<s>
In	O
statistical	O
hypothesis	O
testing	O
,	O
a	O
result	O
has	O
statistical	B-General_Concept
significance	I-General_Concept
when	O
a	O
result	O
at	O
least	O
as	O
"	O
extreme	O
"	O
would	O
be	O
very	O
infrequent	O
if	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
were	O
true	O
.	O
</s>
<s>
More	O
precisely	O
,	O
a	O
study	O
's	O
defined	O
significance	B-General_Concept
level	I-General_Concept
,	O
denoted	O
by	O
,	O
is	O
the	O
probability	O
of	O
the	O
study	O
rejecting	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
given	O
that	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
;	O
and	O
the	O
p-value	B-General_Concept
of	O
a	O
result	O
,	O
,	O
is	O
the	O
probability	O
of	O
obtaining	O
a	O
result	O
at	O
least	O
as	O
extreme	O
,	O
given	O
that	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
.	O
</s>
<s>
name	O
=	O
"	O
Johnson	O
"	O
>xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx1	O
The	O
significance	B-General_Concept
level	I-General_Concept
for	O
a	O
study	O
is	O
chosen	O
before	O
data	O
collection	O
,	O
and	O
is	O
typically	O
set	O
to	O
5%	O
or	O
much	O
lower	O
—	O
depending	O
on	O
the	O
field	O
of	O
study	O
.	O
</s>
<s>
But	O
if	O
the	O
p-value	B-General_Concept
of	O
an	O
observed	O
effect	O
is	O
less	O
than	O
(	O
or	O
equal	O
to	O
)	O
the	O
significance	B-General_Concept
level	I-General_Concept
,	O
an	O
investigator	O
may	O
conclude	O
that	O
the	O
effect	O
reflects	O
the	O
characteristics	O
of	O
the	O
whole	O
population	O
,	O
thereby	O
rejecting	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
This	O
technique	O
for	O
testing	O
the	O
statistical	B-General_Concept
significance	I-General_Concept
of	O
results	O
was	O
developed	O
in	O
the	O
early	O
20th	O
century	O
.	O
</s>
<s>
The	O
term	O
significance	O
does	O
not	O
imply	O
importance	O
here	O
,	O
and	O
the	O
term	O
statistical	B-General_Concept
significance	I-General_Concept
is	O
not	O
the	O
same	O
as	O
research	O
significance	O
,	O
theoretical	O
significance	O
,	O
or	O
practical	O
significance	O
.	O
</s>
<s>
Statistical	B-General_Concept
significance	I-General_Concept
dates	O
to	O
the	O
18th	O
century	O
,	O
in	O
the	O
work	O
of	O
John	O
Arbuthnot	O
and	O
Pierre-Simon	O
Laplace	O
,	O
who	O
computed	O
the	O
p-value	B-General_Concept
for	O
the	O
human	O
sex	O
ratio	O
at	O
birth	O
,	O
assuming	O
a	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
equal	O
probability	O
of	O
male	O
and	O
female	O
births	O
;	O
see	O
for	O
details	O
.	O
</s>
<s>
Fisher	O
suggested	O
a	O
probability	O
of	O
one	O
in	O
twenty	O
(	O
0.05	O
)	O
as	O
a	O
convenient	O
cutoff	O
level	O
to	O
reject	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
In	O
a	O
1933	O
paper	O
,	O
Jerzy	O
Neyman	O
and	O
Egon	O
Pearson	O
called	O
this	O
cutoff	O
the	O
significance	B-General_Concept
level	I-General_Concept
,	O
which	O
they	O
named	O
.	O
</s>
<s>
Despite	O
his	O
initial	O
suggestion	O
of	O
0.05	O
as	O
a	O
significance	B-General_Concept
level	I-General_Concept
,	O
Fisher	O
did	O
not	O
intend	O
this	O
cutoff	O
value	O
to	O
be	O
fixed	O
.	O
</s>
<s>
In	O
his	O
1956	O
publication	O
Statistical	O
Methods	O
and	O
Scientific	O
Inference	O
,	O
he	O
recommended	O
that	O
significance	B-General_Concept
levels	I-General_Concept
be	O
set	O
according	O
to	O
specific	O
circumstances	O
.	O
</s>
<s>
The	O
significance	B-General_Concept
level	I-General_Concept
