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2£©Bartlett's test,Õâ¸ö·½·¨ÊÇÒ»¸önonrobustµÄ·½·¨£¬ÐèÒªÊý¾ÝÕý̬·Ö²¼£¬ RÖк¯ÊýΪbartlett.test(),²»ÐèÒªÔÙ¶îÍâ¼ÓÔØ°ü¡£

RÖÐnormality µÄÈ·¶¨¿ÉÒÔͨ¹ý Shapiro-Wilk test»ñµÃ,RÖк¯ÊýΪ shapiro.test()

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## Levene's test, which is robust in the sense that it does not rely on the normality assumption.
##levene.test(car)
library(car)
library(MASS)
cab<-data.frame(cabbages)
cab$comtreat<-as.factor(paste(cab$Cult,cab$Date,sep="")

with(cab,levene.test(HeadWt,comtreat))
# for HeadWt, p<-0.001, indicates that variance inhomogeneity!
## bartlett.test(), which is a nonrobust test with the normality assumption
##the null that the variances in each of the groups (samples) are the same
with(cab,bartlett.test(HeadWt,comtreat))
with(cab,bartlett.test(VitC,comtreat))
## resulted in the same conclusion as derived from the levene's test.
#### normality analysis
## Shapiro-Wilk test
#####shapiro.test(cab[cab$Cult=="c39","HeadWt"]) # normal distribution
with(cab,tapply(HeadWt,comtreat,shapiro.test))  
# at least one dataset is not a normal distribution

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·½²î·ÖÎöÓÐÁ½¸ö·½³Ì aov() ºÍ manova(), ǰÕßÊÊÓÃÓÚµ¥±äÁ¿Êý¾Ý£¬ºóÕßÊÊÓÃÓÚ¶à±äÁ¿Êý¾Ý¡£ÔÚ±¾ÀýÖй۲âµÄÖ¸±êÓÐÁ½¸ö£¬¼´ÖØÁ¿ºÍvcº¬Á¿¡£Òò´Ë¿ÉÒÔÓ¦ÓÃmanova(), µ«´Ë´¦Ò²¸ø³öaovµÄÓ¦ÓÃ˵Ã÷¡£

datam<-cbind(HW=cab$HeadWt,VC=cab$VitC)
Cul<-as.factor(cab$Clut)
Date<-as.factor(cab$Date)
Datam<-cbind(cab$Headwt,cab$)
aov.1<-aov(cab$HeadWt~Cul*Date)
summary(aov.1)

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aov.2<-manova(datam~Cul*Date)
summary.aov(aov.2)

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cab$comtreat<-as.factor(paste(cab$Cult,cab$Date,sep="")
par(mfrow=c(2,1),mai=c(0,0,0,0),omi=c(0.6,0.6,0.1,0.1))
plot(cab$comtreat,cab$HeadWt,xaxt="n"
legend("topright","A",bty="n"
plot(cab$comtreat,cab$VitC)
legend("topright","B",bty="n"
mtext("Æ·ÖֺͲ¥ÖÖÈÕÆÚ",side=1,adj=0.5,outer=TRUE,line=2)
mtext("ÖØÁ¿(kg)",side=2,at=0.75,adj=0.5,outer=TRUE,line=2)
mtext("άËûÃüº¬Á¿(g/kg)",side=2,at=0.25,adj=0.5,outer=TRUE,line=2)


# ¿´Ò»ÏÂÖØÁ¿ºÍVCº¬Á¿Ö®¼äµÄÏà¹ØÐÔ
plot(cab$HeadWt,cab$VitC)
lm1<-lm(VitC~HeadWt,data=cab)
summary(lm1)
abline(lm1)

Tukey¶àÖØ±È½Ï
ËäÈ»R×Ô¼ºÓÐÒ»¸öTukey¶àÖØ±È½ÏµÄ·½³Ì£¬µ«ÊÇÎÒ·¢ÏÖ agricolaeÕâ¸ö°üÖеÄHSD.test·½³Ì·Ç³£ºÃÓá£Õâ¸ö°üÊÇרÃÅÕë¶ÔũҵÌï¼äÊÔÑéºÍÖ²ÎïÓýÖÖÊÔÑé¶ø¿ª·¢µÄ£¬ÊµÓÃÐԱȽϸߡ£
library(agricolae) #¼ÓÔØ°ü
DFerror<-df.residual(aov.1)
MSerror<-deviance(aov.1)/DFerror
cmp.1<-HSD.test(cab$HeadWt,Cul,DFerror,MSerror,group=TRUE)

