<s>
Equivalence	B-General_Concept
tests	I-General_Concept
are	O
a	O
variety	O
of	O
hypothesis	O
tests	O
used	O
to	O
draw	O
statistical	O
inferences	O
from	O
observed	O
data	O
.	O
</s>
<s>
In	O
these	O
tests	O
,	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
defined	O
as	O
an	O
effect	O
large	O
enough	O
to	O
be	O
deemed	O
interesting	O
,	O
specified	O
by	O
an	O
equivalence	O
bound	O
.	O
</s>
<s>
If	O
the	O
statistical	O
test	O
indicates	O
the	O
observed	O
data	O
is	O
surprising	O
,	O
assuming	O
that	O
true	O
effects	O
are	O
at	O
least	O
as	O
extreme	O
as	O
the	O
equivalence	O
bounds	O
,	O
a	O
Neyman-Pearson	O
approach	O
to	O
statistical	O
inferences	O
can	O
be	O
used	O
to	O
reject	O
effect	B-Application
sizes	I-Application
larger	O
than	O
the	O
equivalence	O
bounds	O
with	O
a	O
pre-specified	O
Type	O
1	O
error	O
rate	O
.	O
</s>
<s>
In	O
essence	O
,	O
equivalence	B-General_Concept
tests	I-General_Concept
consist	O
of	O
calculating	O
a	O
confidence	O
interval	O
around	O
an	O
observed	O
effect	B-Application
size	I-Application
and	O
rejecting	O
effects	O
more	O
extreme	O
than	O
the	O
equivalence	O
bound	O
when	O
the	O
confidence	O
interval	O
does	O
not	O
overlap	O
with	O
the	O
equivalence	O
bound	O
.	O
</s>
<s>
Equivalence	B-General_Concept
tests	I-General_Concept
can	O
be	O
performed	O
in	O
addition	O
to	O
null-hypothesis	B-General_Concept
significance	O
tests	O
.	O
</s>
<s>
Furthermore	O
,	O
equivalence	B-General_Concept
tests	I-General_Concept
can	O
identify	O
effects	O
that	O
are	O
statistically	O
significant	O
but	O
practically	O
insignificant	O
,	O
whenever	O
effects	O
are	O
statistically	O
different	O
from	O
zero	O
,	O
but	O
also	O
statistically	O
smaller	O
than	O
any	O
effect	B-Application
size	I-Application
deemed	O
worthwhile	O
(	O
see	O
the	O
first	O
figure	O
)	O
.	O
</s>
<s>
Equivalence	B-General_Concept
tests	I-General_Concept
were	O
originally	O
used	O
in	O
areas	O
such	O
as	O
pharmaceutics	O
,	O
frequently	O
in	O
bioequivalence	O
trials	O
.	O
</s>
<s>
In	O
this	O
regard	O
,	O
equivalence	B-General_Concept
tests	I-General_Concept
have	O
recently	O
been	O
introduced	O
in	O
evaluation	O
of	O
measurement	O
devices	O
,	O
artificial	O
intelligence	O
as	O
well	O
as	O
exercise	O
physiology	O
and	O
sports	O
science	O
.	O
</s>
<s>
Several	O
tests	O
exist	O
for	O
equivalence	O
analyses	O
;	O
however	O
,	O
more	O
recently	O
the	O
two-one-sided	O
t-tests	B-General_Concept
(	O
TOST	O
)	O
procedure	O
has	O
been	O
garnering	O
considerable	O
attention	O
.	O
</s>
<s>
As	O
outlined	O
below	O
,	O
this	O
approach	O
is	O
an	O
adaptation	O
of	O
the	O
widely	O
known	O
t-test	B-General_Concept
.	O
</s>
<s>
A	O
very	O
simple	O
equivalence	O
testing	O
approach	O
is	O
the	O
‘	O
two	O
one-sided	O
t-tests	B-General_Concept
’	O
(	O
TOST	O
)	O
procedure	O
.	O
</s>
<s>
In	O
the	O
TOST	O
procedure	O
an	O
upper	O
( ΔU	O
)	O
and	O
lower	O
(	O
–	O
ΔL	O
)	O
equivalence	O
bound	O
is	O
specified	O
based	O
on	O
the	O
smallest	O
effect	B-Application