is	O
the	O
threshold	O
for	O
below	O
which	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
rejected	O
even	O
though	O
by	O
assumption	O
it	O
were	O
true	O
,	O
and	O
something	O
else	O
is	O
going	O
on	O
.	O
</s>
<s>
This	O
means	O
that	O
is	O
also	O
the	O
probability	O
of	O
mistakenly	O
rejecting	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
if	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
.	O
</s>
<s>
This	O
is	O
the	O
probability	O
of	O
not	O
rejecting	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
given	O
that	O
it	O
is	O
true	O
.	O
</s>
<s>
Statistical	B-General_Concept
significance	I-General_Concept
plays	O
a	O
pivotal	O
role	O
in	O
statistical	O
hypothesis	O
testing	O
.	O
</s>
<s>
It	O
is	O
used	O
to	O
determine	O
whether	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
should	O
be	O
rejected	O
or	O
retained	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
the	O
default	O
assumption	O
that	O
nothing	O
happened	O
or	O
changed	O
.	O
</s>
<s>
For	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
to	O
be	O
rejected	O
,	O
an	O
observed	O
result	O
has	O
to	O
be	O
statistically	B-General_Concept
significant	I-General_Concept
,	O
i.e.	O
</s>
<s>
the	O
observed	O
p-value	B-General_Concept
is	O
less	O
than	O
the	O
pre-specified	O
significance	B-General_Concept
level	I-General_Concept
.	O
</s>
<s>
To	O
determine	O
whether	O
a	O
result	O
is	O
statistically	B-General_Concept
significant	I-General_Concept
,	O
a	O
researcher	O
calculates	O
a	O
p-value	B-General_Concept
,	O
which	O
is	O
the	O
probability	O
of	O
observing	O
an	O
effect	O
of	O
the	O
same	O
magnitude	O
or	O
more	O
extreme	O
given	O
that	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
rejected	O
if	O
the	O
p-value	B-General_Concept
is	O
less	O
than	O
(	O
or	O
equal	O
to	O
)	O
a	O
predetermined	O
level	O
,	O
.	O
</s>
<s>
is	O
also	O
called	O
the	O
significance	B-General_Concept
level	I-General_Concept
,	O
and	O
is	O
the	O
probability	O
of	O
rejecting	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
given	O
that	O
it	O
is	O
true	O
(	O
a	O
type	O
I	O
error	O
)	O
.	O
</s>
<s>
For	O
example	O
,	O
when	O
is	O
set	O
to	O
5%	O
,	O
the	O
conditional	O
probability	O
of	O
a	O
type	O
I	O
error	O
,	O
given	O
that	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
,	O
is	O
5%	O
,	O
and	O
a	O
statistically	B-General_Concept
significant	I-General_Concept
result	O
is	O
one	O
where	O
the	O
observed	O
p-value	B-General_Concept
is	O
less	O
than	O
(	O
or	O
equal	O
to	O
)	O
5%	O
.	O
</s>
<s>
When	O
drawing	O
data	O
from	O
a	O
sample	O
,	O
this	O
means	O
that	O
the	O
rejection	O
region	O
comprises	O
5%	O
of	O
the	O
sampling	B-General_Concept
distribution	I-General_Concept
.	O
</s>
<s>
These	O
5%	O
can	O
be	O
allocated	O
to	O
one	O
side	O
of	O
the	O
sampling	B-General_Concept
distribution	I-General_Concept
,	O
as	O
in	O
a	O
one-tailed	B-General_Concept
test	I-General_Concept
,	O
or	O
partitioned	O
to	O
both	O
sides	O
of	O
the	O
distribution	O
,	O
as	O
in	O
a	O
two-tailed	B-General_Concept
test	I-General_Concept
,	O
with	O
each	O
tail	O
(	O
or	O
rejection	O
region	O
)	O
containing	O
2.5	O
%	O
of	O
the	O
distribution	O
.	O
</s>
<s>
The	O
use	O
of	O
a	O
one-tailed	B-General_Concept
test	I-General_Concept
is	O
dependent	O
on	O
whether	O
the	O
research	O
question	O
or	O
alternative	B-General_Concept
