O
are	O
also	O
at	O
least	O
four	O
goals	O
of	O
null	B-General_Concept
hypotheses	I-General_Concept
for	O
significance	O
tests	O
:	O
</s>
<s>
Technical	O
null	B-General_Concept
hypotheses	I-General_Concept
are	O
used	O
to	O
verify	O
statistical	O
assumptions	O
.	O
</s>
<s>
Null	B-General_Concept
hypotheses	I-General_Concept
of	O
homogeneity	B-General_Concept
are	O
used	O
to	O
verify	O
that	O
multiple	O
experiments	O
are	O
producing	O
consistent	O
results	O
.	O
</s>
<s>
Null	B-General_Concept
hypotheses	I-General_Concept
that	O
assert	O
the	O
equality	O
of	O
effect	O
of	O
two	O
or	O
more	O
alternative	O
treatments	O
,	O
for	O
example	O
,	O
a	O
drug	O
and	O
a	O
placebo	O
,	O
are	O
used	O
to	O
reduce	O
scientific	O
claims	O
based	O
on	O
statistical	O
noise	O
.	O
</s>
<s>
This	O
is	O
the	O
most	O
popular	O
null	B-General_Concept
hypothesis	I-General_Concept
;	O
It	O
is	O
so	O
popular	O
that	O
many	O
statements	O
about	O
significant	O
testing	O
assume	O
such	O
null	B-General_Concept
hypotheses	I-General_Concept
.	O
</s>
<s>
Rejection	O
of	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
not	O
necessarily	O
the	O
real	O
goal	O
of	O
a	O
significance	O
tester	O
.	O
</s>
<s>
The	O
numerous	O
uses	O
of	O
significance	O
testing	O
were	O
well	O
known	O
to	O
Fisher	O
who	O
discussed	O
many	O
in	O
his	O
book	O
written	O
a	O
decade	O
before	O
defining	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
A	O
statistical	B-General_Concept
significance	I-General_Concept
test	O
shares	O
much	O
mathematics	O
with	O
a	O
confidence	O
interval	O
.	O
</s>
<s>
Whenever	O
the	O
sign	O
of	O
a	O
relationship	O
is	O
important	O
,	O
statistical	B-General_Concept
significance	I-General_Concept
is	O
a	O
worthy	O
goal	O
.	O
</s>
<s>
The	O
choice	O
of	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
associated	O
with	O
sparse	O
and	O
inconsistent	O
advice	O
.	O
</s>
<s>
Fisher	O
mentioned	O
few	O
constraints	O
on	O
the	O
choice	O
and	O
stated	O
that	O
many	O
null	B-General_Concept
hypotheses	I-General_Concept
should	O
be	O
considered	O
and	O
that	O
many	O
tests	O
are	O
possible	O
for	O
each	O
.	O
</s>
<s>
A	O
familiarity	O
with	O
the	O
range	O
of	O
tests	O
available	O
may	O
suggest	O
a	O
particular	O
null	B-General_Concept
hypothesis	I-General_Concept
and	O
test	O
.	O
</s>
<s>
Formulating	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
not	O
automated	O
(	O
though	O
the	O
calculations	O
of	O
significance	O
testing	O
usually	O
are	O
)	O
.	O
</s>
<s>
A	O
statistical	B-General_Concept
significance	I-General_Concept
test	O
is	O
intended	O
to	O
test	O
a	O
hypothesis	O
.	O
</s>
<s>
Example	O
:	O
If	O
a	O
study	O
of	O
last	O
year	O
's	O
weather	O
reports	O
indicates	O
that	O
rain	O
in	O
a	O
region	O
falls	O
primarily	O
on	O
weekends	O
,	O
it	O
is	O
only	O
valid	O
to	O
test	O
that	O
null	B-General_Concept
hypothesis	I-General_Concept
on	O
weather	O
reports	O
from	O
any	O
other	O
year	O
.	O
</s>
<s>
Testing	O
hypotheses	O
suggested	O
by	O
the	O
data	O
is	O
circular	O
reasoning	O
that	O
proves	O
nothing	O
;	O
It	O
is	O
a	O
special	O
limitation	O
on	O
the	O
choice	O
of	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
Translate	O
this	O
to	O
a	O
statistical	O
alternative	B-General_Concept
hypothesis	I-General_Concept
and	O
proceed	O
:	O
"	O
Because	O
Ha	O
expresses	O
the	O
effect	O
that	O
we	O
wish	O
to	O
find	O
evidence	O
for	O
,	O
we	O
often	O
