Hypothesis Testing Overview
Golde Holtzman
HypTest6Step.doc
10/31/2006
Model
and
assumptions
,
e.g.,
Y
~N(?,
σ
)
H
0
:
μ
=
μ
0
H
A
:
μ
<
μ
0
,
μ
>
μ
0
,
μ
≠
μ
0
Design
α
= 0.01, 0.05, 0.10
n
⇒
β
, 1
β
≡
Power
Perform Survey, Experiment, or Observational Study.
Estimator, Standard error, C.I., Test Criterion
Pvalue
P <
α
P >
α
Decision
Reject H
0
NOT Reject H
0
Characterize
Statistically Sig, or
NOT Stat Sig
Conclusion
Method. Assuming [
Y
~N(?,
σ
), verbally], we tested [H
0
vs. H
A
, verbally], using the ztest ([cite
reference]) with significance level [
α
] and sample size [
n
].
Results. There
is
significant statistical evidence that [H
A
, verbally] ([Pvalue]).
There
is NOT
significant statistical evidence that [H
A
, verbally] ([Pvalue]).
Truth Table
True State of Nature
Decision
H
0
H
A
Reject H
0
Type 1 error,
α
Correct Decision,
(1
−
β
)
≡
Power
NOT Reject H
0
Correct
Decision
Type 2 error,
β ≡
O.C.
P
≡
Pvalue
≡
The probability that the distance between
the estimator and the hypothetical
value of the
parameter, in the direction specified by H
A
, would be
as great or greater as that observed, if H
0
were true.
α
≡
significance level
≡
Type 1 error rate, is set by investigator in Design step.
β
≡
operating characteristic
≡
Type 2 error rate =
f
(
δ
;
α
,
n
,
σ
),
δ = μ

μ
0
, i.e., is a function of (i) the
effect
, i.e., the difference between the true and the hypothetical (null) value of the parameter of
interest, (ii) the significance level, (iii) the sample size, and (iv) the underlying variability.
(1
−
β
)
≡
Power
≡
P{Reject H
0

δ
;
α
,
n
,
σ
} = 1
−
f
(
δ
;
α
,
n
,
σ
).
Effect
≡
δ
=
μ
−
μ
0
.
The hypotheses, in
terms of the effect, are
H
0
:
δ
= 0
H
A
:
δ
< 0,
δ
> 0, or
δ
≠
0
Estimated Effect
0
ˆ
μδ
−
=
≡
Y
PValue
= the
probability that the
estimated effect would
be as great as or
greater than that
observed, in the
direction specified by
H
A
, if H
0
were true.
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View Full DocumentHypothesis Testing Overview
Golde Holtzman
HypTest6Step.doc
10/31/2006
Significance level,
α
Sample size,
n
Underlying variability,
σ
Type 1 error rate,
α
Type 2 error rate,
β
Controlled by investigator
Guiding objectives of
Hypothesis Testing
Power, (1
−β
)
−
+
−
−
Effect,
δ
= (
θ − θ
0
)
+
−
α
=
significance level
=
Type 1 error rate
= probability of
rejecting
a
true
null hypothesis.
β
= operating characteristic =
Type 2 error rate
= probability of
not rejecting
a
false
null hypothesis.
(
1
−
β
)
=
power
= sensitivity = probability of
rejecting
a
false
null hypothesis.
δ
= (
θ − θ
0
) =
effect
= unknown true value of the parameter,
θ
, minus null hypothetical
value,
θ
0
.
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 Spring '08
 Staff
 Statistics, Statistical hypothesis testing, Statistical significance, Statistical power, Golde Holtzman

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