Transcript Multidisciplinary COllaboration: Why and How?

Analysis of Variance (ANOVA)
EPP 245
Statistical Analysis of
Laboratory Data
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The Basic Idea
• The analysis of variance is a way of
testing whether observed differences
between groups are too large to be
explained by chance variation
• One-way ANOVA is used when there are
k ≥ 2 groups for one factor, and no other
quantitative variable or classification
factor.
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EPP 245 Statistical Analysis of
Laboratory Data
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Data = Grand Mean +
Row Deviations from grand mean +
Cell Deviations from row mean
Are the row deviations from the grand mean
too big to be accounted for by the cell
deviations from the row means?
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Data
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EPP 245 Statistical Analysis of
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Cell Means
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Deviations from Cell Means
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Red cell folate data
Description:
22 rows and 2 columns.
data on red cell folate levels in patients receiving three
different methods of ventilation during anesthesia.
Format:
folate a numeric vector. Folate concentration (g/l).
ventilation a factor with levels 'N2O+O2,24h': 50% nitrous oxide
and 50% oxygen, continuously for 24 hours; 'N2O+O2,op': 50%
nitrous oxide and 50% oxygen, only during operation;
'O2,24h': no nitrous oxide, but 35-50% oxygen for 24 hours.
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insheet using redcell.csv
summarize folate
tabulate ventilation
tabulate ventilation, summarize (folate)
graph box folate, over (ventilation)
graph export folate1.wmf
oneway folate ventilation
describe ventilation
encode ventilation, generate(dv)
Describe dv
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EPP 245 Statistical Analysis of
Laboratory Data
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. summarize folate
Variable |
Obs
Mean
Std. Dev.
Min
Max
-------------+-------------------------------------------------------folate |
22
283.2273
51.28439
206
392
. tabulate ventilation
ventilation |
Freq.
Percent
Cum.
------------+----------------------------------N2O+O2,24h |
8
36.36
36.36
N2O+O2,op |
9
40.91
77.27
O2,24h |
5
22.73
100.00
------------+----------------------------------Total |
22
100.00
. tabulate ventilation, summarize (folate)
|
Summary of folate
ventilation |
Mean
Std. Dev.
Freq.
------------+-----------------------------------N2O+O2,24h |
316.625
58.717088
8
N2O+O2,op |
256.44444
37.121797
9
O2,24h |
278
33.756481
5
------------+-----------------------------------Total |
283.22727
51.284391
22
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EPP 245 Statistical Analysis of
Laboratory Data
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400
350
300
250
200
N2O+O2,24h
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N2O+O2,op
EPP 245 Statistical Analysis of
Laboratory Data
O2,24h
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. oneway folate ventilation
Analysis of Variance
Source
SS
df
MS
F
Prob > F
-----------------------------------------------------------------------Between groups
15515.7664
2
7757.88321
3.71
0.0436
Within groups
39716.0972
19
2090.32091
-----------------------------------------------------------------------Total
55231.8636
21
2630.08874
Bartlett's test for equal variances:
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chi2(2) =
EPP 245 Statistical Analysis of
Laboratory Data
2.0951
Prob>chi2 = 0.351
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. describe ventilation
storage display
value
variable name
type
format
label
variable label
------------------------------------------------------------------------------ventilation
str10 %10s
. encode ventilation, generate(dv)
. describe dv
storage display
value
variable name
type
format
label
variable label
------------------------------------------------------------------------------dv
long
%10.0g
dv
. anova folate dv
Number of obs =
Root MSE
=
22
45.72
R-squared
=
Adj R-squared =
0.2809
0.2052
Source | Partial SS
df
MS
F
Prob > F
-----------+---------------------------------------------------Model | 15515.7664
2 7757.88321
3.71
0.0436
|
dv | 15515.7664
2 7757.88321
3.71
0.0436
|
Residual | 39716.0972
19 2090.32091
-----------+---------------------------------------------------Total | 55231.8636
21 2630.08874
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EPP 245 Statistical Analysis of
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Laboratory Data
Two- and Multi-way ANOVA
• If there is more than one factor, the sum of
squares can be decomposed according to
each factor, and possibly according to
interactions
• One can also have factors and quantitative
variables in the same model (cf. analysis
of covariance)
• All have similar interpretations
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EPP 245 Statistical Analysis of
Laboratory Data
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Heart rates after enalaprilat
Description:
36 rows and 3 columns.
data for nine patients with congestive heart failure before and
shortly after administration of enalaprilat, in a balanced two-way
layout.
Format:
hr a numeric vector. Heart rate in beats per minute.
subj a factor with levels '1' to '9'.
time a factor with levels '0' (before), '30',
(minutes after administration).
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EPP 245 Statistical Analysis of
Laboratory Data
'60', and
'120'
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. drop _all
. insheet using heart.rate.csv
(4 vars, 36 obs)
. anova hr subj time
Number of obs =
Root MSE
=
36
3.5165
R-squared
=
Adj R-squared =
0.9685
0.9540
Source | Partial SS
df
MS
F
Prob > F
-----------+---------------------------------------------------Model | 9117.52778
11 828.866162
67.03
0.0000
|
subj | 8966.55556
8 1120.81944
90.64
0.0000
time | 150.972222
3 50.3240741
4.07
0.0180
|
Residual | 296.777778
24 12.3657407
-----------+---------------------------------------------------Total | 9414.30556
35 268.980159
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EPP 245 Statistical Analysis of
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140
120
60
80
100
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Laboratory Data
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917
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EPP 245 Statistical Analysis of
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60
Laboratory Data
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. anova hr subj
Number of obs =
36
Root MSE
= 4.07226
R-squared
=
Adj R-squared =
0.9524
0.9383
Source | Partial SS
df
MS
F
Prob > F
-----------+---------------------------------------------------Model | 8966.55556
8 1120.81944
67.59
0.0000
|
subj | 8966.55556
8 1120.81944
67.59
0.0000
|
Residual |
447.75
27 16.5833333
-----------+---------------------------------------------------Total | 9414.30556
35 268.980159
. predict hrhat
(option xb assumed; fitted values)
. generate hrres = hr - hrhat
. graph box hrres, over (time)
. graph export hrresxtime.wmf
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EPP 245 Statistical Analysis of
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-5
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EPP
30245 Statistical Analysis of 60
Laboratory Data
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. anova hr subj time
Number of obs =
Root MSE
=
36
3.5165
R-squared
=
Adj R-squared =
0.9685
0.9540
Source | Partial SS
df
MS
F
Prob > F
-----------+---------------------------------------------------Model | 9117.52778
11 828.866162
67.03
0.0000
|
subj | 8966.55556
8 1120.81944
90.64
0.0000
time | 150.972222
3 50.3240741
4.07
0.0180
|
Residual | 296.777778
24 12.3657407
-----------+---------------------------------------------------Total | 9414.30556
35 268.980159
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rvfplot
graph export hrrvf.wmf
rvpplot subj
graph export hrrvpsubj.wmf
rvpplot time
graph export hrrvptime.wmf
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EPP 245 Statistical
Fitted Analysis
valuesof
Laboratory Data
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EPP 245 Statistical
Analysis of
subj
Laboratory Data
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EPP 245 Statistical
Analysis of
time
Laboratory Data
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