Do we really need statistics in science?

Transcription

1 September 16, 2009 D we really need statistics in science? FWF Graduate Seminar Timthy M. Yung, Ph.D. Assciate Prfessr Department f Frestry, Wildlife & Fisheries Frest Prducts Center

2 Dn t wrry, it will be OK.

3 Overview Definitin f Statistics Variance ( 2 ) Randm variable (sample space) Prbability Definitin f Science 1 st Law f Statistics Key Assumptins Research Prgram

4 Statistics The Measurement f Uncertainty

5 Definitin f Statistics? Many, many definitins.mst peple in this rm wuld have different definitins Cmmn theme f mst definitins: iti.study f variance ( 2 )..quantifying variance.

6 Francis Galtn Variance ( 2 ) Cmpnents f a System If X and Y are tw randm variables, (X,Y dependent): Var(X + Y) = VarX + VarY + 2Cv(X,Y) r, Var(aX + by) = a 2 VarX + b 2 VarY + 2abCv(X,Y) (X,Y independent): Var( X + Y) = VarX + VarY

7 Generalizatin 2 Variance ( 2 ) Cmpnents f a System (dependent d randm variables): n n var[ X ] var[ X ] 2 cv[ X, X ] i i i j i i i j (independent randm variables): n var[ X ] var[ X ] i i n i i

8 2 Variance ( 2 ) Cmpnents f a System Reduce (r increase) variance (dependent randm variables): Var(X + Y) = VarX + VarY + 2Cv(X,Y) (X,Y independent): Var( X + Y) = VarX + VarY r Var( X + Y) = VarX + VarY What is the difficulty: quantifying 2

9 Randm Variable Randm variable (X) is allwed t vary within a sample space fr the set f real numbers e.g., weight, height, misture cntent, number f spts, distance traveled, survival rate, etc.

10 Tw dice: Randm Variable Outcmes: (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12) Prbability f an utcme?

11 Tw dice: Randm Variable 6 Frequenc cy Outcmes

12 Tw dice: Randm Variable 6 Frequenc cy Outcmes

13 Sample Space Tw dice: 6 5 Die Die 2

14 Sample Space Tw dice: Lucky 7? 6 5 Die Die 2

15 Prbability bilit Density Functin Tw dice: (pdf) 6/36 Prbabilit ty 5/36 4/36 3/36 2/36 1/ Outcmes

16 Prbability bilit Density Functin Tw dice: 6/36 (pdf) Discrete Prbabilit ty 5/36 4/36 3/36 2/36 1/ Outcmes

17 Prbability Density Functin (Discrete pdfs) Bernulli Binmiali 1 ( ) x x f x p (1 p) n x f ( x ) p (1 p ) x n x Pissn f ( x ) e x x! Gemetric (r Pascal) Hypergemetric f( x) f ( x) p(1 p) x etc., etc. etc.. K M K x n x M n

18 Prbability bilit Density Functin (pdf) Cntinuus Nrmal r Gaussian (with = 0; = 1)

19 Prbability bilit Density Functin (pdf) Cntinuus (e.g., t distributin) The t statistic was invented by William Sealy Gsset The t statistic was invented by William Sealy Gsset ( ) fr cheaply mnitring the quality f beer brews. Student was his pen name.

20 Prbability Density Functin (Cntinuus pdfs) Nrmal f( x) 1 e 2 (1/2)[( x )/ ] 1 2 (1/2)[( x] Standard Nrmal f( x) e ( = 0; = 1) 2 p 1 ( ) p ( ) p (1 x / p) 2 Student s t f ( x) 1/ 2 2 ( p 1)/ 2 F distributin Weibull p q ( ) p/2 ( p/2) 1 ( ) 2 p x f x p q ( ) ( ) q [1 ( p/ q) x] 2 2 k x f( x) etc., etc. etc.. k 1 e k ( x/ ) 2 ( p q)/2

