Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R.

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1 R version ( ) Copyright (C) 2011 The R Foundation for Statistical Computing ISBN Platform: x86_64-pc-mingw32/x64 (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. 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 HTML browser interface to help. Type 'q()' to quit R. [Previously saved workspace restored] setwd("c:/") # t-test za sparene podatke (bodovi s prvog kolokvija) - svodi se na t-test za jedan uzorak bodovi=read.table("kolokvij1.dat") zad1=bodovi$v1 zad2=bodovi$v2 hist(zad1,breaks=seq(from=-0.5,by=3,length=7)) hist(zad2,breaks=seq(from=-0.5,by=3,length=7)) d=zad1-zad2 n=length(d) n [1] 63 xpotez=mean(d) xpotez [1] s=sd(d) s [1] t=xpotez*sqrt(n)/s t [1] pv=2*(1-pt(t,n-1)) pv [1] #provjera t.test(zad1,zad2,paired=t) Paired t-test data: zad1 and zad2 t = , df = 62, p-value = alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval:

2 sample estimates: mean of the differences # Jednofaktorski model podaci=read.table("vrpce.dat") kvaliteta=podaci$v1 premaz=factor(rep(letters[1:4],c(5,4,7,6))) premaz [1] A A A A A B B B B C C C C C C C D D D D D D Levels: D vrpce=data.frame(premaz,kvaliteta) vrpce premaz kvaliteta 1 A 10 2 A 15 3 A 8 4 A 12 5 A 15 6 B 14 7 B 18 8 B 21 9 B C C C C C C C D D D D D D 15 help(tapply) starting httpd help server... done ni=tapply(kvaliteta,premaz,length) ni D n=sum(ni) n [1] 22 lmean=tapply(kvaliteta,premaz,mean) lmean D plot(lmean,type="b") 2

3 lvar=tapply(kvaliteta,premaz,var) lvar D m=4 xpotez=crossprod(ni,lmean)/n xpotez [1,] 15 xpoteznovi=xpotez[1,1] sst=crossprod(ni,(lmean-xpoteznovi)^2) sst [1,] 68 sse=crossprod(ni-1,lvar) sse [1,] 94 mst=sst/(m-1) mst [1,] mse=sse/(n-m) mse [1,] f=mst/mse f [1,] qf(1-0.05,m-1,n-m) [1] pv=1-pf(f,m-1,n-m) pv [1,] q=(n-m)*log(mse)-sum((ni-1)*log(lvar)) h=1+(sum(1/(ni-1))-1/(n-m))/(3*(m-1)) b=q/h b [1,] pv=1-pchisq(b,m-1) pv [1,] #provjera anova(lm(kvaliteta~premaz)) Analysis of Variance Table Response: kvaliteta Df Sum Sq Mean Sq F value Pr(F) premaz * 3

4 Residuals Signif. codes: 0 *** ** 0.01 * bartlett.test(kvaliteta,premaz) Bartlett test of homogeneity of variances data: kvaliteta and premaz Bartlett's K-squared = 4.123, df = 3, p-value = # Dvofaktorski model podaci=read.table("gorivo.dat") potrosnja=podaci$v1 razred=factor(rep(1:5,c(9,9,9,9,9))) razred [1] [39] Levels: tmp=rep(letters[1:3],c(3,3,3)) tmp [1] "A" "A" "A" "B" "B" "B" "C" "C" "C" marka=factor(rep(tmp,5)) marka [1] A A A B B B C C C A A A B B B C C C A A A B B B C C C A A A B B B C C C A A [39] A B B B C C C Levels: gorivo=data.frame(razred,marka,potrosnja) gorivo razred marka potrosnja 1 1 A A A B B B C C C A A A B B B C C C A A A B 9.6 4

5 23 3 B B C C C A A A B B B C C C A A A B B B C C C 10.3 ni=tapply(potrosnja,list(razred,marka),length) ni n=sum(ni) n [1] 45 lmean=tapply(potrosnja,list(razred,marka),mean) lmean plot(lmean,type="b",ylim=c(8.5,11.5),col="blue") points(lmean[,2],type="b",col="green") points(lmean[,3],type="b",col="red") text(c(1,1,1),lmean[1,]+0.1,letters[1:3]) lvar=tapply(potrosnja,list(razred,marka),var) lvar

6 m1=5 m2=3 l=3 mi=apply(lmean,1,mean) mi mj=apply(lmean,2,mean) mj xpotez=mean(lmean) xpotez [1] sst1=m2*l*sum((mi-xpotez)^2) sst1 [1] sst2=m1*l*sum((mj-xpotez)^2) sst2 [1] sst12=0 for(i in 1:m1) + for(j in 1:m2) + sst12=sum(sst12,l*(lmean[i,j]-mi[i]-mj[j]+xpotez)^2) sst12 [1] sse=(l-1)*sum(lvar) sse [1] 1.16 mst1=sst1/(m1-1) mst1 [1] mst2=sst2/(m2-1) mst2 [1] mst12=sst12/((m1-1)*(m2-1)) mst12 [1] mse=sse/(m1*m2*(l-1)) mse [1] f1=mst1/mse f1 [1] f2=mst2/mse f2 [1] f12=mst12/mse f12 [1] pv1=1-pf(f1,m1-1,m1*m2*(l-1)) pv1 [1] e-16 pv2=1-pf(f2,m2-1,m1*m2*(l-1)) 6

7 pv2 [1] e-13 pv3=1-pf(f12,(m1-1)*(m2-1),m1*m2*(l-1)) pv3 [1] e-10 #provjera anova(lm(potrosnja~razred*marka)) Analysis of Variance Table Response: potrosnja Df Sum Sq Mean Sq F value Pr(F) razred e-16 *** marka e-13 *** razred:marka e-10 *** Residuals Signif. codes: 0 *** ** 0.01 *