size	I-Application
of	O
interest	O
(	O
e.g.	O
,	O
a	O
positive	O
or	O
negative	O
difference	O
of	O
d	O
=	O
0.3	O
)	O
.	O
</s>
<s>
Two	O
composite	O
null	B-General_Concept
hypotheses	I-General_Concept
are	O
tested	O
:	O
H01	O
:	O
Δ	O
≤	O
–	O
ΔL	O
and	O
H02	O
:	O
Δ	O
≥	O
ΔU	O
.	O
</s>
<s>
The	O
equivalence	B-General_Concept
test	I-General_Concept
can	O
be	O
induced	O
from	O
the	O
t-test	B-General_Concept
.	O
</s>
<s>
Consider	O
a	O
t-test	B-General_Concept
at	O
the	O
significance	O
level	O
αt-test	O
with	O
a	O
power	B-General_Concept
of	O
1-βt-test	O
for	O
a	O
relevant	O
effect	B-Application
size	I-Application
dr.	O
</s>
<s>
If	O
Δ	O
=	O
dr	O
as	O
well	O
as	O
αequiv.-test	O
=	O
βt-test	O
and	O
βequiv.-test	O
=	O
αt-test	O
coincide	O
,	O
i.e.	O
</s>
<s>
the	O
error	O
types	O
(	O
type	O
I	O
and	O
type	O
II	O
)	O
are	O
interchanged	O
between	O
the	O
t-test	B-General_Concept
and	O
the	O
equivalence	B-General_Concept
test	I-General_Concept
,	O
then	O
the	O
t-test	B-General_Concept
will	O
obtain	O
the	O
same	O
results	O
as	O
the	O
equivalence	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
To	O
achieve	O
this	O
for	O
the	O
t-test	B-General_Concept
,	O
either	O
the	O
sample	O
size	O
calculation	O
needs	O
to	O
be	O
carried	O
out	O
correctly	O
,	O
or	O
the	O
t-test	B-General_Concept
significance	O
level	O
αt-test	O
needs	O
to	O
be	O
adjusted	O
,	O
referred	O
to	O
as	O
the	O
so-called	O
revised	O
t-test	B-General_Concept
.	O
</s>
<s>
Both	O
approaches	O
have	O
difficulties	O
in	O
practice	O
since	O
sample	O
size	O
planning	O
relies	O
on	O
unverifiable	O
assumptions	O
of	O
the	O
standard	O
deviation	O
,	O
and	O
the	O
revised	O
t-test	B-General_Concept
yields	O
numerical	O
problems	O
.	O
</s>
<s>
Preserving	O
the	O
test	O
behavior	O
,	O
those	O
limitations	O
can	O
be	O
removed	O
by	O
using	O
an	O
equivalence	B-General_Concept
test	I-General_Concept
.	O
</s>
<s>
The	O
figure	O
below	O
allows	O
a	O
visual	O
comparison	O
of	O
the	O
equivalence	B-General_Concept
test	I-General_Concept
and	O
the	O
t-test	B-General_Concept
when	O
the	O
sample	O
size	O
calculation	O
is	O
affected	O
by	O
differences	O
between	O
the	O
a	O
priori	O
standard	O
deviation	O
and	O
the	O
sample	O
's	O
standard	O
deviation	O
,	O
which	O
is	O
a	O
common	O
problem	O
.	O
</s>
<s>
Using	O
an	O
equivalence	B-General_Concept
test	I-General_Concept
instead	O
of	O
a	O
t-test	B-General_Concept
additionally	O
ensures	O
that	O
αequiv.-test	O
is	O
bounded	O
,	O
which	O
the	O
t-test	B-General_Concept
does	O
not	O
do	O
in	O
case	O
that	O
with	O
the	O
type	O
II	O
error	O
growing	O
arbitrary	O
large	O
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
having	O
results	O
in	O
the	O
t-test	B-General_Concept
being	O
stricter	O
than	O
the	O
dr	O
specified	O
in	O
the	O
planning	O
,	O
which	O
may	O
randomly	O
penalize	O
the	O
sample	O
source	O
(	O
e.g.	O
,	O
a	O
device	O
manufacturer	O
)	O
.	O
</s>
<s>
This	O
makes	O
the	O
equivalence	B-General_Concept
test	I-General_Concept
safer	O
to	O
use	O
.	O
</s>
