<s>
Frequentist	B-General_Concept
inference	I-General_Concept
is	O
a	O
type	O
of	O
statistical	O
inference	O
based	O
in	O
frequentist	B-General_Concept
probability	O
,	O
which	O
treats	O
“	O
probability	O
”	O
in	O
equivalent	O
terms	O
to	O
“	O
frequency	O
”	O
and	O
draws	O
conclusions	O
from	O
sample-data	O
by	O
means	O
of	O
emphasizing	O
the	O
frequency	O
or	O
proportion	O
of	O
findings	O
in	O
the	O
data	O
.	O
</s>
<s>
Frequentist-inference	O
underlies	O
frequentist	B-General_Concept
statistics	I-General_Concept
,	O
in	O
which	O
the	O
well-established	O
methodologies	O
of	O
statistical	O
hypothesis	O
testing	O
and	O
confidence	O
intervals	O
are	O
founded	O
.	O
</s>
<s>
The	O
history	O
of	O
frequentist	B-General_Concept
statistics	I-General_Concept
is	O
more	O
recent	O
than	O
its	O
prevailing	O
philosophical	O
rival	O
,	O
Bayesian	O
statistics	O
.	O
</s>
<s>
Frequentist	B-General_Concept
statistics	I-General_Concept
were	O
largely	O
developed	O
in	O
the	O
early	O
20th	O
century	O
and	O
have	O
recently	O
developed	O
to	O
become	O
the	O
dominant	O
paradigm	O
in	O
inferential	O
statistics	O
,	O
while	O
Bayesian	O
statistics	O
were	O
invented	O
in	O
the	O
19th	O
century	O
.	O
</s>
<s>
Despite	O
this	O
dominance	O
,	O
there	O
is	O
no	O
agreement	O
as	O
to	O
whether	O
frequentism	O
is	O
better	O
than	O
Bayesian	O
statistics	O
,	O
with	O
a	O
vocal	O
minority	O
of	O
professionals	O
studying	O
statistical	O
inference	O
decrying	O
frequentist	B-General_Concept
inference	I-General_Concept
for	O
being	O
internally-inconsistent	O
.	O
</s>
<s>
For	O
the	O
purposes	O
of	O
this	O
article	O
,	O
frequentist	B-General_Concept
methodology	O
will	O
be	O
discussed	O
as	O
summarily	O
as	O
possible	O
but	O
it	O
is	O
worth	O
noting	O
that	O
this	O
subject	O
remains	O
controversial	O
even	O
into	O
the	O
modern	O
day	O
.	O
</s>
<s>
Ronald	O
Fisher	O
contributed	O
to	O
frequentist	B-General_Concept
statistics	I-General_Concept
by	O
developing	O
the	O
frequentist	B-General_Concept
concept	O
of	O
"	O
significance	O
testing	O
"	O
,	O
which	O
is	O
the	O
study	O
of	O
the	O
significance	O
of	O
a	O
measure	O
of	O
a	O
statistic	O
when	O
compared	O
to	O
the	O
hypothesis	O
.	O
</s>
<s>
To	O
construct	O
areas	O
of	O
uncertainty	O
in	O
frequentist	B-General_Concept
inference	I-General_Concept
,	O
a	O
pivot	O
is	O
used	O
which	O
defines	O
the	O
area	O
around	O
that	O
can	O
be	O
used	O
to	O
provide	O
an	O
interval	O
to	O
estimate	O
uncertainty	O
.	O
</s>
<s>
Two	O
complementary	O
concepts	O
in	O
frequentist	B-General_Concept
inference	I-General_Concept
are	O
the	O
Fisherian	O
reduction	O
and	O
the	O
Neyman-Pearson	O
operational	O
criteria	O
.	O
</s>
<s>
Together	O
these	O
concepts	O
illustrate	O
a	O
way	O
of	O
constructing	O
frequentist	B-General_Concept
intervals	O
that	O
define	O
the	O
limits	O
for	O
.	O
</s>
<s>
As	O
a	O
point	O
of	O
reference	O
,	O
the	O
complement	O
to	O
this	O
in	O
Bayesian	O
statistics	O
is	O
the	O
minimum	B-General_Concept
Bayes	I-General_Concept
risk	I-General_Concept
criterion	I-General_Concept
.	O
</s>
<s>
Frequentist	B-General_Concept
inferences	I-General_Concept
are	O
associated	O
with	O
the	O
application	O
frequentist	B-General_Concept
probability	O
to	O
experimental	O
design	O
and	O
interpretation	O
,	O
and	O
specifically	O
with	O
the	O
view	O
that	O
any	O
given	O
experiment	O
can	O
be	O
considered	O
one	O
of	O
an	O
infinite	O
sequence	O
of	O
possible	O
repetitions	O
of	O
the	O
same	O
experiment	O
,	O
each	O
capable	O
of	O
producing	O
statistically	O
independent	O
results	O
.	O
</s>
<s>
In	O
this	O
view	O
,	O
the	O
frequentist	B-General_Concept
inference	I-General_Concept
approach	O
to	O
drawing	O
conclusions	O
from	O
data	O
is	O
effectively	O
to	O
require	O
that	O
the	O
correct	O
conclusion	O
should	O
be	O
drawn	O
with	O
a	O
given	O
(	O
high	O
)	O
probability	O
,	O
among	O
this	O
notional	O
set	O
of	O
repetitions	O
.	O
</s>
<s>
This	O
is	O
especially	O
pertinent	O
because	O
the	O
significance	O
of	O
a	O
frequentist	B-General_Concept
