DATA VISUALIZATION
UNIVARIATE (no review- self study)
STEM & LEAF
BOXPLOT
BIVARIATE
SCATTERPLOT (review correlation)
Overlays; jittering
Regression line overlay (see ASA
website:
http://nlvm.usu.edu/en/nav/frames_asid_144_g_4_t_5.html?open=activities
DATA VISUALIZATION
TOPICS
GRAPHICAL DISPLAYS
UNIVARIATE
BIVARIATE
ASSUMPTIONS OF MULTIPLE REGRESSION
LINEARITY
HOMOSCEDASTICITY
ERROR INDEPENDENCE
NORMALITY
FIXING VIOLATIONS
GRAPHICAL DISPLAYS
• Frequency Histogram:
– SPSS ANALYZE: Descriptive Statistics: Explore: Plot:
Stem and Leaf
– SPSS GRAPH: Boxplot (normal curve overlay
available
• or INTERACTIVE: Boxplot or Analyze: Frequencies
– SPSS GRAPH: Histogram or Interactive: Histogram
• # “bins” = 1 + log2(N)
• Example: N= 500; #bins = 1+ 9 = 10
• Log2(512) = 9 (eg., 2x2x2x2x2x2x2x2x2=512)
ANXIETY Stem-and-Leaf Plot
Frequency
.00
22.00
35.00
7.00
39.00
22.00
26.00
22.00
26.00
12.00
26.00
14.00
24.00
31.00
28.00
6.00
15.00
24.00
14.00
Stem & Leaf
3.
3 . 4444444444455555555555
3 . 66666666777777777777777777777777777
3 . 9999999
4 . 000000000000000000000000011111111111111
4 . 2222222222222222222222
4 . 44455555555555555555555555
4 . 6666666667777777777777
4 . 88888888888999999999999999
5 . 111111111111
5 . 22222222222222222223333333
5 . 44444444444444
5 . 666666777777777777777777
5 . 8888888888888999999999999999999
6 . 1111111111111111111111111111
6 . 333333
6 . 444444444444444
6 . 666666666666666666666666
6 . 88888899999999
Stem width:
Each leaf:
10
1 case(s)
70
70
60
ANXIETY
60
50
50
40
40
30
ANXIETY
40
Frequency
30
20
10
Mean = 50.3
Std. Dev. = 10.147
N = 393
0
40
50
ANXIETY
60
70
50
Count
40
30
20
10
40
50
ANXIETY
60
GRAPHICAL DISPLAYS
• Kernel Smoothing
– SPSS Graph: INTERACTIVE: Line: Dots and
Lines: Spline or Lagrange 3rd and 5th order fits
– does not give you the smoother options
(available for bivariate scatterplots- see later
slides)
Dot/Lines show counts
25
Count
20
15
10
5
40
50
ANXIETY
60
70
100
100
75
75
Count
Count
Dot/Lines show counts
50
50
25
25
0
0
10
12
14
age
16
18
10
12
14
age
16
18
Bivariate Displays
• Scatterplots
– Interval data
– Category by interval- jittering
– Regression fits- lowess lines
• Scatterplot Matrices
Interval Scatterplot: SPSS Graphics: Interactive:
Scatterplot: Fit: Method:Smoother
60
ANXIETY
50
40
10
12
age
16
50
60
14
No Smoother
70
ANXIETY
70
18
40
10
12
LLR Smoother
14
16
18
age
with Normal Smoother
Interval Scatterplot: SPSS Graphics: Interactive:
Scatterplot: Fit: Method:Smoother
70
ANXIETY
60
50
40
10
12
LLR Smoother
14
age
16
18
with Uniform
Smoother
70
70
60
50
40
1.00
1.25
1.50
sex
1.75
2.00
60
LLR Smoother
ANXIETY
ANXIETY
Category X-axis: without and with jittering (adding
normal random deviate with SD=.15 for sex)
50
1.00
1.50
sexrev
40
LLR Smoother
2.00
Jittering
• Basic idea- when looking at displays for
two or more groups, it is hard to tell where
data lie due to overlaying of points in most
plot programs, so
• Add a small random score to each “group”
score
– For example, for males (score 1) and females
(score 2), add a random number with std dev.
of say .1 to each male and female score
Jittering
• The result is a spreading out of all scores
around the Male or Female column in a
scatterplot:
.
.
.
Y
.
.
.
.
.
.
.
.
.
.
.
.
.
Male=1
Female=2
DATA VISUALIZATION
BIVARIATE
Loess lines: in SPSS an option under
GRAPH/ Interactive / Scatterplot labeled
“FIT” with METHOD = SMOOTHER
The Bandwidth multiplier has a 1.0
default; a smaller value will create more
bumps or curves in the overall curve
70
ANXIETY
60
50
40
50
LLR Smoother
60
70
80
DEPRESSION
GRAPH/INTERACTIVE/SCATTERPLOT/FIT/BANDWIDTH=1.0
GRAPH/INTERACTIVE/SCATTERPLOT/FIT/BANDWIDTH=.60
70
ANXIETY
60
50
40
50
60
70
DEPRESSION
80
LLR Smoother
