STATS 330: Lecture 3

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STATS 330 Lecture 3
Trellis Graphics
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Class Rep

• Sonia Polak
• spol034_at_aucklanduni.ac.nz

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Todays 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 ( yx zw)

Z and w are the conditioning variables, can be
missing
X and y are the relationship variables
Plot type one of xyplot dotplot bwplot
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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 cont

• Example age and sex.
• Sex is already categorical
• Age not, so divide up the age range as
• 0-17, 18-59, 60
• This gives a 3 x 2 table with 6 cells

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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(yxagesex)
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x categorical, y continuous dotplot
Y is continuous, X has 2 levels, A and B
dotplot(yxagesex)
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x categorical, y continuous bwplot
Y continuous, X has 2 levels, A and B
bwplot(yxagesex)
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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.Bfat 1
female BBall 20.56 19.75 2 female
BBall 20.67 21.30 3 female BBall 21.86
19.88 4 female BBall 21.88 23.66 5
female BBall 18.96 17.64 6 female
BBall 21.04 15.58 7 female BBall 21.69
19.99 8 female BBall 20.62 22.43 9
female BBall 22.64 17.95 10 female
BBall 19.44 15.07 more data (158 lines in
all)
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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
gt ethanol NOx C E 1 3.741 12.0
0.907 2 2.295 12.0 0.761 3 1.498 12.0 1.108 4
2.881 12.0 1.016 5 0.760 12.0 1.189 6 3.120
9.0 1.001 7 0.638 9.0 1.231 8 1.170 9.0
1.123 9 2.358 12.0 1.042 10 0.606 12.0 1.215 11
3.669 12.0 0.930 12 1.000 12.0 1.152 13 0.981
15.0 1.138 14 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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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)

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Testing procedure
Load Force
Amplitude
length
Cycles to failure number of pushes before yarn
breaks
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Yarn data
gt cycles.df cycles length amplitude load 1
674 low low low 2 370 low
low med 3 292 low low high 4
338 low med low 5 266 low
med med 6 210 low med high 7
170 low high low 8 118 low
high med 9 90 low high high 10
1414 med low low more data (27 lines
in all)
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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