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Teaching Statistics using the Computer Emlyn WilliamsCSIROAustralia

• Statistics students in AustraliaDecline in statistics student numbers in AustraliaDuring 2003, 3000 PhDs in AustraliaOnly 186 PhDs in Mathematical and Statistical SciencesWhy?

• Possible reasons for the declinePopularity of Computing ScienceReduced capacity of our Universities to train Maths / Stats professionalsType of Statistics being taught in Secondary SchoolsDistribution theoryProbabilityEquations / formulas

• Some possible directionsData miningMicroarraysNormalizationMultivariateSignificance testingModel selectionResamplingPermutation testsComputer-based techniques

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

• Classroom experimentsBeads experimentMany white and red beads majority whiteSamples of 50 takenPlot the number of red beads over time

Quincunx experimentSimulates a process to produce tubing with 50mm diameterThe process involves several stepsAn operator is employed to monitor the process

• Quincunx board

• One sequence of 25 ballsmean=49.6sd=1.5

• TamperingMethod 2 Process adjustment. The operator tries to compensate for the results of the previous sampleMethod 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)

Chart1

50.153.3

49.846.6

50.150.1

49.851.4

49.851.5

5052.7

5045.1

49.954

5048.6

50.251.6

5045.8

50.247.7

50.146.4

50.251.3

5044.3

49.946.7

5050.4

49.955.8

5054.3

5054.4

49.953.9

5046.7

49.951.2

49.947.4

50.155.6

49.845

50.442.3

50.151.2

5044.8

50.153.9

mean1

mean3

sequence number

mm

Sheet1

sequencemean1mean3sd1sd2sd3

150.153.31.72.56.7

249.846.61.52.13.7

350.150.11.52.15.2

449.851.41.52.14.8

549.851.51.52.35.5

65052.71.62.43.6

75045.11.62.23.7

849.9541.422.5

95048.61.61.94.1

1050.251.61.72.16

115045.81.62.12.6

1250.247.71.51.94.3

1350.146.41.523.3

1450.251.31.62.55.4

155044.31.62.34.2

1649.946.71.52.42.8

175050.41.42.45

1849.955.81.51.92.8

195054.31.622.8

205054.41.82.43.2

2149.953.91.72.23.9

225046.71.72.53.2

2349.951.21.52.65.2

2449.947.41.52.23.8

2550.155.61.623.9

2649.8451.42.43.3

2750.442.31.52.12.3

2850.151.21.626.9

295044.81.51.94.1

3050.153.91.62.23.3

1500.2149446.865.7122.1

50.006666666749.81.562.194.07

Sheet1

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mean1

mean3

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mm

Sheet2

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sd1

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sd3

sequence number

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Sheet3

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

Chart2

1.72.56.7

1.52.13.7

1.52.15.2

1.52.14.8

1.52.35.5

1.62.43.6

1.62.23.7

1.422.5

1.61.94.1

1.72.16

1.62.12.6

1.51.94.3

1.523.3

1.62.55.4

1.62.34.2

1.52.42.8

1.42.45

1.51.92.8

1.622.8

1.82.43.2

1.72.23.9

1.72.53.2

1.52.65.2

1.52.23.8

1.623.9

1.42.43.3

1.52.12.3

1.626.9

1.51.94.1

1.62.23.3

sd1

sd2

sd3

sequence number

mm

Sheet1

sequencemean1mean3sd1sd2sd3

150.153.31.72.56.7

249.846.61.52.13.7

350.150.11.52.15.2

449.851.41.52.14.8

549.851.51.52.35.5

65052.71.62.43.6

75045.11.62.23.7

849.9541.422.5

95048.61.61.94.1

1050.251.61.72.16

115045.81.62.12.6

1250.247.71.51.94.3

1350.146.41.523.3

1450.251.31.62.55.4

155044.31.62.34.2

1649.946.71.52.42.8

175050.41.42.45

1849.955.81.51.92.8

195054.31.622.8

205054.41.82.43.2

2149.953.91.72.23.9

225046.71.72.53.2

2349.951.21.52.65.2

2449.947.41.52.23.8

2550.155.61.623.9

2649.8451.42.43.3

2750.442.31.52.12.3

2850.151.21.626.9

295044.81.51.94.1

3050.153.91.62.23.3

1500.2149446.865.7122.1

50.006666666749.81.562.194.07

Sheet1

00

00

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mean1

mean3

sequence number

mm

Sheet2

000

000

000

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sd1

sd2

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sequence number

mm

Sheet3

• 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 TableSource 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

• Correct Analysis of Variance TableSource 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

• Treatment

Technical ReplicateDye

Array

• TreatmentBiological Replicate

Technical ReplicateDye

Array

• Opening screen of DataPlus

• Step-by-step instructionChoose you experiment design from the listClick the Next button

• Step-by-step instructionType in the numbers of replicates, plots and treesClick the Next button

• Treatment screenNote: plots stratumTreatment Levels: toInput treatment namesTreatment Layout: toInput the treatment layout

• Measurement screen

• Output Summary screen

• Design of ExperimentsDesigns mainly used to be constructed using combinatorics or group theoryThe class of Partially Balanced Incomplete Block designs was defined and developedThese designs did not always focus on quantities of importance to practitionersWe 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 - CycDesigNWindows 95 to XPVisual C++Resolvable / non-resolvableBlock / row-columnOne / two stageCyclic / alpha / otherFactorial / nested treatmentst-Latinized / partially-latinizedUnequal block sizes

• Latinized row-column design for 20 treatments

Column

1

2

3

4

5

16

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