Building Core Concepts with
Computational Software
Robert H. Carver
Stonehill College
Easton MA
August 9, 2004
Core Concept Candidates
Population
Sample
Variation
Observation vs. Experiment
Cross-section vs. longitudinal
data
Comparison
Standardization
Probability
“Random”
Random sampling
“Error”
August 9, 2004
Sampling error
Statistical control
Confidence
Distribution
Null hypothesis
Association
Causation
Statistical significance vs.
Practical significance
Power
Model
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2
Concepts for this segment
Variation
Statistical control
Sampling Error
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ASQ on Statistical Thinking
All work occurs in a system of
interconnected processes
Variation exists in all processes
Understanding and reducing
variation are keys to success
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A tale of continuous improvement…
Wright 1904 Flyer over Huffman Prairie, Dayton OH
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Wilbur Wright on Control, 1901
“This inability to balance and steer
still confronts students of the flying
problem….
“When this one feature has been
worked out, the age of flying
machines will have arrived, for all
other difficulties are of minor
importance.”
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Variation: What’s up with that?
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Mean flight velocity
Time Series Plot of VelMPH
90
80
70
VelMPH
60
50
40
30
20
10
0
1
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9
18
27
36
45
54
Index
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63
72
81
8
Shape—velocity & distance
Histogram of VelMPH
Normal
35
Mean
StDev
N
30
29.50
11.83
68
20
Histogram of Distm
15
Normal
50
10
5
0
40
20
40
60
VelMPH
80
Frequency
Frequency
25
30
20
10
0
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-1000
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0
1000
2000
Distm
3000
4000
9
5000
Comparison: assignable cause?
Boxplot of VelMPH vs PILOT
90
80
70
VelMPH
60
50
40
30
20
10
0
OW
WW
PILOT
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Comparison: assignable cause?
Boxplot of Distm vs Launch
5000
4000
Distm
3000
2000
1000
0
Rail
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Catapult
Launch
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Control & shrinking variation
Time Series Plot of VelMPH
90
80
70
VelMPH
60
50
40
30
20
10
0
1
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9
18
27
36
45
54
Index
JSM Toronto Session 154
63
72
81
12
Control
I Chart of VelMPH
1
90
80
1
Individual Value
70
60
50
40
30
20
10
0
1
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10
19
28
37
46
55
Observation
JSM Toronto Session 154
64
73
82
13
Developing a feel for Sampling Error
10 Random Samples -- Velocity
n = 10 from population of 68 flights
90
Mean Flight Velocity (mph)
80
70
60
50
40
30
29.5
20
10
0
Samp1
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Samp2
Samp3
Samp4
Samp5
Samp6
Samp7
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Samp8
Samp9
Samp10
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Developing a feel for Sampling Error
One-Sample T: Samp1, Samp2, Samp3, Samp4, Samp5, Samp6, Samp7, ...
Variable
Samp1
Samp2
Samp3
Samp4
Samp5
Samp6
Samp7
Samp8
Samp9
Samp10
N
10
10
10
10
10
10
10
10
10
10
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Mean
26.1458
30.8669
23.8366
31.1267
28.7766
28.3671
22.2507
29.3899
28.8168
31.1217
StDev
7.0527
16.0146
8.6156
7.6951
8.6148
8.2640
9.6897
7.5919
11.0398
22.3381
SE Mean
2.2303
5.0643
2.7245
2.4334
2.7242
2.6133
3.0642
2.4008
3.4911
7.0639
JSM Toronto Session 154
95%
(21.1006,
(19.4107,
(17.6734,
(25.6220,
(22.6139,
(22.4554,
(15.3191,
(23.9590,
(20.9194,
(15.1420,
CI
31.1910)
42.3231)
29.9998)
36.6315)
34.9393)
34.2788)
29.1823)
34.8208)
36.7142)
47.1014)
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Guiding Principles
Focus on reading the story in the data
Rely on software to facilitate building
the concepts
Quick, interactive analysis to seize
teachable moments
Demonstration, discovery, iteration
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Sources
American Statistical Association (2004). Curriculum Guidelines for Undergraduate Programs in Statistical
Science. https://www.amstat.org/education
Fisher, R.A. (1966). The Design of Experiments. (New York: Hafner)
Garfield, J., Hogg, R., Schau, C., & Whittinghill, D. (2000). “Best Practices in Introductory Statistics,” draft
position paper prepared for JSM 2000.
Hoerl, R.W. & Snee, R.D. (2002). Statistical Thinking: Improving Business Performance. (Pacific Grove, CA:
Duxbury)
Jakab, P.L. & Young, R., eds. (2000). The Published Writings of Wilbur and Orville Wright. (Washington DC:
Smithsonian)
Kugler, C., Hagen, J. & Singer, F. (2003). “Teaching Statistical Thinking.” Journal of College Science Teaching,
v32, No. 7, 434-439.
McCarthy, P.J. (1957). Introduction to Statistical Reasoning (New York, McGraw-Hill)
Moore, D.S. (1997). Statistics: Concepts and Controversies, 4th Ed. (New York: W.H. Freeman)
Phillips, J. L. Jr. (1992). How to think about statistics. (New York: W.H. Freeman)
Salsburg, D. (2002). The Lady Tasting Tea. (New York: Owl Books)
Tukey, J.W. (1971). Exploratory Data Analysis. (Reading MA: Addison Wesley).
U.S. Centennial of Flight Commission (2003). Flight log: Huffman prairie, 1904.
http://www.centennialofflight.gov/chrono/log/1904HuffmanPrairie.htm
Utts, J. M. )1999). Seeing Through Statistics, 2nd Ed. (Pacific Grove CA: Duxbury)
Wallis, W. A. & Roberts, H. V. (1956). Statististics: A New Approach. (New York, Free Press.)
Wright Redux Association (2001). Wright history. The Wright redux association.
http://www.wrightredux.org/index.cfm?page=5
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Contact Information
Robert H. Carver
Dept. of Business Administration
Stonehill College
Easton MA 02357
e-mail: rcarver@stonehill.edu
Copies of slides and dataset available (after
JSM) at:
http://faculty.stonehill.edu/rcarver/index.htm
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