<s>
In	O
statistical	O
hypothesis	O
testing	O
,	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
is	O
one	O
of	O
the	O
proposed	O
proposition	O
in	O
the	O
hypothesis	O
test	O
.	O
</s>
<s>
In	O
general	O
the	O
goal	O
of	O
hypothesis	O
test	O
is	O
to	O
demonstrate	O
that	O
in	O
the	O
given	O
condition	O
,	O
there	O
is	O
sufficient	O
evidence	O
supporting	O
the	O
credibility	O
of	O
alternative	B-General_Concept
hypothesis	I-General_Concept
instead	O
of	O
the	O
exclusive	O
proposition	O
in	O
the	O
test	O
(	O
null	B-General_Concept
hypothesis	I-General_Concept
)	O
.	O
</s>
<s>
However	O
,	O
the	O
research	O
hypothesis	O
is	O
sometimes	O
consistent	O
with	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
In	O
statistics	O
,	O
alternative	B-General_Concept
hypothesis	I-General_Concept
is	O
often	O
denoted	O
as	O
Ha	O
or	O
H1	O
.	O
</s>
<s>
The	O
alternative	B-General_Concept
hypothesis	I-General_Concept
and	O
null	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
judgments	O
on	O
the	O
basis	O
of	O
data	O
.	O
</s>
<s>
In	O
statistical	O
hypothesis	O
testing	O
,	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
and	O
alternative	B-General_Concept
hypothesis	I-General_Concept
are	O
two	O
mutually	O
exclusive	O
statements	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>
Null	B-General_Concept
hypothesis	I-General_Concept
is	O
often	O
denoted	O
as	O
H0	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>
Alternative	B-General_Concept
hypothesis	I-General_Concept
is	O
often	O
denoted	O
as	O
Ha	O
or	O
H1	O
.	O
</s>
<s>
In	O
statistical	O
hypothesis	O
testing	O
,	O
to	O
prove	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
,	O
it	O
should	O
be	O
shown	O
that	O
the	O
data	O
is	O
contradictory	O
to	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
Namely	O
,	O
there	O
is	O
sufficient	O
evidence	O
against	O
null	B-General_Concept
hypothesis	I-General_Concept
to	O
demonstrate	O
that	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
.	O
</s>
<s>
One	O
example	O
is	O
where	O
water	O
quality	O
in	O
a	O
stream	O
has	O
been	O
observed	O
over	O
many	O
years	O
,	O
and	O
a	O
test	O
is	O
made	O
of	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
that	O
"	O
there	O
is	O
no	O
change	O
in	O
quality	O
between	O
the	O
first	O
and	O
second	O
halves	O
of	O
the	O
data	O
"	O
,	O
against	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
that	O
"	O
the	O
quality	O
is	O
poorer	O
in	O
the	O
second	O
half	O
of	O
the	O
record	O
"	O
.	O
</s>
<s>
If	O
the	O
statistical	O
hypothesis	O
testing	O
is	O
thought	O
of	O
as	O
a	O
judgement	O
in	O
a	O
court	O
trial	O
,	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
corresponds	O
to	O
the	O
position	O
of	O
the	O
defendant	O
(	O
the	O
defendant	O
is	O
innocent	O
)	O
while	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
is	O
in	O
the	O
rival	O
position	O
of	O
prosecutor	O
(	O
the	O
defendant	O
is	O
guilty	O
)	O
.	O
</s>
<s>
The	O
defendant	O
is	O
innocent	O
until	O
proven	O
guilty	O
,	O
so	O
likewise	O
in	O
a	O
hypothesis	O
test	O
,	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
initially	O
presumed	O
to	O
be	O
true	O
.	O
</s>
<s>
To	O
prove	O
the	O
statement	O
of	O
the	O
prosecutor	O
,	O
evidence	O
must	O
be	O
convincing	O
enough	O
to	O
convict	O
the	O
defendant	O
;	O
this	O
is	O
analogous	O
to	O
sufficient	O
statistical	B-General_Concept
significance	I-General_Concept
in	O
a	O
hypothesis	O
test	O
.	O
</s>
<s>
As	O
for	O
hypothesis	O
testing	O
,	O
a	O
reasonable	O
test	B-General_Concept
statistic	I-General_Concept
should	O
be	O
set	O
to	O
measure	O
the	O
statistic	O
significance	O
of	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
Evidence	O
would	O
support	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
if	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
rejected	O
at	O
a	O
certain	O
