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Teaching Statistics using the Computer
Emlyn WilliamsCSIRO
Australia
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?
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
Some possible directions
• Data mining– Microarrays– Normalization– Multivariate
• Significance testing– Model selection– Resampling– Permutation tests
• Computer-based techniques
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
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
Quincunx board
One sequence of 25 balls
mean=49.6
sd=1.5
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
Means of 50 balls for 30 sequences:Methods 1 and 3 (Method 2=50.0)
40
42
44
46
48
50
52
54
56
58
1 4 7 10 13 16 19 22 25 28
sequence number
mm
mean1
mean3
Standard deviations of 50 balls for 30 sequences: Methods 1,2 and 3
1
2
3
4
5
6
7
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
sequence number
mm
sd1
sd2
sd3
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
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 <.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
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 stratumseedlot 4 505.868 126.467 21.30 0.006Residual 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
A
B
•Treatment
•Technical Replicate
•Dye
•Array
• Treatment• Biological Replicate
• Technical Replicate• Dye
• Array
A BA B
Opening screen of DataPlus
Disk drive Working directorydisplayed in the status bar
Top bar menu
Experimental Title which must be filled
Path of working directory.
Directory structure
File display area
File selection type
Button to go to the next screen
Status bar
To create new sub-directory
Step-by-step instruction
• Choose you experiment design from the list
• Click the Next button
Step-by-step instruction
• Type in the numbers of replicates, plots and trees
• Click the Next button
Treatment screen
Note: plots stratum
Treatment Levels: toInput treatment names
Treatment Layout: toInput the treatment layout
Measurement screen
New Spreadsheet: for entering your measurement using Microsoft Excel
Open Data File: for opening existing data file
Derived variate: for declaring new variates (not measured in the field) e.g volume, basal area
Note: trees stratum
Output Summary screen
Output: for generating summary file
View: to view summary data file using Notepad
Select Tree: for selecting trees in inner plot
Modify: to modify data file
GenStat or SAS: to go to GenStat or SAS screen
Note: plots stratum
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
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
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
Latinized row-column design for 20 treatments
Column 1 2 3 4 5
16 17 19 18 13 6 2 4 8 15 Rep 1 12 5 7 10 11 20 9 14 1 3
5 15 1 19 20 4 12 17 3 8 Rep 2 13 18 6 9 7 10 14 11 16 2
15 7 3 17 10 19 1 2 13 12 Rep 3 8 16 5 14 6 11 4 18 20 9
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