Building Core Concepts with Computational Software

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Building Core Concepts with Computational Software

• Robert H. Carver
• Stonehill College
• Easton MA

August 9, 2004
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Core Concept Candidates

• Population
• Sample
• Variation
• Observation vs. Experiment
• Cross-section vs. longitudinal data
• Comparison
• Standardization
• Probability
• Random
• Random sampling
• Error

• Sampling error
• Statistical control
• Confidence
• Distribution
• Null hypothesis
• Association
• Causation
• Statistical significance vs. Practical
  significance
• Power
• Model

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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 Whats up with that?
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Mean flight velocity
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Shapevelocity distance
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Comparison assignable cause?
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Comparison assignable cause?
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Control shrinking variation
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Control
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Developing a feel for Sampling Error
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Developing a feel for Sampling Error
One-Sample T Samp1, Samp2, Samp3, Samp4, Samp5,
Samp6, Samp7, ... Variable N Mean
StDev SE Mean 95 CI Samp1 10
26.1458 7.0527 2.2303 (21.1006,
31.1910) Samp2 10 30.8669 16.0146 5.0643
(19.4107, 42.3231) Samp3 10 23.8366 8.6156
2.7245 (17.6734, 29.9998) Samp4 10
31.1267 7.6951 2.4334 (25.6220,
36.6315) Samp5 10 28.7766 8.6148 2.7242
(22.6139, 34.9393) Samp6 10 28.3671 8.2640
2.6133 (22.4554, 34.2788) Samp7 10
22.2507 9.6897 3.0642 (15.3191,
29.1823) Samp8 10 29.3899 7.5919 2.4008
(23.9590, 34.8208) Samp9 10 28.8168 11.0398
3.4911 (20.9194, 36.7142) Samp10 10
31.1217 22.3381 7.0639 (15.1420, 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/edu
  cation
• 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/1904H
  uffmanPrairie.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.wrightred
  ux.org/index.cfm?page5

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Contact Information

• Robert H. Carver
• Dept. of Business Administration
• Stonehill College
• Easton MA 02357
• e-mail rcarver_at_stonehill.edu
• Copies of slides and dataset available (after
  JSM) at
• http//faculty.stonehill.edu/rcarver/index.htm