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1 Math Treibergs Peanut xample: 2 5 alf Replication Factorial xperiment Name: xample Feb. 8, 2014 We describe a 2 5 experimental design with one half replicate per cell. It comes from a paper by Kligo, n application of fractional experimental factorial designs Quality ngineering,1, (1989) who studied a process to extract oil from peanuts. It is quoted from evine, Ramsey and Smidt, pplied Statistics for ngineers and Scientists,Prentice all, The defining contrast is. The testing combinations are the words that have an even number of symbols in common with. The paired ones are the odds which are confounded (in data set order) vens Odds 1 The estimators for effects may be determined as contrasts. For example, the experimental combination is included if the combination word. For example, to determine +1 signs in the contrast, see which treatment combination includes the word, for example is included if W or the power of in W is odd: 1,,,,,,,,,,,,,,, so = 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1 (α) = 1 (1) + () () + () () + () () + () 1 () + () () + () () + () () + () Similarly, the estimator for a two letter effect is included if there is an even number of letters in common 1,,,,,,,,,,,,,,, so = 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1 (αβ) = 1 (1) () () + () + () () () + () 1 +() () () + () + () () () + () 1
2 ata Set Used in this nalysis : # Math Peanut ata Feb. 9, 2014 # Treibergs # # The paper by Kligo, "n application of fractional experimental factorial # designs" Quality ngineering 1, (1989) studied a process to extract # oil from peanuts. Quoted from evine, Ramsey and Smidt, pplied # Statistics for ngineers and Scientists, Prentice all, # # The response is the amount of oil (solubility) that could dissolve in the # carbon dioxide. # # Factors (evels =high, =low) # = arbon dioxide pressure # = arbon dioxide temperature # = Peanut moisture # = arbon dioxide flow rate # = Peanut particle size # "" "" "" "" "" "Solubility" R Session: R version ( ) opyright () 2011 The R Foundation for Statistical omputing ISN Platform: i38-apple-darwin9.8.0/i38 (32-bit) R is free software and comes with SOUTY NO WRRNTY. You are welcome to redistribute it under certain conditions. Type license() or licence() for distribution details. Natural language support but running in an nglish locale R is a collaborative project with many contributors. 2
3 Type contributors() for more information and citation() on how to cite R or R packages in publications. Type demo() for some demos, help() for on-line help, or help.start() for an TM browser interface to help. Type q() to quit R. [R.app GUI 1.41 (5874) i38-apple-darwin9.8.0] [istory restored from /Users/andrejstreibergs/.Rapp.history] > tt=read.table("m3082atapeanut.txt",header=t) > attach(tt) > tt Solubility > =factor(); =factor(); =factor(); =factor(); =factor() > ######## NYSIS OF VRIN ################################# > a1=aov(solubility~++++); summary(a1) f Sum Sq Mean Sq F value Pr(>F) * * Residuals Signif. codes: 0 *** ** 0.01 * > ########### INTRTION POTS #################################### > layout(matrix(c(1,11,12,13,2,5,14,15,3,,8,1,4,7,9,10),ncol=4)) > interaction.plot(,,solubility,main="interaction Plots") > interaction.plot(,,solubility) > interaction.plot(,,solubility) > interaction.plot(,,solubility) > interaction.plot(,,solubility) 3
4 > interaction.plot(,,solubility) > interaction.plot(,,solubility) > interaction.plot(,,solubility) > interaction.plot(,,solubility) > interaction.plot(,,solubility) > > ############# TS OF MNS N FFTS ################### > model.tables(a1,"means") Tables of means Grand mean > model.tables(a1) Tables of effects > ################# IGNOSTI POTS ############################## > plot(a1) 4
5 > ############ FFTS S ONTRSTS ############################### > # GRN MN > e1=sum(solubility*c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1))/1; e1 [1] > e=sum(solubility*c(-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1))/1; e [1] > e=sum(solubility*c(-1,-1,1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1))/1; e [1] > e=sum(solubility*c(1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1))/1; e [1] > e=sum(solubility*c(-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1))/1; e [1] > e=sum(solubility*c(1,-1,1,-1,-1,1,-1,1, 1,-1,1,-1,-1,1,-1,1))/1; e [1] > e=sum(solubility*c(1,1,-1,-1,-1,-1,1,1, 1,1,-1,-1,-1,-1,1,1))/1; e [1] > e=sum(solubility*c(-1,-1,-1,-1,-1,-1,-1,-1, 1,1,1,1,1,1,1,1))/1; e [1] > e=sum(solubility*c(1,-1,1,-1,1,-1,1,-1, -1,1,-1,1,-1,1,-1,1))/1; e [1] > e=sum(solubility*c(1,1,-1,-1,1,1,-1,-1, -1,-1,1,1,-1,-1,1,1))/1; e [1] > e=sum(solubility*c(1,1,1,1,-1,-1,-1,-1, -1,-1,-1,-1,1,1,1,1))/1; e [1] > e=sum(solubility*c(-1,1,1,-1,1,-1,-1,1, 1,-1,-1,1,-1,1,1,-1))/1; e [1] > e=sum(solubility*c(1,1,-1,-1,-1,-1,1,1, -1,-1,1,1,1,1,-1,-1))/1; e [1] > e=sum(solubility*c(1,-1,1,-1,-1,1,-1,1, -1,1,-1,1,1,-1,1,-1))/1; e [1] > e=sum(solubility*c(1,-1,-1,1,1,-1,-1,1, -1,1,1,-1,1,1,1,-1))/1; e [1] > e=sum(solubility*c(1,-1,-1,1,-1,1,1,-1, 1,-1,-1,1,-1,1,1,-1))/1; e [1] > ef=c(e,e,e,e,e,e,e,e,e,e,e,e,e,e,e) > ############### POT QQPOT OF FFTS. OUTIRS R SIGNIFINT ###### > layout(1) > qqnorm(ef);qqline(ef) 5
6 Interaction Plots
7 Residuals vs Fitted Normal Q-Q Residuals Standardized residuals Fitted values Theoretical Quantiles Standardized residuals Scale-ocation Standardized residuals : onstant everage: Residuals vs Factor evels 1 9 Fitted values Factor evel ombinations 7
8 Normal Q-Q Plot Sample Quantiles Theoretical Quantiles 8
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