DAA12

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2 Observed Data (Total variance) Predicted Data (prediction variance) Errors in Prediction (error variance) Shoesize male female male mean female mean overall mean Shoesize predicted male predicted female male mean female mean overall mean = + female male Shoesize female male predicted male predicted female male mean female mean overall mean male Gender Gender Gender Observed Data (Total variance) Predicted Data (prediction variance) Errors in Prediction (error variance) Shoesize male female male mean female mean overall mean female male Gender Shoesize predicted male predicted female male mean female mean overall mean female male Gender Shoesize predicted male predicted female male mean female mean overall mean female male Gender

3 ! " : $ % = $ ' ; *,,! - : $ % $ ' ; *, $ % $ ' ; *,!01 = 2 3,4, : ;< + 1 : ;> 2 a: m: df: Error MSE

4 TukeyHSD(dat.aov) Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov(formula = shoesize ~ club, data = dat3) karate tennis tetsudo $club diff lwr upr p adj tennis-karate tetsudo-karate tetsudo-tennis

5 !"# = 1 1 # '

7 !"# = 1 1 # ' # = 1 1 # * +!"#, = 1 1 #, ' = # * ' + = 1 1 ' 1 # + + = 1 1 # = #

8 ! " : ( %&' ) % *+ % = 0!. : ( %&' ) % *+ % 0 0 = %&' ( ) % *+ % 123 % ( ) % 4 5 %

9 source(" adj.alpha(#_contarst, alpha) > adj.alpha(5,0.05) [1]

10 dat<-read.csv(" dat$method=factor(dat$method, levels(dat$method)[c(1,3,4,2)]) dat.aov<-aov(result~method, data=dat) summary(dat.aov) Factor

11 dat.means<-tapply(dat$result,dat$method,mean) new.alpha = 1-(1-0.05)^(1/5) cont=c(-3,1,1,1) bunshi=sum(cont*dat.means) bunbo=sqrt(5.29*(sum((cont^2)/8))) t.value=bunshi/bunbo 2*(1-pt(t.value,28)) [1] > 2*(1-pt(t.value,28)) > new.alpha [1] TRUE! = $%& ' ( $ )* $ +,- $ ' ( $. / $ = 3 )* )* )* 849:. + )* <'=> = = 1.243

12 cu.bonf1f(anova_object, data, contrast, new.alpha) > new.alpha<-adj.alpha(5,0.05) > cu.bonf1f(dat.aov,dat,c(-3,1,1,1),new.alpha) multiple t-test w/ bon ferroni t-value p-value adj. alpha [1,] fail to reject (i.e accept) Null Hypo.! = $%& ' ( $ )* $ +,- $ ' ( $. / $ = 3 )* )* )* 849:. + )* <'=> = = 1.243

13 ! = $%& ' ( $ )* $ +,- $ ' ( $. / $ > cu.bonf1f(dat.aov,dat,c(-1,1,0,0),new.alpha) multiple t-test w/ bon ferroni t-value p-value adj. alpha [1,] fail to reject (i.e accept) Null Hypo. = 1 )* )* )* 849:. + 0 )* <'=> = = 2.61

14 ! = $%& ' ( $ )* $ +,- $ ' ( $. / $ > cu.bonf1f(dat.aov,dat,c(-1,0,1,0),new.alpha) multiple t-test w/ bon ferroni t-value p-value adj. alpha [1,] fail to reject (i.e accept) Null Hypo. = 1 )* )* )* 849:. + 0 )* <'=> = = 2.61

15 ! = $%& ' ( $ )* $ +,- $ ' ( $. / $ > cu.bonf1f(dat.aov,dat,c(-1,0,0,1),new.alpha) multiple t-test w/ bon ferroni t-value p-value adj. alpha [1,] reject Null Hypo. = 1 )* )* )* 849:. + 1 )* <'=> = = 3.045

16 ! = $%& ' ( $ )* $ +,- $ ' ( $. / $ = 0 )* )* )* 93:;. + 1 )* ='>? = = > cu.bonf1f(dat.aov,dat,c(0,-2,1,1),new.alpha) multiple t-test w/ bon ferroni t-value p-value adj. alpha [1,] e reject Null Hypo.

17 ! = # $ = ) &'( * & +, & -./ & ) * & $ 0 & $ = &'( ) $ * & +, & -./ ) * & $ & 0 &! 1234 = 5 1! 8,):(,;<=

18 adj.f(m, m-1, dfe, alpha) > new.f<-adj.f(4,3,28,0.05) > new.f [1]

19 cu.scheffe1f(anova_object, data, contrast) > cu.scheffe1f(dat.aov,dat,c(-3,1,1,1)) multiple t-test w/ Scheffe f-value p-value critical F [1,] fail to reject (i.e accept) Null Hypo.

