<s>
Data	B-Algorithm
dredging	I-Algorithm
(	O
also	O
known	O
as	O
data	B-Algorithm
snooping	I-Algorithm
or	O
p-hacking	B-Algorithm
)	O
is	O
the	O
misuse	O
of	O
data	B-General_Concept
analysis	I-General_Concept
to	O
find	O
patterns	O
in	O
data	O
that	O
can	O
be	O
presented	O
as	O
statistically	B-General_Concept
significant	I-General_Concept
,	O
thus	O
dramatically	O
increasing	O
and	O
understating	O
the	O
risk	O
of	O
false	O
positives	O
.	O
</s>
<s>
The	O
process	O
of	O
data	B-Algorithm
dredging	I-Algorithm
involves	O
testing	O
multiple	O
hypotheses	O
using	O
a	O
single	O
data	B-General_Concept
set	I-General_Concept
by	O
exhaustively	B-Algorithm
searching	I-Algorithm
—	O
perhaps	O
for	O
combinations	O
of	O
variables	O
that	O
might	O
show	O
a	O
correlation	O
,	O
and	O
perhaps	O
for	O
groups	O
of	O
cases	O
or	O
observations	O
that	O
show	O
differences	O
in	O
their	O
mean	O
or	O
in	O
their	O
breakdown	O
by	O
some	O
other	O
variable	O
.	O
</s>
<s>
Conventional	O
tests	O
of	O
statistical	B-General_Concept
significance	I-General_Concept
are	O
based	O
on	O
the	O
probability	O
that	O
a	O
particular	O
result	O
would	O
arise	O
if	O
chance	O
alone	O
were	O
at	O
work	O
,	O
and	O
necessarily	O
accept	O
some	O
risk	O
of	O
mistaken	O
conclusions	O
of	O
a	O
certain	O
type	O
(	O
mistaken	O
rejections	O
of	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
)	O
.	O
</s>
<s>
When	O
large	O
numbers	O
of	O
tests	O
are	O
performed	O
,	O
some	O
produce	O
false	O
results	O
of	O
this	O
type	O
;	O
hence	O
5%	O
of	O
randomly	O
chosen	O
hypotheses	O
might	O
be	O
(	O
erroneously	O
)	O
reported	O
to	O
be	O
statistically	B-General_Concept
significant	I-General_Concept
at	O
the	O
5%	O
significance	B-General_Concept
level	I-General_Concept
,	O
1%	O
might	O
be	O
(	O
erroneously	O
)	O
reported	O
to	O
be	O
statistically	B-General_Concept
significant	I-General_Concept
at	O
the	O
1%	O
significance	B-General_Concept
level	I-General_Concept
,	O
and	O
so	O
on	O
,	O
by	O
chance	O
alone	O
.	O
</s>
<s>
When	O
enough	O
hypotheses	O
are	O
tested	O
,	O
it	O
is	O
virtually	O
certain	O
that	O
some	O
will	O
be	O
reported	O
to	O
be	O
statistically	B-General_Concept
significant	I-General_Concept
(	O
even	O
though	O
this	O
is	O
misleading	O
)	O
,	O
since	O
almost	O
every	O
data	B-General_Concept
set	I-General_Concept
with	O
any	O
degree	O
of	O
randomness	O
is	O
likely	O
to	O
contain	O
(	O
for	O
example	O
)	O
some	O
spurious	O
correlations	O
.	O
</s>
<s>
Data	B-Algorithm
dredging	I-Algorithm
is	O
an	O
example	O
of	O
disregarding	O
the	O
multiple	B-General_Concept
comparisons	I-General_Concept
problem	I-General_Concept
.	O
</s>
<s>
The	O
conventional	O
frequentist	O
statistical	O
hypothesis	O
testing	O
procedure	O
is	O
to	O
formulate	O
a	O
research	O
hypothesis	O
,	O
such	O
as	O
"	O
people	O
in	O
higher	O
social	O
classes	O
live	O
longer	O
"	O
,	O
then	O
collect	O
relevant	O
data	O
,	O
followed	O
by	O
carrying	O
out	O
a	O
statistical	B-General_Concept
significance	I-General_Concept
test	O
to	O
see	O
how	O
likely	O
such	O
results	O
would	O
be	O
found	O
if	O
chance	O
alone	O
were	O
at	O
work	O
.	O
</s>
<s>
(	O
The	O
last	O
step	O
is	O
called	O
testing	O
against	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
