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Quality of Life Differences After Liver Transplantation: t-Test and ANOVA Analysis, Lecture notes of Statistical Physics

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.

Typology: Lecture notes

2021/2022

Uploaded on 09/27/2022

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The
The t
t-
-test and ANOVA
test and ANOVA
David L. Streiner, Ph.D.
David L. Streiner, Ph.D.
Director,
Director, Kunin
Kunin-
-Lunenfeld
Lunenfeld Applied Research Unit
Applied 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
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Download Quality of Life Differences After Liver Transplantation: t-Test and ANOVA Analysis and more Lecture notes Statistical Physics in PDF only on Docsity!

The

The

t

t

test and ANOVA

test and ANOVA

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

Background

Background

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

It Depends On

It Depends On

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

Mean Difference

Mean Difference

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?

Spread of Mean Estimates

Spread of Mean Estimates

Wide Wide

Narrow Narrow

Summarizing

Summarizing

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

Writing it Out as an Equation

Writing it Out as an Equation

n

s

n

s

M

M

t

Adding More Groups

Adding More Groups

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

Problems with Many

Problems with Many

t

t

tests

tests

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

Difference for >2 Means

Difference for >2 Means

0 0

5 5

10 10

15 15

20 20

25 25

30 30

35 35

TAU

PSI

OT

Difference for >2 Means

Difference for >2 Means

Step 1: Find the Grand Mean ( Step 1: Find the Grand Mean (

M
M

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.

Difference for >2 Means

Difference for >2 Means

Step 1: Find the Grand Mean ( Step 1: Find the Grand Mean (

M
M

G G

Step 2: Determine the deviation ( Step 2: Determine the deviation (

d

d

) of ) of

each mean from each mean from

M
M

G G

Difference for >2 Means

Difference for >2 Means

0 0

5 5

10 10

15 15

20 20

25 25

30 30

35 35

Grand Mean

d

1

d

2

d

3