Divisional Presentation Template

1
Teaching Statistics using the Computer
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Emlyn Williams CSIRO Australia
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Statistics students in Australia

• Decline in statistics student numbers in
  Australia
• During 2003, 3000 PhDs in Australia
• Only 186 PhDs in Mathematical and Statistical
  Sciences
• Why?

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Possible reasons for the decline

• Popularity of Computing Science
• Reduced capacity of our Universities to train
  Maths / Stats professionals
• Type of Statistics being taught in Secondary
  Schools
• Distribution theory
• Probability
• Equations / formulas

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Some possible directions

• Data mining
• Microarrays
• Normalization
• Multivariate
• Significance testing
• Model selection
• Resampling
• Permutation tests
• Computer-based techniques

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Understanding variation

• ..the central problem in management and
  leadership is failure to understand the
  information in variation Dr W. Edwards Deming
• Concept can be grasped without emphasizing
  mathematics or formulas
• Hands-on experiments
• Book Statistical Thinking for Managers by J.A.
  John, D. Whitaker and D.G. Johnson

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Classroom experiments

• Beads experiment
• Many white and red beads majority white
• Samples of 50 taken
• Plot the number of red beads over time
• Quincunx experiment
• Simulates a process to produce tubing with 50mm
  diameter
• The process involves several steps
• An operator is employed to monitor the process

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Quincunx board
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One sequence of 25 balls
mean49.6 sd1.5
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Tampering

• Method 2 Process adjustment. The operator
  tries to compensate for the results of the
  previous sample
• Method 3 Variability reduction. The operator
  adjusts to try and achieve the same result as the
  previous sample

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Means of 50 balls for 30 sequencesMethods 1 and
3 (Method 250.0)
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Standard deviations of 50 balls for 30
sequences Methods 1,2 and 3
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Analysis of Designed Experiments
  Replicate Seedlot Tree  
4 X X X X X X X X
3 X X X X X X X X
1 5 X X X X X X X X
2 X X X X X X X X
1 X X X X X X X X  
4 X X X X X X X X
1 X X X X X X X X
2 3 X X X X X X X X
5 X X X X X X X X
2 X X X X X X X X  
Seedlots 1 Acacia
2 Angophora 3
Casuarina 4 Melaleuca
5 Petalostigma
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Analysis of Variance Table
Source of variation d.f. s.s.
m.s. v.r. F pr. repl
1 20.301 20.301 7.54 seedlot
4 505.868 126.467 49.94 lt.001
Residual 74 199.350
2.694 Total 79 725.529
Tables of means Grand mean 6.12
seedlot Acacia Angophora Casuarina
Melaleuca Petalostigma 10.29
7.10 5.51 4.94 2.73
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Correct Analysis of Variance Table
Source of variation d.f. s.s.
m.s. v.r. F pr. repl stratum
1 20.301 20.301 3.42 repl.plot
stratum seedlot 4 505.868
126.467 21.30 0.006 Residual
4 23.746 5.936 2.37 repl.plot.tree
stratum 70 175.614 2.509 Total
79 725.529 Tables of
means Grand mean 6.12 seedlot Acacia
Angophora Casuarina Melaleuca Petalostigma
10.29 7.10 5.51 4.94
2.73
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• Treatment
• Technical Replicate
• Dye
• Array

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• Treatment
• Biological Replicate
• Technical Replicate
• Dye
• Array

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Opening screen of DataPlus
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Step-by-step instruction

• Choose you experiment design from the list
• Click the Next button

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Step-by-step instruction

• Type in the numbers of replicates, plots and
  trees
• Click the Next button

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Treatment screen
Treatment Levels to Input treatment names
Treatment Layout to Input the treatment layout
Note plots stratum
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Measurement screen
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Output Summary screen
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Design of Experiments

• Designs mainly used to be constructed using
  combinatorics or group theory
• The class of Partially Balanced Incomplete Block
  designs was defined and developed
• These designs did not always focus on quantities
  of importance to practitioners
• We need to maximize the amount of treatment
  information in the lowest stratum (where we have
  most precision)
• The average efficiency factor does this and can
  be used as an objective function in a computer
  search algorithm

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Two possible arrangements for an incomplete
block design with 9 treatments
  Replicate 1 Replicate
2   Block 1 2 3 1 2
3 ____________
___________   1 4 7
1 2 3 2 5 8
4 5 6 3 6 9 7
8 9       Replicate 1
Replicate 2   Block 1 2 3
1 2 3 ___________
___________   1 4 7
1 5 4 2 5 8 2
8 6 3 6 9 3
9 7
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Software - CycDesigN

• Windows 95 to XP
• Visual C
• Resolvable / non-resolvable
• Block / row-column
• One / two stage
• Cyclic / alpha / other
• Factorial / nested treatments
• t-Latinized / partially-latinized
• Unequal block sizes

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Latinized row-column design for 20 treatments
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Summary

• In Australia (and probably elsewhere) we need to
  change some of the teaching practice and content
  in secondary schools and universities in order to
  prevent a continuing decline in the number of
  statistics students
• Development of and education using computer-based
  statistical techniques may provide an attractive
  addition to existing curricula