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The use of t-test and ANOVA in analyzing the difference in quality of life (QOL) between two groups of liver transplant patients - one receiving treatment as usual (TAU) and the other receiving psychosocial intervention (PSI). The document also covers the concept of a clinically important difference, statistical significance, and the impact of sample size and standard error of the mean on the results.
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David L. Streiner, Ph.D. David L. Streiner, Ph.D.
Director, Director,
Kunin Kunin
- -
LunenfeldLunenfeld
Applied Research UnitApplied Research Unit
Assistant V.P., Research Assistant V.P., Research
Baycrest Centre for Geriatric Care Baycrest Centre for Geriatric Care
Professor, Department of Psychiatry Professor, Department of Psychiatry
University of Toronto University of Toronto
Question: Does a psychosocial inter Question: Does a psychosocial inter
vention vention
improve quality of life (QOL) improve quality of life (QOL)
following liver transplantation? following liver transplantation?
Two groups of transplant patients Two groups of transplant patients
One gets treatment as usual (TAU) One gets treatment as usual (TAU)
Other gets psychosocial intervention (PSI) Other gets psychosocial intervention (PSI)
Measure QOL 6 months post Measure QOL 6 months post
op op
How big is the difference? How big is the difference?
The bigger the difference, the more likely the The bigger the difference, the more likely the
results are significant results are significant
0 0
5 5
10 10
15 15
20 20
25 25
30 30
35 35
TAU
PSI
Does that mean that a large difference will Does that mean that a large difference will
be significant? be significant?
Again, it all depends Again, it all depends
How accurately was each mean estimated? How accurately was each mean estimated?
If we repeated the study 100 times, how close If we repeated the study 100 times, how close
to one another are the estimates of each to one another are the estimates of each
group group
’
’
s mean? s mean?
Wide Wide
Narrow Narrow
Difference between groups more likely to Difference between groups more likely to
be significant if there is: be significant if there is:
Large difference between means Large difference between means
Small SD in each group Small SD in each group
Large Large
N N
in each group in each group
Let Let
s add a third group: occupational s add a third group: occupational
therapy (OT) therapy (OT)
How do we check for differences? How do we check for differences?
Can do Can do
t t
tests comparing: tests comparing:
TAU TAU
versus
versus
PSI PSI
TAU TAU
versus
versus
OT OT
PSI PSI
versus versus
OT OT
There are two problems with multiple There are two problems with multiple
t t
tests: tests:
Inflates probability of Type I error Inflates probability of Type I error
Tests not independent of each other Tests not independent of each other
If PSI > OT, and If PSI > OT, and
OT > TAU, then OT > TAU, then
PSI PSI
must bemust be
TAU TAU
0 0
5 5
10 10
15 15
20 20
25 25
30 30
35 35
TAU
PSI
OT
Step 1: Find the Grand Mean ( Step 1: Find the Grand Mean (
G G
the the
mean of the 3 means; or the mean of all mean of the 3 means; or the mean of all
people, irrespective of group people, irrespective of group
Assuming all groups have same sample size, Assuming all groups have same sample size,
it is (12. 5 + 22.5 + 25.0) / 3 = 60 / 3 = 20. it is (12. 5 + 22.5 + 25.0) / 3 = 60 / 3 = 20.
Step 1: Find the Grand Mean ( Step 1: Find the Grand Mean (
G G
Step 2: Determine the deviation ( Step 2: Determine the deviation (
d
d
) of ) of
each mean from each mean from
G G
0 0
5 5
10 10
15 15
20 20
25 25
30 30
35 35
Grand Mean
d
1
d
2
d
3