21 Why are the prbability density functins imprtant? Weibull Nrmal Nn-central t

22 Hw are yur data cllected frm sme sample space?

23 Statistical Methds Parametric Methds Analysis f variance (ANOVA) Chi-square test Crrelatin Factr Analysis Mann-Whitney U Mean Square Weighted Deviatin MSWD Pearsn prduct-mment crrelatin cefficient Regressin analysis Lgistic regressin Spearman's rank crrelatin cefficient Student's t-test Time Series Analysis etc., etc., etc. Nn-Parametric Methds Andersn-Darling test Cchran's Q Chen's kappa Efrn-Petrsian test Friedman tw-way analysis Kendall's tau Kendall's W Klmgrv-Smirnv test Kruskal-Wallis ne-way analysis Kuiper's test Wilcxn rank sum test Pitman's permutatin test Rank prducts Siegel-Tukey test Wilcxn signed-rank test. etc., etc., etc

24 Statistical Inference Statistical inference (r statistical inductin) is the use f statistics and randm sampling t make inferences cncerning sme unknwn aspect f the ppulatin.

25 Definitin f Science?

26 Definitin f Science? The wrd science cmes frm Latin "scientia," meaning knwledge. Science is an intellectual activity carried n by humans that is designed t discver infrmatin abut the natural wrld in which humans live and t discver the ways in which this infrmatin can be rganized dit int meaningful patterns It is dne thrugh bservatin f natural phenmena, and/r thrugh experimentatin that tries t simulate natural prcesses under cntrlled cnditins A primary aim f science is t cllect facts (data) An ultimate purpse f science is t discern the rder that exists between and amngst the varius facts..systematic knwledge-base r prescriptive practice that is capable f resulting in a predictin r predictable type f utcme

27 Definitin f Science? Scientific Reasning r Inference Deductive Reasning: Knwledge Thery Hypthesis Data

28 Definitin f Science? Scientific Reasning r Inference Deductive Reasning: Knwledge Thery Hypthesis Inductive Reasning: Data Data Hypthesis Thery Knwledge

29 D we really need Statistics in Science? Observatins (data) Meaningful patterns Experimentatin Discern rder between and amngst facts Hypthesis testing (r generatin) Predictin etc., etc., etc.

30 D we really need Statistics in Science? Hw will yu quantify variance ( 2 ) f bservatinal data withut the use f statistical methds? An apprximate answer t the right questin is wrth a gd deal mre than the exact answer t an apprximate prblem Jhn W. Tukey ( )

31 First Law f Applied Statistics (Gleser 1996).tw individuals using the same statistical methd n the same data shuld arrive at the same cnclusin.

32 Key Assumptins What is the questin (prblem definitin)? Sample space (bias?) Data quality Parametric (pdf) assumptin? Mst apprpriate methd t prvide the apprximate answer t a welldefined questin

33 Research Prgram (Bi-based Prducts Industries) Statistical Prcess Cntrl Decisin Thery Ensemble Prcess Mdeling Training Statistical Thinking

34 Statistical Prcess Cntrl 99.7% Special-Cause Variatin Upper Cntrl Limit ~ + 3 Standard Deviatins Meas surement Cmmn-Cause Variatin ~ 3 Standard Deviatins Average Special-Cause Variatin Lwer Cntrl Limit Time Ordered

35 Statistical Prcess Cntrl Hardwd/Sftwd Sawmills Hypthesis, a priri, the use f real-time statistical prcess cntrl t mnitr and reduce lumber thickness variatin des nt imprve lumber recvery, lumber quality r financial perfrmance. 35

36 Statistical Prcess Cntrl Hardwd/Sftwd Sawmills Summary - Sawmill A Quercus rubra 36

37 Statistical Prcess Cntrl Hardwd/Sftwd Sawmills Cmpany Investment Return ROI A $15,000 $180,000 12:1 B $27,000 $752,000 28:1 C (sftwd) $13,000 $210,000 16:1 D $21,000 $147,000 7:1 Ttal: $76,000 $1,289,000 17:1 37

38 Statistical Prcess Cntrl Staves fr Burbn Barrels Hypthesis: A reductin in stave width variability and bilge variability in any f the 15 jinter wheels will reduce bth within and between barrel circumference variability 38