)	O
</s>
<s>
This	O
is	O
critical	O
because	O
every	O
data	B-General_Concept
set	I-General_Concept
contains	O
some	O
patterns	O
due	O
entirely	O
to	O
chance	O
.	O
</s>
<s>
If	O
the	O
hypothesis	O
is	O
not	O
tested	O
on	O
a	O
different	O
data	B-General_Concept
set	I-General_Concept
from	O
the	O
same	O
statistical	O
population	O
,	O
it	O
is	O
impossible	O
to	O
assess	O
the	O
likelihood	O
that	O
chance	O
alone	O
would	O
produce	O
such	O
patterns	O
.	O
</s>
<s>
If	O
this	O
hypothesis	O
is	O
then	O
tested	O
on	O
the	O
existing	O
data	B-General_Concept
set	I-General_Concept
,	O
it	O
is	O
confirmed	O
,	O
but	O
the	O
confirmation	O
is	O
meaningless	O
.	O
</s>
<s>
It	O
is	O
important	O
to	O
realize	O
that	O
the	O
statistical	B-General_Concept
significance	I-General_Concept
under	O
the	O
incorrect	O
procedure	O
is	O
completely	O
spurious	O
–	O
significance	O
tests	O
do	O
not	O
protect	O
against	O
data	B-Algorithm
dredging	I-Algorithm
.	O
</s>
<s>
Someone	O
engaged	O
in	O
data	B-Algorithm
snooping	I-Algorithm
might	O
try	O
to	O
find	O
additional	O
similarities	O
between	O
Mary	O
and	O
John	O
.	O
</s>
<s>
A	O
hypothesis	O
,	O
biased	O
by	O
data	B-Algorithm
snooping	I-Algorithm
,	O
could	O
then	O
be	O
"	O
People	O
born	O
on	O
August	O
7	O
have	O
a	O
much	O
higher	O
chance	O
of	O
switching	O
minors	O
more	O
than	O
twice	O
in	O
college.	O
"	O
</s>
<s>
By	O
selecting	O
papers	O
with	O
a	O
significant	O
p-value	B-General_Concept
,	O
negative	O
studies	O
are	O
selected	O
against	O
—	O
which	O
is	O
the	O
publication	O
bias	O
.	O
</s>
<s>
This	O
is	O
also	O
known	O
as	O
"	O
file	O
drawer	O
bias	O
"	O
,	O
because	O
less	O
significant	O
p-value	B-General_Concept
results	O
are	O
left	O
in	O
the	O
file	O
drawer	O
and	O
never	O
published	O
.	O
</s>
<s>
Not	O
only	O
does	O
this	O
alter	O
the	O
performance	O
of	O
all	O
subsequent	O
tests	O
on	O
the	O
retained	O
explanatory	O
model	O
,	O
but	O
it	O
may	O
also	O
introduce	O
bias	O
and	O
alter	O
mean	B-Algorithm
square	I-Algorithm
error	I-Algorithm
in	O
estimation	O
.	O
</s>
<s>
Of	O
course	O
,	O
such	O
a	O
discipline	O
necessitates	O
waiting	O
for	O
new	O
data	O
to	O
come	O
in	O
,	O
to	O
show	O
the	O
formulated	O
theory	O
's	O
predictive	O
power	O
versus	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
This	O
process	O
ensures	O
that	O
no	O
one	O
can	O
accuse	O
the	O
researcher	O
of	O
hand-tailoring	O
the	O
predictive	B-General_Concept
model	I-General_Concept
to	O
the	O
data	O
on	O
hand	O
,	O
since	O
the	O
upcoming	O
weather	O
is	O
not	O
yet	O
available	O
.	O
</s>
<s>
Note	O
that	O
a	O
p-value	B-General_Concept
of	O
0.01	O
suggests	O
that	O
1%	O
of	O
the	O
time	O
a	O
result	O
at	O
least	O
that	O
extreme	O
would	O
be	O
obtained	O
by	O
chance	O
;	O
if	O
hundreds	O
or	O
thousands	O
of	O
hypotheses	O
(	O
with	O
mutually	O
relatively	O
uncorrelated	O
independent	O
variables	O
)	O
are	O
tested	O
,	O
then	O
one	O
is	O
likely	O
to	O
obtain	O
a	O
p-value	B-General_Concept
less	O
than	O
0.01	O
for	O
many	O
null	B-General_Concept
hypotheses	I-General_Concept
.	O
</s>
<s>
This	O
is	O
an	O
important	O
finding	O
because	O
t-values	O
are	O
inversely	O
proportional	O
to	O
p-values	B-General_Concept
,	O
meaning	O
higher	O
t-values	O
(	O
t	O
>	O
2.8	O
)	O
