Berechnen innerhalb und zwischen den Varianzen und Konfidenzintervalle in R
https://stackoverflow.com/questions/1401894
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05-07-2019 - |
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Ich brauche die innerhalb und zwischen den Laufabweichungen von einigen Daten im Rahmen der Entwicklung eine neue analytische Chemie Methode zu berechnen. Ich brauche auch Konfidenzintervall aus diesen Daten der R Sprache mit
Ich nehme an, ich brauche anova oder etwas verwenden?
Meine Daten wie
> variance
Run Rep Value
1 1 1 9.85
2 1 2 9.95
3 1 3 10.00
4 2 1 9.90
5 2 2 8.80
6 2 3 9.50
7 3 1 11.20
8 3 2 11.10
9 3 3 9.80
10 4 1 9.70
11 4 2 10.10
12 4 3 10.00
Lösung 4
Ich habe bei einem ähnlichen Problem gesucht. Ich habe Bezug auf caluclating Konfidenzintervall von Burdick und Graybill (Burdick, R. und Graybill, F. 1992 Konfidenzintervalle auf Varianzkomponenten, CRC Press)
gefundeneinige Code verwenden Ich habe versucht, ich diese Werte zu erhalten
> kiaraov = aov(Value~Run+Error(Run),data=kiar)
> summary(kiaraov)
Error: Run
Df Sum Sq Mean Sq
Run 3 2.57583 0.85861
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
Residuals 8 1.93833 0.24229
> confint = 95
> a = (1-(confint/100))/2
> grandmean = as.vector(kiaraov$"(Intercept)"[[1]][1]) # Grand Mean (I think)
> within = summary(kiaraov)$"Error: Within"[[1]]$"Mean Sq" # S2^2Mean Square Value for Within Run
> dfRun = summary(kiaraov)$"Error: Run"[[1]]$"Df"
> dfWithin = summary(kiaraov)$"Error: Within"[[1]]$"Df"
> Run = summary(kiaraov)$"Error: Run"[[1]]$"Mean Sq" # S1^2Mean Square for between Run
> between = (Run-within)/((dfWithin/(dfRun+1))+1) # (S1^2-S2^2)/J
> total = between+within
> between # Between Run Variance
[1] 0.2054398
> within # Within Run Variance
[1] 0.2422917
> total # Total Variance
[1] 0.4477315
> betweenCV = sqrt(between)/grandmean * 100 # Between Run CV%
> withinCV = sqrt(within)/grandmean * 100 # Within Run CV%
> totalCV = sqrt(total)/grandmean * 100 # Total CV%
> #within confidence intervals
> withinLCB = within/qf(1-a,8,Inf) # Within LCB
> withinUCB = within/qf(a,8,Inf) # Within UCB
> #Between Confidence Intervals
> n1 = dfRun
> n2 = dfWithin
> G1 = 1-(1/qf(1-a,n1,Inf)) # According to Burdick and Graybill this should be a
> G2 = 1-(1/qf(1-a,n2,Inf))
> H1 = (1/qf(a,n1,Inf))-1 # and this should be 1-a, but my results don't agree
> H2 = (1/qf(a,n2,Inf))-1
> G12 = ((qf(1-a,n1,n2)-1)^2-(G1^2*qf(1-a,n1,n2)^2)-(H2^2))/qf(1-a,n1,n2) # again, should be a, not 1-a
> H12 = ((1-qf(a,n1,n2))^2-H1^2*qf(a,n1,n2)^2-G2^2)/qf(a,n1,n2) # again, should be 1-a, not a
> Vu = H1^2*Run^2+G2^2*within^2+H12*Run*within
> Vl = G1^2*Run^2+H2^2*within^2+G12*within*Run
> betweenLCB = (Run-within-sqrt(Vl))/J # Betwen LCB
> betweenUCB = (Run-within+sqrt(Vu))/J # Between UCB
> #Total Confidence Intervals
> y = (Run+(J-1)*within)/J
> totalLCB = y-(sqrt(G1^2*Run^2+G2^2*(J-1)^2*within^2)/J) # Total LCB
> totalUCB = y+(sqrt(H1^2*Run^2+H2^2*(J-1)^2*within^2)/J) # Total UCB
> result = data.frame(Name=c("within", "between", "total"),CV=c(withinCV,betweenCV,totalCV),LCB=c(sqrt(withinLCB)/grandmean*100,sqrt(betweenLCB)/grandmean*100,sqrt(totalLCB)/grandmean*100),UCB=c(sqrt(withinUCB)/grandmean*100,sqrt(betweenUCB)/grandmean*100,sqrt(totalUCB)/grandmean*100))
> result
Name CV LCB UCB
1 within 4.926418 3.327584 9.43789
2 between 4.536327 NaN 19.73568
3 total 6.696855 4.846030 20.42647
Hier ist der untere Konfidenzintervall für zwischen Lauf CV kleiner als Null ist, so wie NaN berichtet.