test	O
can	O
vary	O
under	O
model	O
selection	O
,	O
a	O
violation	O
of	O
the	O
likelihood	O
principle	O
.	O
</s>
<s>
As	O
such	O
,	O
frequentist	B-General_Concept
analysis	O
must	O
be	O
formulated	O
with	O
consideration	O
to	O
the	O
assumptions	O
of	O
the	O
problem	O
frequentism	O
attempts	O
to	O
analyze	O
.	O
</s>
<s>
This	O
can	O
only	O
be	O
done	O
with	O
Bayesian	O
statistics	O
,	O
where	O
the	O
interpretation	O
of	O
probability	O
is	O
straightforward	O
because	O
Bayesian	O
statistics	O
is	O
conditional	O
on	O
the	O
entire	O
sample	O
space	O
,	O
whereas	O
frequentist	B-General_Concept
testing	O
is	O
concerned	O
with	O
the	O
whole	O
experimental	O
design	O
.	O
</s>
<s>
Frequentist	B-General_Concept
statistics	I-General_Concept
is	O
conditioned	O
not	O
on	O
solely	O
the	O
data	O
but	O
also	O
on	O
the	O
experimental	O
design	O
.	O
</s>
<s>
In	O
frequentist	B-General_Concept
statistics	I-General_Concept
,	O
the	O
cutoff	O
for	O
understanding	O
the	O
frequency	O
occurrence	O
is	O
derived	O
from	O
the	O
family	O
distribution	O
used	O
in	O
the	O
experiment	O
design	O
.	O
</s>
<s>
For	O
example	O
,	O
a	O
binomial	O
distribution	O
and	O
a	O
negative	O
binomial	O
distribution	O
can	O
be	O
used	O
to	O
analyze	O
exactly	O
the	O
same	O
data	O
,	O
but	O
because	O
their	O
tail	O
ends	O
are	O
different	O
the	O
frequentist	B-General_Concept
analysis	O
will	O
realize	O
different	O
levels	O
of	O
statistical	O
significance	O
for	O
the	O
same	O
data	O
that	O
assumes	O
different	O
probability	O
distributions	O
.	O
</s>
<s>
For	O
more	O
,	O
see	O
the	O
likelihood	O
principle	O
,	O
which	O
frequentist	B-General_Concept
statistics	I-General_Concept
inherently	O
violates	O
.	O
</s>
<s>
For	O
the	O
epidemiological	O
approach	O
,	O
the	O
central	O
idea	O
behind	O
frequentist	B-General_Concept
statistics	I-General_Concept
must	O
be	O
discussed	O
.	O
</s>
<s>
Frequentist	B-General_Concept
statistics	I-General_Concept
is	O
designed	O
so	O
that	O
,	O
in	O
the	O
long-run	O
,	O
the	O
frequency	O
of	O
a	O
statistic	O
may	O
be	O
understood	O
,	O
and	O
in	O
the	O
long-run	O
the	O
range	O
of	O
the	O
true	O
mean	O
of	O
a	O
statistic	O
can	O
be	O
inferred	O
.	O
</s>
<s>
This	O
allows	O
for	O
inference	O
where	O
,	O
in	O
the	O
long-run	O
,	O
we	O
can	O
define	O
that	O
the	O
combined	O
results	O
of	O
multiple	O
frequentist	B-General_Concept
inferences	I-General_Concept
to	O
mean	O
that	O
a	O
95%	O
confidence	O
interval	O
literally	O
means	O
the	O
true	O
mean	O
lies	O
in	O
the	O
confidence	O
interval	O
95%	O
of	O
the	O
time	O
,	O
but	O
not	O
that	O
the	O
mean	O
is	O
in	O
a	O
particular	O
confidence	O
interval	O
with	O
95%	O
certainty	O
.	O
</s>
<s>
Frequentist	B-General_Concept
inferences	I-General_Concept
stand	O
in	O
contrast	O
to	O
other	O
types	O
of	O
statistical	O
inferences	O
,	O
such	O
as	O
Bayesian	O
inferences	O
and	O
fiducial	B-Error_Name
inferences	I-Error_Name
.	O
</s>
<s>
Bayesian	O
inference	O
is	O
based	O
in	O
Bayesian	O
probability	O
,	O
which	O
treats	O
“	O
probability	O
”	O
as	O
equivalent	O
with	O
“	O
certainty	O
”	O
,	O
and	O
thus	O
that	O
the	O
essential	O
difference	O
between	O
the	O
frequentist	B-General_Concept
inference	I-General_Concept
and	O
the	O
Bayesian	O
inference	O
is	O
the	O
same	O
as	O
the	O
difference	O
between	O
the	O
two	O
interpretations	O
of	O
what	O
a	O
“	O
probability	O
”	O
means	O
.	O
</s>
<s>
There	O
are	O
two	O
major	O
differences	O
in	O
the	O
frequentist	B-General_Concept
and	O
Bayesian	O
approaches	O
to	O
inference	O
that	O
are	O
not	O
included	O
in	O
the	O
above	O
consideration	O
of	O
the	O
interpretation	O
of	O
probability	O
:	O
</s>
<s>
In	O
a	O
frequentist	B-General_Concept
approach	O
to	O
inference	O
,	O
unknown	O
parameters	O
are	O
typically	O
considered	O
as	O
being	O
fixed	O
,	O
rather	O
than	O
as	O
being	O
random	O
variates	O
.	O
</s>
<s>
The	O
result	O
of	O
a	O
frequentist	B-General_Concept
approach	O
is	O
either	O
a	O
decision	O
from	O
a	O
significance	O
test	O
or	O
a	O
confidence	O
interval	O
.	O
</s>
