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Inferential Statistics 10. (Statistical Hypotheses Testing (Tests (One…
Inferential Statistics 10.
Inferential Statistics
Goal
Making Inferences From the Sample to the Population
Lecture Topics
Logic Behind Inferential Statistics
Sampling Distribution
Hypotheses Testing
Statistical Significance
Type I and II Errors
Statistical Strenght
Statistical Hypotheses Testing
Hypothesis
Definition
a Claim bt the Population
that a Parameter of the Population
has a Specific Value (or Set of Values)
Ex. The average height of
the male population is 1.80m
Hypotethico-Deductive Method
canNot Prove that Smth is True,
but can Disprove it (+/-)
Instead of 1 Hypothesis
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Procedure for
Testing an Hypothesis:
we wish to Test a
Research Hypothesis
(H1)
. we
Draw
a
Randomized Sample
under
both Conditions
(H0, H1)
Formulate
a
Null-Hypothesis
Theoretical Sample Distribution IF H0
is
True
(
Null-Distribution
)
Given the
Null-Distribution
,
How Probable
are
Our Results
(
p
)
IF
p < α
, our
Results
are
Statistically Significant
:
Discard H0
, and
Accept H1
Tests
One-Tailed Test
H0
=
no Diff.
btw Male and Female Average Heights
H1
either:
the Average Male Height is
Higher
than Women's,
or
the Avrg. male height is
Lower
Two-Tailed Test
H0
=
no Diff.
btw Male and Female Average Heights
H1
=
there is a Diff.
we
Always
use this
when
we
Can
has a
higher p
-Value,
more
Strict Test
Critical Limit
/
Critical Region
how Extreme
must our
Results
be
before they
get Significant
given:
α
=
0.05
One-Tailed
Test
p >= 1.65
Standard Error (
SE
)
Two-Tailed
Test
p >=
± 1.96 SE
(
≈ 2
)
2 Main Errors
we can do
Type 1 and 2 Errors
Type 1 Error
(
α
)
Null-Hypothesis
was
True
,
but we
Discarded
it
Sometimes
happens to get
Extreme Results
that are
Just due to Chance
False Positive
(in relation w
H1
)
we
Say H1
is
True
while it's s
Not
we
Say H0
is
Wrong
while it's
Not
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Type 2 Error
(
ß
)
we Mantain (
Accept
) the
Null-Hypothesis
even if its'
Wrong
False Negative
(in relation w
H1
)
we
Say
our
Results
are
Significant
(
True
) while they're
Not
- (?)
we
Say H0
is
True
while it's
Not
Statistical Strenght
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Difficult to Find Out
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