# ½á¹û±íÃ÷Æ·ÖÖC39µÄÖØÁ¿ÏÔÖø¸ßÓÚÁíһƷÖÖ
#ΪÁ˵õ½ËùÓÐ×éºÏÖ®¼äµÄ±È½Ï£¬ÎÒÃǽøÐÐÁíÍâÒ»ÖÖ·½²î·ÖÎö£º
aov.3<-aov(HeadWt~comtreat,data=cab)
summary(aov.3)
DFerror<-df.residual(aov.3)
MSerror<-deviance(aov.3)/DFerror
cmp.2<-HSD.test(cab$HeadWt,cab$comtreat,DFerror,MSerror,group=TRUE)

#´ÓÖÐÌáÈ¡´¦Àí£¬¾ùÖµ£¬Îó²îºÍ·Ö×é×Öĸ£¬¹¹³ÉÒ»¸ö¾ØÕóÒ»±ãºóÃæÖù״ͼµÄ²Ù×÷¡£
group1<-matrix(c(cmp.2$means,cmp.2$M,cmp.2$std.err),
nrow=6,ncol=3,byrow=TRUE,dimnames=list(cmp.2$trt,c("mean","significant","se"))

barplot(group1[1:6,1],beside=TRUE,angle=c(0,45,90,180,0,0),density=c(-1,20,20,20,-1,-1),ylim=c(0,4.5),col=c(1,2,3,4,5,6))
box()

5. ͼ±íÖÆ×÷

ÏÖÔÚ¶àÖØ±È½ÏµÄ½á¹ûÒ²³öÀ´ÁË£¬Ê£ÏµıãÊÇÔõô°Ñ½á¹û³ÊÏÖ³öÀ´¡£¶ÔÕâ¸öÊý¾Ý×飬ÕâÀᄀÁ¿ÔËÓöàÖÖ·½Ê½£¬°üÀ¨ÈýÏß±í¡¢Öù״ͼºÍÕÛÏßͼ¡£
5.1 ½á¹ûÊä³ö¼°±íµÄÖÆ×÷
#´ÓÖÐÌáÈ¡ÖØÁ¿µÄ¾ùÖµ¡¢Îó²îºÍ·Ö×é×Öĸ£¬È»ºó°Ñ½á¹ûÊä³öµ½ExcelÖнøÐбíµÄÖÆ×÷¡£
#°ÑÖØÁ¿¶àÖØ±È½ÏµÄ½á¹ûÌáÈ¡³öÀ´£¬°üÀ¨µÄÐÅÏ¢Óд¦Àí¡¢Æ·¾ùÖµ¡¢±ê×¼Îó²îºÍ·Ö×é×Öĸ¡£
groupwt<-data.frame(Treat=cmp.2$trt,Cul=substr(cmp.2$trt,2,3),Date=substr(cmp.2$trt,5,6), Meanwt=cmp.2$means,Groupwt=cmp.2$M,SEwt=cmp.2$std.err)
#ͬÑù¶Ôvcº¬Á¿×÷ÀàËÆ²Ù×÷
aov.4<-aov(VitC~comtreat,data=cab)
summary(aov.4)
DFerror<-df.residual(aov.4)
MSerror<-deviance(aov.4)/DFerror
cmp.3<-HSD.test(cab$VitC,cab$comtreat,DFerror,MSerror,group=TRUE)
groupvc<-data.frame(Treat=cmp.3$trt,Cul=substr(cmp.3$trt,2,3),Date=substr(cmp.3$trt,5,6),
Meanvc=cmp.3$means,Groupvc=cmp.3$M,SEvc=cmp.3$std.err)
#½«Á½×éÊý¾ÝºÏ²¢µ½Ò»¸öÊý¾ÝÖУ¬µ±È»Õâ¸ö²¢·Ç±ØÐèµÄ£¬Ö»ÊÇչʾһÏÂÏàÓ¦µÄÊý¾Ý²Ù×÷¡£
group<-merge(groupwt,groupvc,by=c("Cul","Date")
#½«½á¹ûÊä³öµ½ExcelÖÐ
write.table(group,"clipboard",sep="\t"
Ö®ºó¾­¹ýºÜÈÝÒ׵IJÙ×÷±ã¿ÉÒԵõ½±í1µÄ½á¹û¡£
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c39d16   3.18   a   50.3   cd
c39d20   2.8   ab   49.4   d
c39d21   2.74   ab   54.8   bcd
c52d16   2.26   bc   62.5   b
c52d20   3.11   ab   58.9   bc
c52d21   1.47   c   71.8   a
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[ Last edited by zwdbordeaux on 2010-2-17 at 04:44 ]
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library(MASS)
cab<-data.frame(cabbages)
cab[1,]

