Title: Divisional Presentation Template
1Teaching Statistics using the Computer
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Emlyn Williams CSIRO Australia
2Statistics 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?
3Possible 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
4Some possible directions
- Data mining
- Microarrays
- Normalization
- Multivariate
- Significance testing
- Model selection
- Resampling
- Permutation tests
- Computer-based techniques
5Understanding 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
6Classroom 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
7Quincunx board
8One sequence of 25 balls
mean49.6 sd1.5
9Tampering
- 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
10Means of 50 balls for 30 sequencesMethods 1 and
3 (Method 250.0)
11Standard deviations of 50 balls for 30
sequences Methods 1,2 and 3
12Analysis 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
13Analysis 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
14Correct 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
15- Treatment
- Technical Replicate
- Dye
- Array
16- Treatment
- Biological Replicate
- Technical Replicate
- Dye
- Array
17Opening screen of DataPlus
18Step-by-step instruction
- Choose you experiment design from the list
- Click the Next button
19Step-by-step instruction
- Type in the numbers of replicates, plots and
trees - Click the Next button
20Treatment screen
Treatment Levels to Input treatment names
Treatment Layout to Input the treatment layout
Note plots stratum
21Measurement screen
22Output Summary screen
23Design 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
24Two 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
25Software - 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
26Latinized row-column design for 20 treatments
27Summary
- 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