indicate	O
lower	O
p-values	B-General_Concept
.	O
</s>
<s>
By	O
controlling	O
for	O
gender	O
,	O
one	O
can	O
artificially	O
inflate	O
the	O
t-value	O
,	O
thus	O
artificially	O
deflating	O
the	O
p-value	B-General_Concept
as	O
well	O
.	O
</s>
<s>
According	O
to	O
Bohannon	O
,	O
to	O
reduce	O
the	O
p-value	B-General_Concept
to	O
below	O
0.05	O
,	O
taking	O
18	O
different	O
variables	O
into	O
consideration	O
when	O
testing	O
was	O
crucial	O
.	O
</s>
<s>
One	O
way	O
to	O
construct	O
hypotheses	O
while	O
avoiding	O
data	B-Algorithm
dredging	I-Algorithm
is	O
to	O
conduct	O
randomized	O
out-of-sample	O
tests	O
.	O
</s>
<s>
The	O
researcher	O
collects	O
a	O
data	B-General_Concept
set	I-General_Concept
,	O
then	O
randomly	O
partitions	O
it	O
into	O
two	O
subsets	O
,	O
A	O
and	O
B	O
.	O
</s>
<s>
(	O
This	O
is	O
a	O
simple	O
type	O
of	O
cross-validation	B-Application
and	O
is	O
often	O
termed	O
training-test	O
or	O
split-half	O
validation	O
.	O
)	O
</s>
<s>
Another	O
remedy	O
for	O
data	B-Algorithm
dredging	I-Algorithm
is	O
to	O
record	O
the	O
number	O
of	O
all	O
significance	O
tests	O
conducted	O
during	O
the	O
study	O
and	O
simply	O
divide	O
one	O
's	O
criterion	O
for	O
significance	O
(	O
"	O
alpha	O
"	O
)	O
by	O
this	O
number	O
;	O
this	O
is	O
the	O
Bonferroni	B-General_Concept
correction	I-General_Concept
.	O
</s>
<s>
Methods	O
particularly	O
useful	O
in	O
analysis	O
of	O
variance	O
,	O
and	O
in	O
constructing	O
simultaneous	O
confidence	O
bands	O
for	O
regressions	O
involving	O
basis	O
functions	O
are	O
the	O
Scheffé	O
method	O
and	O
,	O
if	O
the	O
researcher	O
has	O
in	O
mind	O
only	O
pairwise	O
comparisons	O
,	O
the	O
Tukey	B-General_Concept
method	I-General_Concept
.	O
</s>
<s>
The	O
use	O
of	O
Benjamini	O
and	O
Hochberg	O
's	O
false	B-General_Concept
discovery	I-General_Concept
rate	I-General_Concept
is	O
a	O
more	O
sophisticated	O
approach	O
that	O
has	O
become	O
a	O
popular	O
method	O
for	O
control	O
of	O
multiple	O
hypothesis	O
tests	O
.	O
</s>
<s>
When	O
neither	O
approach	O
is	O
practical	O
,	O
one	O
can	O
make	O
a	O
clear	O
distinction	O
between	O
data	O
analyses	O
that	O
are	O
confirmatory	O
and	O
analyses	O
that	O
are	O
exploratory	B-General_Concept
.	O
</s>
<s>
Ultimately	O
,	O
the	O
statistical	B-General_Concept
significance	I-General_Concept
of	O
a	O
test	O
and	O
the	O
statistical	O
confidence	O
of	O
a	O
finding	O
are	O
joint	O
properties	O
of	O
data	O
and	O
the	O
method	O
used	O
to	O
examine	O
the	O
data	O
.	O
</s>
<s>
No	O
claim	O
of	O
statistical	B-General_Concept
significance	I-General_Concept
can	O
be	O
made	O
by	O
only	O
looking	O
,	O
without	O
due	O
regard	O
to	O
the	O
method	O
used	O
to	O
assess	O
the	O
data	O
.	O
</s>
<s>
Academic	O
journals	O
increasingly	O
shift	O
to	O
the	O
registered	O
report	O
format	O
,	O
which	O
aims	O
to	O
counteract	O
very	O
serious	O
issues	O
such	O
as	O
data	B-Algorithm
dredging	I-Algorithm
and	O
,	O
which	O
have	O
made	O
theory-testing	O
research	O
very	O
unreliable	O
.	O
</s>
<s>
Methods	O
and	O
results	O
can	O
also	O
be	O
made	O
publicly	O
available	O
,	O
as	O
in	O
the	O
open	O
science	O
approach	O
,	O
making	O
it	O
yet	O
more	O
difficult	O
for	O
data	B-Algorithm
dredging	I-Algorithm
to	O
take	O
place	O
.	O
</s>
