Transcript Significance and Meaningfulness

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Dependent t-tests
When the two samples are
correlated (i.e. not
independent)
KNR 445
Statistics
Dependent t
Slide 2
Dependent? What’s that?
 Well, not independent…2 ways…
 Same individuals measured twice (known as repeated
measures, or within subjects variables)
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 Pre-test, post-test
 Each person receiving both experimental conditions
 Matched subjects
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 Form pairs based upon pairs’ similarity on a variable; then
assign one of each pair to condition A, & one to condition B
 Twins studies are an example of this (matched on genes,
therefore - supposedly - matching on all sorts of other things)
KNR 445
Statistics
Dependent t
Slide 3
Standard deviation of the distn.
 SEM of difference between dependent means
SE X 1  X 2
SD1  SD2  2r12SD1SD2

npairs
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Key point: SEM is reduced in proportion with
the correlation between the 2 sets of scores (in
comparison with independent formula for SEM)
KNR 445
Statistics
Dependent t
Slide 4
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So why use paired samples?
 Because of that correlation
 The larger the r, the larger the reduction in SEM, and the
likelier it is you’ll get significant results
 Wise use of dependent samples will normally increase
power, increase effect size, increase likelihood of
significant result
KNR 445
Statistics
Dependent t
Slide 5
Dependent t-test in SPSS
Data format: Data
from each sample
must now be placed
in separate columns.
Note each person’s
data (one pair of
scores) fits on each
row
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KNR 445
Statistics
Dependent t
Slide 6
Dependent t-test in SPSS
SPSS
procedure:
choose the
appropriate
command…
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KNR 445
Statistics
Dependent t
Slide 7
Dependent t-test in SPSS
Choose
variables:
slide the pair
over from
here…
Choose
variables: to
here
And select
ok
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KNR 445
Statistics
Dependent t
Slide 8
Dependent t-test in SPSS
Descriptives
SPSS output
Paired Samples Statistics
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Pair
1
PRE
POST
2
Mean
3.3000
4.7000
N
10
10
Std. Deviation
.9487
1.3375
Std. Error
Mean
.3000
.4230
Paired Samples Correlations
N
Pair 1
PRE & POST
10
Correlation
-.622
r between samples
(justification for
choosing the test)
Sig.
.055
Paired Samples Test
Significance level
Paired Differences
Pair 1
PRE - POST
Mean
-1.4000
Std. Deviation
2.0656
Std. Error
Mean
.6532
95% Confidence
Interval of the
Difference
Lower
Upper
-2.8776 7.763E-02
t
-2.143
df
9
3
Sig. (2-tailed)
.061
Note: what if we’d assumed
independence?
KNR 445
Statistics
Dependent t
Slide 9
Group Statistics
Fitnes s score
Grouping Variable
1.00
2.00
N
10
10
Mean
3.3000
4.7000
Std. Deviation
.9487
1.3375
Std. Error
Mean
.3000
.4230
Independent Samples Test
Levene's Tes t for
Equality of Variances
F
Fitnes s score
Equal variances
ass umed
Equal variances
not as sumed
1.645
Sig.
.216
t-tes t for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
-2.700
18
.015
-1.4000
.5185
-2.4894
-.3106
-2.700
16.227
.016
-1.4000
.5185
-2.4980
-.3020
Weird: now it’s significant…but I
thought the dependent t-test was
more powerful???
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KNR 445
Statistics
Dependent t
Slide 10
Note: what if we’d assumed
independence?
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SE X 1  X 2
2
SD1  SD2  2r12SD1SD2

npairs
But look – you
subtract the
product of r and
the SEM.
Paired Samples Correlations
N
Pair 1
PRE & POST
10
3
Correlation
-.622
Sig.
.055
& r was negative,
right? So that
means the SE term
grows rather than
shrinks in the
paired t-test –
meaning less
likelihood of
significance
KNR 445
Statistics
Dependent t
Slide 11
How dependent samples normally
work…
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 To prove the point…
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KNR 445
Statistics
Dependent t
Slide 12
How dependent samples normally
work…
 To prove the point…
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KNR 445
Statistics
Dependent t
Slide 13
How dependent samples normally
work…
 To prove the point…
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KNR 445
Statistics
Dependent t
Slide 14
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Finally, for the skeptics…
 Comparing same data via independent t-tests…
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KNR 445
Statistics
Dependent t
Slide 15
Finally, for the skeptics…
 Comparing same data via independent t-tests…
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