Ich würde gerne einen besseren Weg, dies zu tun. Wenn ich Zeit habe ich könnte versuchen, eine Funktion zu erstellen, dies zu tun.
Paul.
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Edit: Ich habe schließlich eine Funktion schreiben, hier ist es (caveat emptor)
#' avar Function
#'
#' Calculate thewithin, between and total %CV of a dataset by ANOVA, and the
#' associated confidence intervals
#'
#' @param dataf - The data frame to use, in long format
#' @param afactor Character string representing the column in dataf that contains the factor
#' @param aresponse Charactyer string representing the column in dataf that contains the response value
#' @param aconfidence What Confidence limits to use, default = 95%
#' @param digits Significant Digits to report to, default = 3
#' @param debug Boolean, Should debug messages be displayed, default=FALSE
#' @returnType dataframe containing the Mean, Within, Between and Total %CV and LCB and UCB for each
#' @return
#' @author Paul Hurley
#' @export
#' @examples
#' #Using the BGBottles data from Burdick and Graybill Page 62
#' assayvar(dataf=BGBottles, afactor="Machine", aresponse="weight")
avar<-function(dataf, afactor, aresponse, aconfidence=95, digits=3, debug=FALSE){
dataf<-subset(dataf,!is.na(with(dataf,get(aresponse))))
nmissing<-function(x) sum(!is.na(x))
n<-nrow(subset(dataf,is.numeric(with(dataf,get(aresponse)))))
datadesc<-ddply(dataf, afactor, colwise(nmissing,aresponse))
I<-nrow(datadesc)
if(debug){print(datadesc)}
if(min(datadesc[,2])==max(datadesc[,2])){
balance<-TRUE
J<-min(datadesc[,2])
if(debug){message(paste("Dataset is balanced, J=",J,"I is ",I,sep=""))}
} else {
balance<-FALSE
Jh<-I/(sum(1/datadesc[,2], na.rm = TRUE))
J<-Jh
m<-min(datadesc[,2])
M<-max(datadesc[,2])
if(debug){message(paste("Dataset is unbalanced, like me, I is ",I,sep=""))}
if(debug){message(paste("Jh is ",Jh, ", m is ",m, ", M is ",M, sep=""))}
}
if(debug){message(paste("Call afactor=",afactor,", aresponse=",aresponse,sep=""))}
formulatext<-paste(as.character(aresponse)," ~ 1 + Error(",as.character(afactor),")",sep="")
if(debug){message(paste("formula text is ",formulatext,sep=""))}
aovformula<-formula(formulatext)
if(debug){message(paste("Formula is ",as.character(aovformula),sep=""))}
assayaov<-aov(formula=aovformula,data=dataf)
if(debug){
print(assayaov)
print(summary(assayaov))
}
a<-1-((1-(aconfidence/100))/2)
if(debug){message(paste("confidence is ",aconfidence,", alpha is ",a,sep=""))}
grandmean<-as.vector(assayaov$"(Intercept)"[[1]][1]) # Grand Mean (I think)
if(debug){message(paste("n is",n,sep=""))}
#This line commented out, seems to choke with an aov object built from an external formula
#grandmean<-as.vector(model.tables(assayaov,type="means")[[1]]$`Grand mean`) # Grand Mean (I think)
within<-summary(assayaov)[[2]][[1]]$"Mean Sq" # d2e, S2^2 Mean Square Value for Within Machine = 0.1819
dfRun<-summary(assayaov)[[1]][[1]]$"Df" # DF for within = 3
dfWithin<-summary(assayaov)[[2]][[1]]$"Df" # DF for within = 8
Run<-summary(assayaov)[[1]][[1]]$"Mean Sq" # S1^2Mean Square for Machine
if(debug){message(paste("mean square for Run ?",Run,sep=""))}
#Was between<-(Run-within)/((dfWithin/(dfRun+1))+1) but my comment suggests this should be just J, so I'll use J !