20 > cu.scheffe1f(dat.aov,dat,c(-1,0,1,0)) multiple t-test w/ Scheffe f-value p-value critical F [1,] fail to reject (i.e accept) Null Hypo. > cu.scheffe1f(dat.aov,dat,c(-1,0,0,1)) multiple t-test w/ Scheffe f-value p-value critical F [1,] reject Null Hypo.

22 !"#$% = '$()*+%() + -(".#$ + %$$#$ / 01 = !!56% = '$()*+%() + 7%)*%$ + %$$#$!! 0,9:;<:= = :;<:= + 4 0,9:;<:=!"#$% = '$()*+%() + -(".#$> + -(".#$? + %$$#$ / 01D = E D + 3 E 1D D!!56% = '$()*+%() + 7%)*%$ + (FF5G5(.5)# + %$$#$!! 0,9:;<:= = :;<:= + E HII0J + 3 E 9:;<:=,HII0J + 4 0,9:;<:=,HII0J

23 ! "#$ = & + ( # + ) $ + ( ) #$ + + "#$! "#$ =,-.. + /-.#. / /-..$ / /-.#$ /-.#. /-..$ + /-... +! "#$ /-.#$ " # "! "#$,-.. 5 = 1 " # " " # " /-.#. / " /-..$ / # " /-.#$ /-.#. /-..$ + / " 5 1 1! "#$ /-.#$ # "

24 ! " : $ %. = $ %(. *, * (!, : $ %. $ %(. *! " : $./ = $./( 0, 0 (!, : $./ $./( 0! " : $ %/ $ % 2 / $ %/ 2 + $ % 2 / 2 = 0 *, *(, 0, 0 (!, : $ %/ $ % 2 / $ %/ 2 + $ % 2 / 2 0 *, 0

25 ! " : $ %&'()&. = $ '()&.!, : $ %&'()&. $ '()&.! " : $../ = $.0/1!, : $../ $.0/1! " : $ %&'()&,./ $ '()&,./ $ %&'()&,0/1 + $ '()&,0/1 = 0!, : $ %&'()&,./ $ '()&,./ $ %&'()&,0/1 + $ '()&,0/1 0

26 ! " : $ %&'()&,+, $ '()&,+, $ %&'()&,.,/ + $ '()&,.,/ = 0! 3 : $ %&'()&,+, $ '()&,+, $ %&'()&,.,/ + $ '()&,.,/ 0 DV score CS Male Psy Male PSY CS CS Female Psy Female DV score CS Male Psy Male PSY CS CS Female Psy Female male female male female Gender Gender

27 ! " : $ %&'()&,+, $ '()&,+, $ %&'()&,.,/ + $ '()&,.,/ = 0! 3 : $ %&'()&,+, $ '()&,+, $ %&'()&,.,/ + $ '()&,.,/ 0 DV score CS Male Psy Male PSY CS Psy Female CS Female DV score CS Male Psy Male PSY CS CS Female Psy Female male female male female Gender Gender

28 interaction.plot(dat$gender, dat$affil, dat$shoesize, Y pch=c(20,20), col=c("skyblue","orange"), xlab="gender", ylab="shoesize", lwd=3,type='b',cex=2, trace.label="affiliation") Legend X shoesize Affiliation psy cs F M

29 dat.aov=aov(shoesize~gender*affil, data=dat) dat.aov.sum=summary(dat.aov)

31 shoesize CogSci PsySci

32 shoesize CogSci PsySci gender

33 !! " $ = & ) - ( * ( +, 0 ) ) - ( * ( +, - -!! = & 89:; <= +?;89:;<= 0 - ) 89:; <= +?;89:; <=!! = ) !! F7 = )

34 means<-tapply(dat$shoesize, list(dat$gender,dat$affil), mean) SS_gen_CS<- 5*(means[2,1]^2 + means[1,1]^2-0.5*sum(means[,1])^2) # SS_gender CS SS_gen_PS<- 5*(means[2,2]^2 + means[1,2]^2-0.5*sum(means[,2])^2) # SS_gender PS dat.aov.sum=summary(dat.aov) # ANOVA table MSe=dat.aov.sum[[1]][4,3] # MSE from ANOVA table or MSe=0.62 dfe=dat.aov.sum[[1]][4,1] # DF for error or dfe=16 dfg=1 # DF for gender F_gen_CS=(SS_gen_CS/dfG)/MSe # F-value for gender effect given CS F_gen_PS=(SS_gen_PS/dfG)/MSe # F-value for gender effect given PS P_gen_CS=1-pf(F_gen_CS,1,dfE) # p-value for gender effect given CS P_gen_PS=1-pf(F_gen_PS,1,dfE) # p-value for gender effect given PS

35 !"# = % -". &,(,)*+, /

36 !! " $ = & ) - ( * +, ( 0 ) ) - ( * +, ( - -!! = & 7! 5 + 9!5 0 - ) 7! 5 + 9! 5!! = ) !! = )