begin	O
with	O
Ha	O
and	O
then	O
set	O
up	O
H0	O
as	O
the	O
statement	O
that	O
the	O
hoped-for	O
effect	O
is	O
not	O
present.	O
"	O
</s>
<s>
The	O
standard	O
"	O
no	O
difference	O
"	O
null	B-General_Concept
hypothesis	I-General_Concept
may	O
reward	O
the	O
pharmaceutical	O
company	O
for	O
gathering	O
inadequate	O
data	O
.	O
</s>
<s>
"	O
Difference	O
"	O
is	O
a	O
better	O
null	B-General_Concept
hypothesis	I-General_Concept
in	O
this	O
case	O
,	O
but	O
statistical	B-General_Concept
significance	I-General_Concept
is	O
not	O
an	O
adequate	O
criterion	O
for	O
reaching	O
a	O
nuanced	O
conclusion	O
which	O
requires	O
a	O
good	O
numeric	O
estimate	O
of	O
the	O
drug	O
's	O
effectiveness	O
.	O
</s>
<s>
A	O
"	O
minor	O
"	O
or	O
"	O
simple	O
"	O
proposed	O
change	O
in	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
((new vs old )	O
rather	O
than	O
(	O
new	O
vs	O
placebo	O
)	O
)	O
can	O
have	O
a	O
dramatic	O
effect	O
on	O
the	O
utility	O
of	O
a	O
test	O
for	O
complex	O
non-statistical	O
reasons	O
.	O
</s>
<s>
The	O
choice	O
of	O
null	B-General_Concept
hypothesis	I-General_Concept
(	O
H0	O
)	O
and	O
consideration	O
of	O
directionality	O
(	O
see	O
"	O
one-tailed	B-General_Concept
test	I-General_Concept
"	O
)	O
is	O
critical	O
.	O
</s>
<s>
A	O
potential	O
null	B-General_Concept
hypothesis	I-General_Concept
implying	O
a	O
one-tail	O
test	O
is	O
"	O
this	O
coin	O
is	O
not	O
biased	O
toward	O
heads	O
"	O
.	O
</s>
<s>
Therefore	O
,	O
the	O
observations	O
are	O
not	O
likely	O
enough	O
for	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
to	O
hold	O
,	O
and	O
the	O
test	O
refutes	O
it	O
.	O
</s>
<s>
Alternatively	O
,	O
a	O
null	B-General_Concept
hypothesis	I-General_Concept
implying	O
a	O
two-tailed	B-General_Concept
test	I-General_Concept
is	O
"	O
this	O
coin	O
is	O
fair	O
"	O
.	O
</s>
<s>
This	O
one	O
null	B-General_Concept
hypothesis	I-General_Concept
could	O
be	O
examined	O
by	O
looking	O
out	O
for	O
either	O
too	O
many	O
tails	O
or	O
too	O
many	O
heads	O
in	O
the	O
experiments	O
.	O
</s>
<s>
The	O
outcomes	O
that	O
would	O
tend	O
to	O
refuse	O
this	O
null	B-General_Concept
hypothesis	I-General_Concept
are	O
those	O
with	O
a	O
large	O
number	O
of	O
heads	O
or	O
a	O
large	O
number	O
of	O
tails	O
,	O
and	O
our	O
experiment	O
with	O
5	O
heads	O
would	O
seem	O
to	O
belong	O
to	O
this	O
class	O
.	O
</s>
<s>
Hence	O
,	O
under	O
this	O
two-tailed	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
the	O
observation	O
receives	O
a	O
probability	B-General_Concept
value	I-General_Concept
of	O
0.063	O
.	O
</s>
<s>
Hence	O
again	O
,	O
with	O
the	O
same	O
significance	O
threshold	O
used	O
for	O
the	O
one-tailed	B-General_Concept
test	I-General_Concept
(	O
0.05	O
)	O
,	O
the	O
same	O
outcome	O
is	O
not	O
statistically	B-General_Concept
significant	I-General_Concept
.	O
</s>
<s>
Therefore	O
,	O
the	O
two-tailed	O
null	B-General_Concept
hypothesis	I-General_Concept
will	O
be	O
preserved	O
in	O
this	O
case	O
,	O
not	O
supporting	O
the	O
conclusion	O
reached	O
with	O
the	O
single-tailed	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
that	O
the	O
coin	O
is	O
biased	O
towards	O
heads	O
.	O
</s>
<s>
This	O
example	O
illustrates	O
that	O
the	O
conclusion	O
reached	O
from	O
a	O
statistical	O
test	O
may	O
depend	O
on	O
the	O
precise	O
formulation	O
of	O
the	O
null	O
and	O
alternative	B-General_Concept
hypotheses	I-General_Concept
.	O
</s>
<s>
