Plotting Data
When Analyzing data, always plot the data!
• Always plot original data points.
– This is the first thing to do when analyzing
data
– This is very important!
*
Plotting helps avoid big mistakes
1000
Fetal Weight (g)
100
10
1
0.1
1
10
100
Placental Weight (g)
0.1
The decimal point was left out for some of the data points
Plotting Cancer Study Results
• The following plots are from a study by Dr.
Terry Rose-Hellekant in the Medical School
Duluth
• Treatments
– Tamoxifen
– Placebo
• Some mice develop breast cancer
• The data are RT-PCR expressions
corresponding to particular genes
– In RT-PCR the values are roughly a log base 2
scale of the RNA content.
• PUM1 Is a “housekeeping” gene
– Account for RNA quality in the sample
– For example time since death for a study of
schizophrenia on deceased patients’ brains
A dot diagram of fishing line strength
XL
11.8
11.7
11.6
11.5
11.4
11.3
11.2
11.1
11.0
10.9
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XT
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*
*
Stren
*
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Two groups can be compared with back to
back stem and leaf diagrams
e.g. Stopping distances of bikes
Treaded tire
5
64
1
20
34
35
36
37
38
39
40
Or dot diagrams
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| * | ** |
|*
340 350 360 370 380 390
|*** | * |
| * |
|*
Smooth tire
189
5
5
1
|**
400
|
Treaded
Smooth
When there are associations between sets of data values,
plot the data accordingly.
E.g., Snowfall for duluth and White Bear Lake 1972-2000
A not very good way to plot the data
WB Lake
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130
120
110
100
90
80
70
60
50
40
30
20
Duluth
*
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*****
******
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snow_total
Snowfall plot
140
130
120
110
100
90
80
70
60
50
40
30
20
10
0
Duluth
White Bear
1972
1977
1982
1987
year
1992
1997
A study of trace metals in South
Indian River
5
3
1
2
6
4
T=top water zinc concentration (mg/L)
B=bottom water zinc (mg/L)
1
2
3
4
5
6
Top
0.415 0.238 0.390 0.410 0.605 0.609
Bottom
0.430 0.266 0.567 0.531 0.707 0.716
• One of the first things to do when analyzing data is
to PLOT the data
Zinc In River
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
Depth 1=Top 2=Bottom
3
• This is not a useful way to plot the data. There is not
a clear distinction between bottom water and top
water zinc
• even though Bottom>Top at all 6 locations.
A better way
0.7
0.6
Zinc 0.5
0.4
0.3
0.2
Top
Connect points in the same pair.
Bottom
A better way
0.8
0.6
Bottom=Top
0.4
0.2
0
0
0.2
0.4
0.6
0.8
This following plot would imply a natural ordering of sites from 1 to 6.
This would not be the best way to plot the data unless the sites 1-6 correspond to a
natural ordering such as distance downstream of a factory.
0.8
Zinc
0.7
0.6
0.5
0.4
Top
Bottom
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0.2
0.1
0
0
1
2
3
4
Site
5
6
7