hypothesis	I-General_Concept
specifies	O
a	O
direction	O
such	O
as	O
whether	O
a	O
group	O
of	O
objects	O
is	O
heavier	O
or	O
the	O
performance	O
of	O
students	O
on	O
an	O
assessment	O
is	O
better	O
.	O
</s>
<s>
A	O
two-tailed	B-General_Concept
test	I-General_Concept
may	O
still	O
be	O
used	O
but	O
it	O
will	O
be	O
less	O
powerful	B-General_Concept
than	O
a	O
one-tailed	B-General_Concept
test	I-General_Concept
,	O
because	O
the	O
rejection	O
region	O
for	O
a	O
one-tailed	B-General_Concept
test	I-General_Concept
is	O
concentrated	O
on	O
one	O
end	O
of	O
the	O
null	O
distribution	O
and	O
is	O
twice	O
the	O
size	O
(	O
5%	O
vs.	O
2.5	O
%	O
)	O
of	O
each	O
rejection	O
region	O
for	O
a	O
two-tailed	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
As	O
a	O
result	O
,	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
can	O
be	O
rejected	O
with	O
a	O
less	O
extreme	O
result	O
if	O
a	O
one-tailed	B-General_Concept
test	I-General_Concept
was	O
used	O
.	O
</s>
<s>
The	O
one-tailed	B-General_Concept
test	I-General_Concept
is	O
only	O
more	O
powerful	B-General_Concept
than	O
a	O
two-tailed	B-General_Concept
test	I-General_Concept
if	O
the	O
specified	O
direction	O
of	O
the	O
alternative	B-General_Concept
hypothesis	I-General_Concept
is	O
correct	O
.	O
</s>
<s>
If	O
it	O
is	O
wrong	O
,	O
however	O
,	O
then	O
the	O
one-tailed	B-General_Concept
test	I-General_Concept
has	O
no	O
power	O
.	O
</s>
<s>
In	O
specific	O
fields	O
such	O
as	O
particle	O
physics	O
and	O
manufacturing	O
,	O
statistical	B-General_Concept
significance	I-General_Concept
is	O
often	O
expressed	O
in	O
multiples	O
of	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
or	O
sigma	O
( σ	O
)	O
of	O
a	O
normal	O
distribution	O
,	O
with	O
significance	O
thresholds	O
set	O
at	O
a	O
much	O
stricter	O
level	O
(	O
for	O
example	O
5σ	O
)	O
.	O
</s>
<s>
For	O
instance	O
,	O
the	O
certainty	O
of	O
the	O
Higgs	O
boson	O
particle	O
's	O
existence	O
was	O
based	O
on	O
the	O
5σ	O
criterion	O
,	O
which	O
corresponds	O
to	O
a	O
p-value	B-General_Concept
of	O
about	O
1	O
in	O
3.5	O
million	O
.	O
</s>
<s>
In	O
other	O
fields	O
of	O
scientific	O
research	O
such	O
as	O
genome-wide	O
association	O
studies	O
,	O
significance	B-General_Concept
levels	I-General_Concept
as	O
low	O
as	O
are	O
not	O
uncommon	O
—	O
as	O
the	O
number	O
of	O
tests	O
performed	O
is	O
extremely	O
large	O
.	O
</s>
<s>
Researchers	O
focusing	O
solely	O
on	O
whether	O
their	O
results	O
are	O
statistically	B-General_Concept
significant	I-General_Concept
might	O
report	O
findings	O
that	O
are	O
not	O
substantive	O
and	O
not	O
replicable	O
.	O
</s>
<s>
There	O
is	O
also	O
a	O
difference	O
between	O
statistical	B-General_Concept
significance	I-General_Concept
and	O
practical	O
significance	O
.	O
</s>
<s>
A	O
study	O
that	O
is	O
found	O
to	O
be	O
statistically	B-General_Concept
significant	I-General_Concept
may	O
not	O
necessarily	O
be	O
practically	O
significant	O
.	O
</s>
<s>
Effect	B-Application
size	I-Application
is	O
a	O
measure	O
of	O
a	O
study	O
's	O
practical	O
significance	O
.	O
</s>
<s>
A	O
statistically	B-General_Concept
significant	I-General_Concept
result	O
may	O
have	O
a	O
weak	O
effect	O
.	O
</s>
<s>
To	O
gauge	O
the	O
research	O
significance	O
of	O
their	O
result	O
,	O
researchers	O
are	O
encouraged	O
to	O
always	O
report	O
an	O
effect	B-Application
size	I-Application
along	O