Fisher	O
said	O
,	O
"	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
must	O
be	O
exact	O
,	O
that	O
is	O
free	O
of	O
vagueness	O
and	O
ambiguity	O
,	O
because	O
it	O
must	O
supply	O
the	O
basis	O
of	O
the	O
'	O
problem	O
of	O
distribution	O
,	O
'	O
of	O
which	O
the	O
test	O
of	O
significance	O
is	O
the	O
solution	O
"	O
,	O
implying	O
a	O
more	O
restrictive	O
domain	O
for	O
H0	O
.	O
</s>
<s>
According	O
to	O
this	O
view	O
,	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
must	O
be	O
numerically	O
exact	O
—	O
it	O
must	O
state	O
that	O
a	O
particular	O
quantity	O
or	O
difference	O
is	O
equal	O
to	O
a	O
particular	O
number	O
.	O
</s>
<s>
Most	O
statisticians	O
believe	O
that	O
it	O
is	O
valid	O
to	O
state	O
direction	O
as	O
a	O
part	O
of	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
or	O
as	O
part	O
of	O
a	O
null	O
hypothesis/alternative	O
hypothesis	O
pair	O
.	O
</s>
<s>
For	O
example	O
,	O
consider	O
an	O
H0	O
that	O
claims	O
the	O
population	O
mean	O
for	O
a	O
new	O
treatment	O
is	O
an	O
improvement	O
on	O
a	O
well-established	O
treatment	O
with	O
population	O
(	O
known	O
from	O
long	O
experience	O
)	O
,	O
with	O
the	O
one-tailed	B-General_Concept
alternative	O
being	O
that	O
the	O
new	O
treatment	O
's	O
.	O
</s>
<s>
To	O
overcome	O
any	O
possible	O
ambiguity	O
in	O
reporting	O
the	O
result	O
of	O
the	O
test	O
of	O
a	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
it	O
is	O
best	O
to	O
indicate	O
whether	O
the	O
test	O
was	O
two-sided	O
and	O
,	O
if	O
one-sided	O
,	O
to	O
include	O
the	O
direction	O
of	O
the	O
effect	O
being	O
tested	O
.	O
</s>
<s>
The	O
explicit	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
Fisher	O
's	O
Lady	O
tasting	O
tea	O
example	O
was	O
that	O
the	O
Lady	O
had	O
no	O
such	O
ability	O
,	O
which	O
led	O
to	O
a	O
symmetric	O
probability	O
distribution	O
.	O
</s>
<s>
The	O
one-tailed	B-General_Concept
nature	O
of	O
the	O
test	O
resulted	O
from	O
the	O
one-tailed	B-General_Concept
alternate	B-General_Concept
hypothesis	I-General_Concept
(	O
a	O
term	O
not	O
used	O
by	O
Fisher	O
)	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
became	O
implicitly	O
one-tailed	B-General_Concept
.	O
</s>
<s>
The	O
logical	O
negation	O
of	O
the	O
Lady	O
's	O
one-tailed	B-General_Concept
claim	O
was	O
also	O
one-tailed	B-General_Concept
.	O
</s>
<s>
Pure	O
arguments	O
over	O
the	O
use	O
of	O
one-tailed	B-General_Concept
tests	I-General_Concept
are	O
complicated	O
by	O
the	O
variety	O
of	O
tests	O
.	O
</s>
<s>
Some	O
tests	O
(	O
for	O
instance	O
the	O
χ2	O
goodness	O
of	O
fit	O
test	O
)	O
are	O
inherently	O
one-tailed	B-General_Concept
.	O
</s>
<s>
Advice	O
concerning	O
the	O
use	O
of	O
one-tailed	B-General_Concept
hypotheses	O
has	O
been	O
inconsistent	O
and	O
accepted	O
practice	O
varies	O
among	O
fields	O
.	O
</s>
<s>
The	O
greatest	O
objection	O
to	O
one-tailed	B-General_Concept
hypotheses	O
is	O
their	O
potential	O
subjectivity	O
.	O
</s>
<s>
A	O
non-significant	O
result	O
can	O
sometimes	O
be	O
converted	O
to	O
a	O
significant	O
result	O
by	O
the	O
use	O
of	O
a	O
one-tailed	B-General_Concept
hypothesis	I-General_Concept
(	O
as	O
the	O
fair	O
coin	O
test	O
,	O
at	O
the	O
whim	O
of	O
the	O
analyst	O
)	O
.	O
</s>
<s>
The	O
flip	O
side	O
of	O
the	O
argument	O
:	O
One-sided	B-General_Concept
tests	I-General_Concept
are	O
less	O
likely	O
to	O
ignore	O
a	O
real	O
effect	O
.	O
</s>
<s>