significance	B-General_Concept
level	I-General_Concept
.	O
</s>
<s>
However	O
,	O
this	O
does	O
not	O
necessarily	O
mean	O
that	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
due	O
to	O
the	O
potential	O
presence	O
of	O
a	O
type	O
I	O
error	O
.	O
</s>
<s>
In	O
order	O
to	O
quantify	O
the	O
statistical	B-General_Concept
significance	I-General_Concept
,	O
the	O
test	B-General_Concept
statistic	I-General_Concept
variables	O
are	O
assumed	O
to	O
follow	O
a	O
certain	O
probability	O
distribution	O
such	O
as	O
the	O
normal	O
distribution	O
or	O
t-distribution	O
to	O
determine	O
the	O
probability	O
of	O
obtaining	O
test	O
results	O
at	O
least	O
as	O
extreme	O
as	O
the	O
results	O
actually	O
observed	O
,	O
under	O
the	O
assumption	O
that	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
correct	O
,	O
which	O
is	O
defined	O
as	O
the	O
p-value	B-General_Concept
.	O
</s>
<s>
If	O
the	O
p-value	B-General_Concept
is	O
smaller	O
than	O
the	O
than	O
the	O
chosen	O
significance	B-General_Concept
level	I-General_Concept
( α	O
)	O
,	O
it	O
can	O
be	O
claimed	O
that	O
observed	O
data	O
is	O
sufficiently	O
inconsistent	O
with	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
and	O
hence	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
may	O
be	O
rejected	O
.	O
</s>
<s>
After	O
testing	O
,	O
a	O
valid	O
claim	O
would	O
be	O
"	O
at	O
the	O
significance	B-General_Concept
level	I-General_Concept
of	O
( α	O
)	O
,	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
rejected	O
,	O
supporting	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
instead	O
"	O
.	O
</s>
<s>
The	O
concept	O
of	O
an	O
alternative	B-General_Concept
hypothesis	I-General_Concept
in	O
testing	O
was	O
devised	O
by	O
Jerzy	O
Neyman	O
and	O
Egon	O
Pearson	O
,	O
and	O
it	O
is	O
used	O
in	O
the	O
Neyman	O
–	O
Pearson	O
lemma	O
.	O
</s>
<s>
In	O
Fisher	O
's	O
approach	O
to	O
testing	O
,	O
the	O
central	O
idea	O
is	O
to	O
assess	O
whether	O
the	O
observed	O
dataset	O
could	O
have	O
resulted	O
from	O
chance	O
if	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
were	O
assumed	O
to	O
hold	O
,	O
notionally	O
without	O
preconceptions	O
about	O
what	O
other	O
models	O
might	O
hold	O
.	O
</s>
<s>
Modern	O
statistical	O
hypothesis	O
testing	O
accommodates	O
this	O
type	O
of	O
test	O
since	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
can	O
be	O
just	O
the	O
negation	O
of	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
In	O
the	O
case	O
of	O
a	O
scalar	O
parameter	O
,	O
there	O
are	O
four	O
principal	O
types	O
of	O
alternative	B-General_Concept
hypothesis	I-General_Concept
:	O
</s>
<s>
Point	O
alternative	B-General_Concept
hypotheses	I-General_Concept
occur	O
when	O
the	O
hypothesis	O
test	O
is	O
framed	O
so	O
that	O
the	O
population	O
distribution	O
under	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
is	O
a	O
fully	O
defined	O
distribution	O
,	O
with	O
no	O
unknown	O
parameters	O
;	O
such	O
hypotheses	O
are	O
usually	O
of	O
no	O
practical	O
interest	O
but	O
are	O
fundamental	O
to	O
theoretical	O
considerations	O
of	O
statistical	O
inference	O
and	O
are	O
the	O
basis	O
of	O
the	O
Neyman	O
–	O
Pearson	O
lemma	O
.	O
</s>
<s>
A	O
one-tailed	O
directional	O
alternative	B-General_Concept
hypothesis	I-General_Concept
is	O
concerned	O
with	O
the	O
region	O
of	O
rejection	O
for	O
only	O
one	O
tail	O
of	O
the	O
sampling	O
distribution	O
.	O
</s>
<s>
A	O
two-tailed	O
directional	O
alternative	B-General_Concept
hypothesis	I-General_Concept
is	O
concerned	O
with	O
both	O
regions	O
of	O
rejection	O
of	O
the	O
sampling	O
distribution	O
.	O
</s>
<s>
A	O
non-directional	O
alternative	B-General_Concept
hypothesis	I-General_Concept
is	O
not	O
concerned	O
with	O
either	O
region	O
of	O
rejection	O
,	O
but	O
,	O
rather	O
,	O
it	O
is	O
only	O
concerned	O
that	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
not	O
true	O
.	O
</s>