with	O
p-values	B-General_Concept
.	O
</s>
<s>
An	O
effect	B-Application
size	I-Application
measure	O
quantifies	O
the	O
strength	O
of	O
an	O
effect	O
,	O
such	O
as	O
the	O
distance	O
between	O
two	O
means	O
in	O
units	O
of	O
standard	B-General_Concept
deviation	I-General_Concept
(	O
cf	O
.	O
</s>
<s>
A	O
statistically	B-General_Concept
significant	I-General_Concept
result	O
may	O
not	O
be	O
easy	O
to	O
reproduce	O
.	O
</s>
<s>
In	O
particular	O
,	O
some	O
statistically	B-General_Concept
significant	I-General_Concept
results	O
will	O
in	O
fact	O
be	O
false	O
positives	O
.	O
</s>
<s>
Some	O
journals	O
encouraged	O
authors	O
to	O
do	O
more	O
detailed	O
analysis	O
than	O
just	O
a	O
statistical	B-General_Concept
significance	I-General_Concept
test	O
.	O
</s>
<s>
Other	O
editors	O
,	O
commenting	O
on	O
this	O
ban	O
have	O
noted	O
:	O
"	O
Banning	O
the	O
reporting	O
of	O
p-values	B-General_Concept
,	O
as	O
Basic	O
and	O
Applied	O
Social	O
Psychology	O
recently	O
did	O
,	O
is	O
not	O
going	O
to	O
solve	O
the	O
problem	O
because	O
it	O
is	O
merely	O
treating	O
a	O
symptom	O
of	O
the	O
problem	O
.	O
</s>
<s>
There	O
is	O
nothing	O
wrong	O
with	O
hypothesis	O
testing	O
and	O
p-values	B-General_Concept
per	O
se	O
as	O
long	O
as	O
authors	O
,	O
reviewers	O
,	O
and	O
action	O
editors	O
use	O
them	O
correctly.	O
"	O
</s>
<s>
Some	O
statisticians	O
prefer	O
to	O
use	O
alternative	O
measures	O
of	O
evidence	O
,	O
such	O
as	O
likelihood	O
ratios	O
or	O
Bayes	B-General_Concept
factors	I-General_Concept
.	O
</s>
<s>
The	O
widespread	O
abuse	O
of	O
statistical	B-General_Concept
significance	I-General_Concept
represents	O
an	O
important	O
topic	O
of	O
research	O
in	O
metascience	O
.	O
</s>
<s>
In	O
2016	O
,	O
the	O
American	O
Statistical	O
Association	O
(	O
ASA	O
)	O
published	O
a	O
statement	O
on	O
p-values	B-General_Concept
,	O
saying	O
that	O
"	O
the	O
widespread	O
use	O
of	O
'	O
statistical	B-General_Concept
significance	I-General_Concept
 '	O
(	O
generally	O
interpreted	O
as	O
'	O
p≤	O
0.05	O
'	O
)	O
as	O
a	O
license	O
for	O
making	O
a	O
claim	O
of	O
a	O
scientific	O
finding	O
(	O
or	O
implied	O
truth	O
)	O
leads	O
to	O
considerable	O
distortion	O
of	O
the	O
scientific	O
process	O
"	O
.	O
</s>
<s>
In	O
2017	O
,	O
a	O
group	O
of	O
72	O
authors	O
proposed	O
to	O
enhance	O
reproducibility	O
by	O
changing	O
the	O
p-value	B-General_Concept
threshold	O
for	O
statistical	B-General_Concept
significance	I-General_Concept
from	O
0.05	O
to	O
0.005	O
.	O
</s>
<s>
Other	O
researchers	O
responded	O
that	O
imposing	O
a	O
more	O
stringent	O
significance	O
threshold	O
would	O
aggravate	O
problems	O
such	O
as	O
data	B-Algorithm
dredging	I-Algorithm
;	O
alternative	O
propositions	O
are	O
thus	O
to	O
select	O
and	O
justify	O
flexible	O
p-value	B-General_Concept
thresholds	O
before	O
collecting	O
data	O
,	O
or	O
to	O
interpret	O
p-values	B-General_Concept
as	O
continuous	O
indices	O
,	O
thereby	O
discarding	O
thresholds	O
and	O
statistical	B-General_Concept
significance	I-General_Concept
.	O
</s>
<s>
In	O
2019	O
,	O
over	O
800	O
statisticians	O
and	O
scientists	O
signed	O
a	O
message	O
calling	O
for	O
the	O
abandonment	O
of	O
the	O
term	O
"	O
statistical	B-General_Concept
significance	I-General_Concept
"	O
in	O
science	O
,	O
and	O
the	O
ASA	O
published	O
a	O
further	O
official	O
statement	O
declaring	O
(	O
page	O
2	O
)	O
:	O
</s>