One-tailed	B-General_Concept
tests	I-General_Concept
can	O
suppress	O
the	O
publication	O
of	O
data	O
that	O
differs	O
in	O
sign	O
from	O
predictions	O
.	O
</s>
<s>
It	O
is	O
a	O
common	O
practice	O
to	O
use	O
a	O
one-tailed	B-General_Concept
hypothesis	I-General_Concept
by	O
default	O
.	O
</s>
<s>
Disagreements	O
over	O
one-tailed	B-General_Concept
tests	I-General_Concept
flow	O
from	O
the	O
philosophy	O
of	O
science	O
.	O
</s>
<s>
Poor	O
statistical	O
reporting	O
practices	O
have	O
contributed	O
to	O
disagreements	O
over	O
one-tailed	B-General_Concept
tests	I-General_Concept
.	O
</s>
<s>
Statistical	B-General_Concept
significance	I-General_Concept
resulting	O
from	O
two-tailed	B-General_Concept
tests	I-General_Concept
is	O
insensitive	O
to	O
the	O
sign	O
of	O
the	O
relationship	O
;	O
Reporting	O
significance	O
alone	O
is	O
inadequate	O
.	O
</s>
<s>
"	O
The	O
treatment	O
has	O
an	O
effect	O
"	O
is	O
the	O
uninformative	O
result	O
of	O
a	O
two-tailed	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
"	O
The	O
treatment	O
has	O
a	O
beneficial	O
effect	O
"	O
is	O
the	O
more	O
informative	O
result	O
of	O
a	O
one-tailed	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
Explicitly	O
reporting	O
a	O
numeric	O
result	O
eliminates	O
a	O
philosophical	O
advantage	O
of	O
a	O
one-tailed	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
The	O
history	O
of	O
the	O
null	O
and	O
alternative	B-General_Concept
hypotheses	I-General_Concept
is	O
embedded	O
in	O
the	O
history	O
of	O
statistical	O
tests	O
.	O
</s>
<s>
Before	O
1925	O
:	O
There	O
are	O
occasional	O
transient	O
traces	O
of	O
statistical	O
tests	O
for	O
centuries	O
in	O
the	O
past	O
,	O
which	O
provide	O
early	O
examples	O
of	O
null	B-General_Concept
hypotheses	I-General_Concept
.	O
</s>
<s>
In	O
the	O
late	O
19th	O
century	O
statistical	B-General_Concept
significance	I-General_Concept
was	O
defined	O
.	O
</s>
<s>
1925	O
:	O
Fisher	O
published	O
the	O
first	O
edition	O
of	O
Statistical	O
Methods	O
for	O
Research	O
Workers	O
which	O
defined	O
the	O
statistical	B-General_Concept
significance	I-General_Concept
test	O
and	O
made	O
it	O
a	O
mainstream	O
method	O
of	O
analysis	O
for	O
much	O
of	O
experimental	O
science	O
.	O
</s>
<s>
The	O
papers	O
provided	O
much	O
of	O
the	O
terminology	O
for	O
statistical	O
tests	O
including	O
alternative	B-General_Concept
hypothesis	I-General_Concept
and	O
H0	O
as	O
a	O
hypothesis	O
to	O
be	O
tested	O
using	O
observational	O
data	O
(	O
with	O
H1	O
,	O
H2	O
...	O
as	O
alternatives	O
)	O
.	O
</s>
<s>
Neyman	O
did	O
not	O
use	O
the	O
term	O
null	B-General_Concept
hypothesis	I-General_Concept
in	O
later	O
writings	O
about	O
his	O
method	O
.	O
</s>
<s>
1935	O
:	O
Fisher	O
published	O
the	O
first	O
edition	O
of	O
the	O
book	O
The	O
Design	O
of	O
Experiments	O
which	O
introduced	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
(	O
by	O
example	O
rather	O
than	O
by	O
definition	O
)	O
and	O
carefully	O
explained	O
the	O
rationale	O
for	O
significance	O
tests	O
in	O
the	O
context	O
of	O
the	O
interpretation	O
of	O
experimental	O
results	O
;	O
see	O
quotations	O
regarding	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
Statistical	B-General_Concept
significance	I-General_Concept
has	O
become	O
a	O
rigidly	O
defined	O
and	O
enforced	O
criterion	O
for	O
the	O
publication	O
of	O
experimental	O
results	O
in	O
many	O
scientific	O
journals	O
.	O
</s>