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library(sciplot)
bargraph.CI(Cult, HeadWt, group =Date , data =cab,
           xlab = NA, ylab = NA, cex.lab = 1.5, x.leg = 1,
           col = "black", angle = 45, cex.names = 1.25,
           density = c(0,20,100), legend = TRUE,ylim=c(0,5))
box()

bargraph.CI(Date, HeadWt, group =Cult , data =cab,
           xlab = NA, ylab = NA, cex.lab = 1.5, x.leg = 1,
           col = "black", angle = 45, cex.names = 1.25,
           density = c(0,20), legend = TRUE,ylim=c(0,5))
box()
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#ÔÚgroupÊý¾ÝÖÐÌí¼ÓÒ»Áв¥ÖÖÈÕÆÚ£¬×¢ÒâÁíÍâÒ»¸ö²¥ÖÖÈÕÆÚÁеÄÊôÐÔ(mode)Ϊfactor,Ò²¾Í˵ËûÃǻᱻÈÏΪÊÇ×Ö·û¡£
group$date2<-rep(c(16,20,22),2)
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library(plotrix)
#¼ÆËãÖØÁ¿ºÍVCº¬Á¿µÄ±ä»¯·¶Î§£¬ÕâÑù¿ÉÒÔ·½±ã¶¨ÒåYÖáµÄ¿Ì¶È·¶Î§£¨ylim£©
ran.wt<-range(cab$HeadWt)
ran.vc<-range(cab$VitC)
#ͬÑùµÄ¶Ôͼ½øÐÐ×éºÏ
par(mfrow=c(2,1),mai=c(0,0,0,0),omi=c(0.6,0.6,0.1,0.1))
#Ê×ÏȰÑͼµÄ¿ò¼Ü»­³öÀ´
plot(group$date2,group$Meanwt,type="n",ylim=ran.wt,xaxt="n"
#Ìí¼ÓÆ·ÖÖ39µÄ½á¹ûºÍËüÃǵıê×¼Îó²î
plotCI(x=group[group$Cul=="39","date2"],y=group[group$Cul=="39","Meanwt"],liw=group[group$Cul=="39","SEwt"],uiw=group[group$Cul=="39","SEwt"],pch=2,add=TRUE)
#Ìí¼ÓÁ¬½ÓµÄÕÛÏß
lines(x=group[group$Cul=="39","date2"],y=group[group$Cul=="39","Meanwt"],lty=1,lwd=2)
#Ìí¼ÓÆ·ÖÖ52µÄÊý¾ÝµãºÍ±ê×¼Îó²î
plotCI(x=group[group$Cul=="52","date2"],y=group[group$Cul=="52","Meanwt"],liw=group[group$Cul=="52","SEwt"],uiw=group[group$Cul=="52","SEwt"],pch=0,add=TRUE)
#Ìí¼ÓÕÛÏß
lines(x=group[group$Cul=="52","date2"],y=group[group$Cul=="52","Meanwt"],lty=2,lwd=2)
#Ìí¼ÓСͼ±êÖ¾
text(16,4,"A",font=2)
#Ìí¼ÓͼÀý
legend(18,4,legend=c("CV39","CV52",lty=c(1,2),pch=c(1,0),bty="n"
#¶Ôvcº¬Á¿½øÐÐÀàËÆ²Ù×÷¡£¶ÁÕß¿ÉÒÔÓë֮ǰ±È½Ï¿´ÕâЩÃüÁîÖ®¼ä¸Ä¶¯µÄµØ·½£¬ÊìϤ֮ºóÆäʵ¿ÉÒÔ¸´ÖÆÕ³ÌúÌæ»»¾ÍÇáËɸ㶨ÁË¡£
plot(group$date2,group$Meanvc,type="n",ylim=ran.vc)
plotCI(x=group[group$Cul=="39","date2"],y=group[group$Cul=="39","Meanvc"],liw=group[group$Cul=="39","SEvc"],uiw=group[group$Cul=="39","SEvc"],pch=2,add=TRUE)
lines(x=group[group$Cul=="39","date2"],y=group[group$Cul=="39","Meanvc"],lty=1,lwd=2)
plotCI(x=group[group$Cul=="52","date2"],y=group[group$Cul=="52","Meanvc"],liw=group[group$Cul=="52","SEvc"],uiw=group[group$Cul=="52","SEvc"],pch=0,add=TRUE)
