1. Replace this box with a picture? Just click : Insert Picture – from file Locate your image Click – insert Position picture over box Crop/scale etc. Select picture, hold down shift key and click on white background then Click Draw –rder – send to back The top of your picture should be hidden by the top shape. Teaching Statistics using the Computer Emlyn Williams CSIRO Australia

2. 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?

3. 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

4. Some possible directions Data mining –Microarrays –Normalization –Multivariate Significance testing –Model selection –Resampling –Permutation tests Computer-based techniques

5. 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

6. 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

7. Quincunx board

8. One sequence of 25 balls mean=49.6 sd=1.5

9. 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

10. Means of 50 balls for 30 sequences: Methods 1 and 3 (Method 2=50.0)

11. Standard deviations of 50 balls for 30 sequences: Methods 1,2 and 3

12. 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

13. 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

14. 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

15. A B Treatment Technical Replicate Dye Array

16. Treatment Biological Replicate Technical Replicate Dye Array ABA B

17. Opening screen of DataPlus Disk driveWorking directory displayed 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

18. Step-by-step instruction Choose you experiment design from the list Click the Next button

19. Step-by-step instruction Type in the numbers of replicates, plots and trees Click the Next button

20. Treatment screen Note: plots stratum Treatment Levels: to Input treatment names Treatment Layout: to Input the treatment layout

21. 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

22. 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

23. 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

24. 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

25. 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

26. Latinized row-column design for 20 treatments

27. 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