37 SS_affil_F<- 5*(means[1,1]^2+means[1,2]^2-0.5*sum(means[1,])^2) #SS_affil F SS_affil_M<- 5*(means[2,1]^2+means[2,2]^2-0.5*sum(means[2,])^2) #SS_affil M dfa=1 # DF for affil F_affil_F=SS_affil_F/dfA/MSe # F-value for affiliation effect F F_affil_M=SS_affil_M/dfA/MSe # F-value for affiliation effect M P_affil_F=1-pf(F_affil_F,1,dfE) # p-value for affiliation effect F P_affil_M=1-pf(F_affil_M,1,dfE) # p-value for affiliation effect M

39 CRF.tsme(anova_object, data) > tsme = CRF.tsme(dat.aov, dat) simple main effect test for BETWEEEN subject factor1 ss df ms f p cs e-03 psy e-06 residual Tukey HSD test - between subject affil = cs F M F FALSE TRUE M TRUE FALSE Tukey HSD test - between subject affil = psy F M F FALSE TRUE M TRUE FALSE

40 CRF.tsme(dat.aov, dat) > tsme = CRF.tsme(dat.aov, dat) simple main effect test for BETWEEN subject factor2 ss df ms f p F M residual

42 interaction.plot(dat$duration,dat$method,dat$result, pch=c(20,20), col=c("skyblue","orange"), ylab="score", xlab="duration",lwd=3,type='b',cex=2,trace.label="method") score Method method.x method.y 1hour 2hours 3hours 4hours

43 mod1=aov(result~method+duration,data=dat) mod1.sum=print(summary(mod1)) score Method method.x method.y 1hour 2hours 3hours 4hours Duration

44 mod2=aov(result~method*duration,data=dat) mod2.sum=print(summary(mod2)) score Method method.x method.y 1hour 2hours 3hours 4hours Duration

45 !! " $ = & ) - ( * ( +, 0 ) ) - ( * ( +, - -!! = & :7 0 - ) : 7!! ; 0< = = 2.5!! ; -< = = 0.4!! ; D< = = 12.10!! ; G< = = 32.4

46 score Method method.x method.y 1hour 2hours 3hours 4hours Duration

47 !! " $ = & ) - ( * ( +, 0 ) ) - ( * ( +, !! = & 1; 9 + 2;9 + 3;9 + 4;9 0 - ) 1; 9 + 2; 9 + 3; 9 + 4; A = = G = = 1

48 score Method method.x method.y 1hour 2hours 3hours 4hours Duration

49 !"# = % -". &,(,)*+, /

50 !"# = % -". &,(,)*+, / = % ,3,45, 5 = 2.65 qv=qtukey(0.95,dfd+1,dfe) hsd=qv*(sqrt(mse/5)) hsd [1]

51 > CRF.tsme(mod2, dat) simple main effect test for BETWEEEN subject factor1 ss df ms f p 1hour hours hours hours residual Tukey HSD test - between subject duration = 3hours method.x method.y method.x FALSE TRUE method.y TRUE FALSE Tukey HSD test - between subject duration = 4hours method.x method.y method.x FALSE TRUE method.y TRUE FALSE

52 simple main effect test for BETWEEN subject factor2 ss df ms f p method.x method.y residual Tukey HSD test - within subject method = method.x 1hour 2hours 3hours 4hours 1hour FALSE FALSE TRUE TRUE 2hours FALSE FALSE FALSE FALSE 3hours TRUE FALSE FALSE FALSE 4hours TRUE FALSE FALSE FALSE

53 dat<-read.table(" means<-tapply(dat$shoesize,list(dat$gender, dat$affil),mean) Ns<-tapply(dat$shoesize,list(dat$gender, dat$affil),length) sds<-tapply(dat$shoesize,list(dat$gender, dat$affil),sd) sems<-sds/sqrt(ns) plot(c(0,1),means[,1],type='o',col='skyblue', xlim=c(-0.1,1.1), lwd=2, cex=2, pch=20, ylim=c(min(means)*0.975, max(means)*1.025), xlab="gender", ylab="shoesize", xaxt="n") axis(1,c(0,1),c("female","male")) lines(c(0,1),means[,2],type='o',col='orange',lwd=2,cex=2,pch=20) lines(c(0,0),c(means[1,1]-sems[1,1],means[1,1]+sems[1,1]),col="skyblue",lwd=2) lines(c(0,0),c(means[1,2]-sems[1,2],means[1,2]+sems[1,2]),col="orange",lwd=2) lines(c(1,1),c(means[2,1]-sems[2,1],means[2,1]+sems[2,1]),col="skyblue",lwd=2) lines(c(1,1),c(means[2,2]-sems[2,2],means[2,2]+sems[2,2]),col="orange",lwd=2) legend("topleft",c("cogsci","psysci"),col=c("skyblue","orange"),lwd=2)

DAA04

DAA04 # plot(x,y, ) plot(dat$shoesize, dat$h, main="relationship b/w shoesize and height, xlab = 'shoesize, ylab='height, pch=19, col='red ) Relationship b/w shoesize and height height 150 160 170 180 21 22