39 Statistical Prcess Cntrl Staves fr Burbn Barrels 39

40 Statistical Prcess Cntrl Staves fr Burbn Barrels Stand dard Errr Jul '08 Aug '08 Sept '08 Oct '08 Nv '08 Dec '09 Mnth and Year Table 1 Wheel 1 Table 1 Wheel 2 Table 1 Wheel 3 Table 1 Wheel 4 Table 1 Wheel 5 Table 2 Wheel 1 Table 2 Wheel 2 Table 2 Wheel 3 Table 2 Wheel 4 Table 2 Wheel 5 Table 3 Wheel 1 Table 3 Wheel 2 Table 3 Wheel 3 Table 3 Wheel 4 Table 3 Wheel 5 40

41 Statistical Prcess Cntrl Staves fr Burbn Barrels Barrel circumference variatin was reduced Allwed fr increase in barrel target circumference size Yield per barrell (Official Prf Gallns) at Jack Daniels imprved by 0.3 OPG after SPC Additinal 938 barrels f Jack Daniels and apprximately $300,000 f cst savings ver the sixmnth study perid (estimated by Brwn Frman) 41

42 Ensemble Prcess Mdeling Questin: Can imprved methdlgies fr real-time prcess mdeling imprve the scientific understanding f undiscvered crrelatins in bi-based prducts manufacturing (facilitate t imprved causatin investigatin)?

43 Ensemble Prcess Mdeling Idea: Reduce generalized errr f predictin by cmbining predictins frm several mdels and varius types f algrithms int an ensemble MLR Regressin Trees Partial Least Squares Ridge Regressin Neural Netwrks Bxplts f MLR and RT Residuals fr Validatin Data MDF 0.750" IB Residual MLR MDF 0.750" (n=70) RT MDF 0.750" (n=70)

44 Ensemble Prcess Mdeling Several large prjects with USDA SBIR cmpetitive grants and private industry (T: $1.6M)

45 Ensemble Prcess Mdeling BiSAT Mdel: Mdeling system fr determining ptimal lcatins fr bimass using facilities in the eastern U.S. ( Quantity (dry tns)

46 Y Y Y 5 Ensemble Prcess Mdeling Regressin Trees 25 Regressin Tree: Piecewise estimate f a regressin functin Cnstructed by recursively partitining the data and sample space Y X X N X>1.5 N Yes X> Yes X X

47 Ensemble Prcess Mdeling Regressin Tree Mdels High Explanatry Value Quantile Regressin n= 100 Nde 2 (n=70) Rfi Refiner steam pressure 54.6 Refiner steam pressure > 54.6 Nde 3 (n=30) Dry fuel bin speed 27.7 Mean IB = 132 Dry fuel bin speed > 27.7 Press start cntrl Mean IB = 151 Press start cntrl > Mean IB = 143 Nde 4T (n=12) Press start cntrl Mean IB = 138 Nde 10T (n=19) Cre scavenger resin 6.0 Press start cntrl > 931 Mean IB = 144 Nde 11T (n=16) Cre scavenger resin > 6.0 Fiber temperature 89.7 Mean IB = 134 Nde 12T (n=11) Nde 6T (n=15) Fiber temperature > 89.7 Mean IB = 144 Nde 13T (n=12) Bx s (1979): All mdels are wrng but sme are useful IB Nde 7T (n=15) Observed Predicted Time Series

48 Training Statistical Thinking Cntinuus imprvement using statistical prcess cntrl fr the bibased prducts industries Advanced statistical seminars fr the bi-based prducts industries Applied design f experiments fr the bi-based prducts industries 48

49 Cnclusin Statistics is a key fundatin f science Bttm-line: Statistics helps minimize the risk f being wrng What makes a scientist great is the care that he/she takes in telling yu what is wrng with his/her results, s that yu will nt misuse them W. Edwards Deming ( )

50 Questins & Discussin html Fr Tday s Graduate, Just One Wrd: Statistics