Teaching Statistical Concepts with Simulated Data

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Teaching Statistical Concepts with Simulated Data

• Andrej Blejec
• National Institute of Biology andUniversity of
  Ljubljana
• Ljubljana, Slovenia
• andrej.blejec_at_nib.si

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Kinds of data

• real life data
• invented data
• simulated data

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Real life data

• interesting for students
• need subject matter knowledge to interpret
  statistical results
• oversimplified problems
• complex problems
• unclear relevance of statistical results

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Invented data

• a collection of data, no story
• useful mostly for calculation drill
• no possible interpretation of results
• uninteresting for students

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Simulated data

• sampled from known distribution
• composed according to prespecified modele.g.
  Y a b X e, with known distribution of X
  and e
• known statistical propertiese.g. mean, variance,
  regression coefficient
• analysis results can be compared to true values

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Goals of teaching statistics

• interest for statistics
• understanding of statistical methods
• skills in use of statistics
• experiences in analyzing data
• other ( insert your own ) ___________

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Absorption spectrum
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Least squares estimate of the mean
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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Mean squared deviations
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True mean value µ
LS estimate
Mean squared deviations
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Maximum likelihood estimation of the mean
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ML estimate
True mean value µ
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Maximum likelihood estimate of standard deviation
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ML estimate
True standard deviation s
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Hypothesis testingsignificance
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Hypothesis testingsignificance
or rather a surprise ?
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Confidence intervals
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Weldon, K.L. Statistics A Conceptual Approach..
Prentice-Hall. New York. 1986
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Bad sampling implies bias
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Bias due to leave max out
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Confidence intervals for variance

• Biased and unbiased estimators

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Confidence intervals for variancewhat if
assumptions are not met?

• Case of asymetric parent population

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Confidence band in linear regression
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Coefficient of determination
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Final remarks

• Graphically supported simulations can - to some
  extent - replace the proofs, usually not
  understandable to non-mathematics majors. Maybe
  they are the answer to some questions
• "If an audience is not convinced by proof, why do
  proof? (Moore, 1996)
• Do students need to know the theory or do they
  need to understand the concept? (J Brown and I
  David, ICOTS8, 2010)

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• Simulated data have to be combined with real life
  data and projects
• Simulated data can serve as pure and simple data
  on which we can train our perception for
  statistical results and learn what patterns and
  properties in data can be revealed by applied
  method
• After such preparation students will be able to
  interpret the real life and subject matter data
  in all their complexity