lines(x=group[group$Cul=="52","date2"],y=group[group$Cul=="52","Meanvc"],lty=2,lwd=2)
text(16,80,"B",font=2)
mtext("²¥ÖÖÈÕÆÚ",side=1,adj=0.5,outer=TRUE,line=2)
mtext("ÖØÁ¿(kg)",side=2,at=0.75,adj=0.5,outer=TRUE,line=2)
mtext("άËûÃüº¬Á¿(mg/kg)",side=2,at=0.25,adj=0.5,outer=TRUE,line=2)
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par(mfrow=c(2,1),mai=c(0,0,0,0),omi=c(0.6,0.6,0.1,0.1))
#ÔËÓÃËùÓй۲âÖµ×÷ͼºÍ·ÖÎö
plot(cab$HeadWt,cab$VitC,type="n",xaxt="n"
points(cab[cab$Cul=="c39","HeadWt"],cab[cab$Cul=="c39","VitC"],pch=1)
points(cab[cab$Cul=="c52","HeadWt"],cab[cab$Cul=="c52","VitC"],pch=0)
#ÏßÐÔÄ£Ð͵ķÖÎö
lm1<-lm(VitC~HeadWt,data=cab)
#½á¹ûµÄ×ܽá
summary(lm1)
#ÔÚͼÖÐÌí¼ÓÄâºÏµÄÖ±Ïß
abline(lm1)
Ìí¼Ó·½³Ì
text(1.7,47, "y=77.6-7.57x\n(P<0.0001,n=58)"
legend("topright",legend=c("CV39","CV52",pch=c(1,0),title="A"
#ÔËÓþùÖµ×÷ͼ
plot(cab$HeadWt,cab$VitC,type="n"
#Ìí¼ÓxÖá·½ÏòµÄÎó²îÏß
plotCI(x=group[group$Cul=="39","Meanwt"],y=group[group$Cul=="39","Meanvc"],err="x",liw=group[group$Cul=="39","SEwt"],uiw=group[group$Cul=="39","SEwt"],pch=2,add=TRUE)
plotCI(x=group[group$Cul=="52","Meanwt"],y=group[group$Cul=="52","Meanvc"],err="x",liw=group[group$Cul=="52","SEwt"],uiw=group[group$Cul=="52","SEwt"],pch=0,add=TRUE)
#Ìí¼ÓyÖá·½ÏòµÄÎó²îÏß
plotCI(x=group[group$Cul=="39","Meanwt"],y=group[group$Cul=="39","Meanvc"],err="y",liw=group[group$Cul=="39","SEvc"],uiw=group[group$Cul=="39","SEvc"],pch=2,add=TRUE)
plotCI(x=group[group$Cul=="52","Meanwt"],y=group[group$Cul=="52","Meanvc"],err="y",liw=group[group$Cul=="52","SEvc"],uiw=group[group$Cul=="52","SEvc"],pch=0,add=TRUE)
#¶Ô¾ùÖµ×÷ÏßÐÔÄâºÏ
lm2<-lm(Meanvc~Meanwt,data=group)
summary(lm2)
abline(lm2)
text(1.7,47, "y=87.5-11.4x\n(P<0.05,n=58)"
legend("topright",legend="B",bty="n"
mtext("ÖØÁ¿(kg)",side=1,at=0.5,adj=0.5,outer=TRUE,line=2)
mtext("άËûÃüº¬Á¿(mg/kg)",side=2,at=0.5,adj=0.5,outer=TRUE,line=2)
10Â¥2010-02-17 04:47:18
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A Quick Guide to Teaching R Programming to Computational Biology Students

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Eglen SJ (2009) A Quick Guide to Teaching R Programming to Computational Biology Students. PLoS Comput Biol 5(8): e1000482. doi:10.1371/journal.pcbi.1000482
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