stats 330: lecture 3
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STATS 330: Lecture 3. Trellis Graphics. Class Rep. ?????? ???????????. Today’s lecture: More on Trellis graphics. Aim of the lecture: To give you an idea of the scope of trellis graphics To discuss several examples and show how Trellis graphics reveal important insights into the data. - PowerPoint PPT PresentationTRANSCRIPT
04/22/23 330 lecture 3 1
STATS 330: Lecture 3
Class Rep??????
???????????
04/22/23 330 lecture 3 2
04/22/23 330 lecture 3 3
Today’s lecture: More on Trellis graphics
Aim of the lecture:
To give you an idea of the scope of trellis graphics
To discuss several examples and show how Trellis graphics reveal important insights into the data
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Recall last time: Last lecture we discussed coplots: Coplots show how the relationship
between 2 variables x and y changes as the value of a third variable z changes
We can generalize this to more than one variable z: i.e. conditioning on more than one variable
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Coplots: syntax plot ( y~x | z*w)
Plot type – one of xyplotdotplotbwplot
X and y are the “relationship”
variables
Z and w are the “conditioning”
variables, can be missing
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Conditioning on two variables
Suppose we have 2 conditioning variables Z and W.
No problem if both are categorical If one or both are continuous variables, we
turn them into categorical variables by using subranges e.g.– turn ages into 10 yr age groups – turn marks into grades
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Two variables: contExample: age and sex. Sex is already categorical
Age not, so divide up the age range as0-17, 18-59, 60+
This gives a 3 x 2 table with 6 “cells”:
F M
0-17
18-59
60+
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Relationship between x and y
In each of the 6 “cells” of the table, we can draw a graph that illustrates the relationship between x and y for individuals having that age and sex
Type of graph will depend on the type of x and y i.e. continuous/categorical– Both continuous: scatterplot– One continuous: boxplots, dotplots, etc
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x & y continuous: xyplot
xyplot(y~x|age*sex)
x
y
8
10
12
18 20 22 24
F60+
M60+
F18-59
8
10
12
M18-59
8
10
12
F0-17
M0-17
18 20 22 24
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x categorical, y continuous: dotplot
Y is continuous, X has 2 levels, “A” and “B”
dotplot(y~x|age*sex)
y
8
10
12
A B
F60+
A B
M60+
F18-59
8
10
12
M18-59
8
10
12
F0-17
M0-17
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x categorical, y continuous: bwplot
Y continuous, X has 2 levels, “A” and “B”
bwplot(y~x|age*sex)y
8
10
12
A B
F60+
A B
M60+
F18-59
8
10
12
M18-59
8
10
12
F0-17
M0-17
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To summarize: The conditioning variables determine the
layout of the “cells”
The x/y variables determine the kind of graph to draw in each cell
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Example: sports In a study on athletes at the Australian Institute
of Sport, various physical measurements were made.
In this example we look at the relationship between body fat and BMI and how it differs between athletes of either sex playing different sports. BMI = weight(kg) / height(m)2
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Data sex sport BMI X.Bfat1 female BBall 20.56 19.752 female BBall 20.67 21.303 female BBall 21.86 19.884 female BBall 21.88 23.665 female BBall 18.96 17.646 female BBall 21.04 15.587 female BBall 21.69 19.998 female BBall 20.62 22.439 female BBall 22.64 17.9510 female BBall 19.44 15.07
… more data (158 lines in all)
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BMI
X.B
fat
5
10
15
20
25
30
20 25 30 35
Athleticsfemale
BBallfemale
20 25 30 35
Rowfemale
Swimfemale
20 25 30 35
Tennisfemale
Athleticsmale
BBallmale
20 25 30 35
Rowmale
Swimmale
20 25 30 35
5
10
15
20
25
30Tennismale
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Example: engines In a study of engine emissions, a test engine
was run under different conditions and the amount of nitrogen oxide (NOx) emitted was measured.
The conditions involved different settings of the compression ratio C, and the Equivalence ratio, E (related to fuel/air mixture)
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Data> ethanol.df NOx C E1 3.741 12.0 0.9072 2.295 12.0 0.7613 1.498 12.0 1.1084 2.881 12.0 1.0165 0.760 12.0 1.1896 3.120 9.0 1.0017 0.638 9.0 1.2318 1.170 9.0 1.1239 2.358 12.0 1.04210 0.606 12.0 1.21511 3.669 12.0 0.93012 1.000 12.0 1.15213 0.981 15.0 1.13814 1.192 18.0 0.601
… more data (88 lines)
How does NOx relate to E? does the relationship depend on C?
There are only 5 settings of C
(7.5, 9.0, 12.0, 15.0, 18.0)
so we condition on these.
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E
NO
x
1
2
3
4
0.6 0.8 1 1.2
C C
0.6 0.8 1 1.2
C
C C
0.6 0.8 1 1.2
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0.6 0.7 0.8 0.9 1.0 1.1 1.2
12
34
E
NO
x
C= 7.5C= 9.0C=12.0C=15.0C=18.0
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Example: Yarn In an experiment to test the strength of
different yarns, lengths of yarn are repeatedly stressed until they break (cycles to failure).It is desired to see yow this variable is related to the length of the yarn samples, and the amplitude and the load (two variables related to the amount of stress). The experiment involved using 3 amplitudes, 3 lengths and 3 loads, for a total of 27 = 3 x 3 x 3 different experimental conditions. (Coursebook p 9)
Testing procedure
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length
Load = ForceAmplitude
Cycles to failure: number of “pushes” before yarn breaks
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Yarn data> cycles.df cycles length amplitude load1 674 low low low2 370 low low med3 292 low low high4 338 low med low5 266 low med med6 210 low med high7 170 low high low8 118 low high med9 90 low high high10 1414 med low low
… more data (27 lines in all)
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cycles
leng
th
low
med
high
0 1000 2000 3000
amp: lowload: low
amp: medload: low
0 1000 2000 3000
amp: highload: low
low
med
high
amp: lowload: med
amp: medload: med
amp: highload: med
low
med
high
amp: lowload: high
amp: medload: high
0 1000 2000 3000
amp: highload: high
Conclusions For longer lengths, the cycles to failure are
higher. ( less likely to break) High loads reduce the cycles to failure
(more likely to break) High amplitudes reduce the cycles to
failure (more likely to break) Most likely to break when load and
amplitude are high and length is low
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