between<-(Run-within)/J # d2a (S1^2-S2^2)/J
if(debug){message(paste("S1^2 mean square machine is ",Run,", S2^2 mean square within is ",within))}
total<-between+within
between # Between Run Variance
within # Within Run Variance
total # Total Variance
if(debug){message(paste("between is ",between,", within is ",within,", Total is ",total,sep=""))}
betweenCV<-sqrt(between)/grandmean * 100 # Between Run CV%
withinCV<-sqrt(within)/grandmean * 100 # Within Run CV%
totalCV<-sqrt(total)/grandmean * 100 # Total CV%
n1<-dfRun
n2<-dfWithin
if(debug){message(paste("n1 is ",n1,", n2 is ",n2,sep=""))}
#within confidence intervals
if(balance){
withinLCB<-within/qf(a,n2,Inf) # Within LCB
withinUCB<-within/qf(1-a,n2,Inf) # Within UCB
} else {
withinLCB<-within/qf(a,n2,Inf) # Within LCB
withinUCB<-within/qf(1-a,n2,Inf) # Within UCB
}
#Mean Confidence Intervals
if(debug){message(paste(grandmean,"+/-(sqrt(",Run,"/",n,")*qt(",a,",df=",I-1,"))",sep=""))}
meanLCB<-grandmean+(sqrt(Run/n)*qt(1-a,df=I-1)) # wrong
meanUCB<-grandmean-(sqrt(Run/n)*qt(1-a,df=I-1)) # wrong
if(debug){message(paste("Grandmean is ",grandmean,", meanLCB = ",meanLCB,", meanUCB = ",meanUCB,aresponse,sep=""))}
if(debug){print(summary(assayaov))}
#Between Confidence Intervals
G1<-1-(1/qf(a,n1,Inf))
G2<-1-(1/qf(a,n2,Inf))
H1<-(1/qf(1-a,n1,Inf))-1
H2<-(1/qf(1-a,n2,Inf))-1
G12<-((qf(a,n1,n2)-1)^2-(G1^2*qf(a,n1,n2)^2)-(H2^2))/qf(a,n1,n2)
H12<-((1-qf(1-a,n1,n2))^2-H1^2*qf(1-a,n1,n2)^2-G2^2)/qf(1-a,n1,n2)
if(debug){message(paste("G1 is ",G1,", G2 is ",G2,sep=""))
message(paste("H1 is ",H1,", H2 is ",H2,sep=""))
message(paste("G12 is ",G12,", H12 is ",H12,sep=""))
}
if(balance){
Vu<-H1^2*Run^2+G2^2*within^2+H12*Run*within
Vl<-G1^2*Run^2+H2^2*within^2+G12*within*Run
betweenLCB<-(Run-within-sqrt(Vl))/J # Betwen LCB
betweenUCB<-(Run-within+sqrt(Vu))/J # Between UCB
} else {
#Burdick and Graybill seem to suggest calculating anova of mean values to find n1S12u/Jh
meandataf<-ddply(.data=dataf,.variable=afactor, .fun=function(df){mean(with(df, get(aresponse)), na.rm=TRUE)})
meandataaov<-aov(formula(paste("V1~",afactor,sep="")), data=meandataf)
sumsquare<-summary(meandataaov)[[1]]$`Sum Sq`
#so maybe S12u is just that bit ?
Runu<-(sumsquare*Jh)/n1
if(debug){message(paste("n1S12u/Jh is ",sumsquare,", so S12u is ",Runu,sep=""))}
Vu<-H1^2*Runu^2+G2^2*within^2+H12*Runu*within
Vl<-G1^2*Runu^2+H2^2*within^2+G12*within*Runu
betweenLCB<-(Runu-within-sqrt(Vl))/Jh # Betwen LCB
betweenUCB<-(Runu-within+sqrt(Vu))/Jh # Between UCB
if(debug){message(paste("betweenLCB is ",betweenLCB,", between UCB is ",betweenUCB,sep=""))}
}
#Total Confidence Intervals
if(balance){
y<-(Run+(J-1)*within)/J
if(debug){message(paste("y is ",y,sep=""))}
totalLCB<-y-(sqrt(G1^2*Run^2+G2^2*(J-1)^2*within^2)/J) # Total LCB
totalUCB<-y+(sqrt(H1^2*Run^2+H2^2*(J-1)^2*within^2)/J) # Total UCB
} else {
y<-(Runu+(Jh-1)*within)/Jh
if(debug){message(paste("y is ",y,sep=""))}
totalLCB<-y-(sqrt(G1^2*Runu^2+G2^2*(Jh-1)^2*within^2)/Jh) # Total LCB
totalUCB<-y+(sqrt(H1^2*Runu^2+H2^2*(Jh-1)^2*within^2)/Jh) # Total UCB
}
if(debug){message(paste("totalLCB is ",totalLCB,", total UCB is ",totalUCB,sep=""))}
# result<-data.frame(Name=c("within", "between", "total"),CV=c(withinCV,betweenCV,totalCV),
# LCB=c(sqrt(withinLCB)/grandmean*100,sqrt(betweenLCB)/grandmean*100,sqrt(totalLCB)/grandmean*100),
# UCB=c(sqrt(withinUCB)/grandmean*100,sqrt(betweenUCB)/grandmean*100,sqrt(totalUCB)/grandmean*100))
result<-data.frame(Mean=grandmean,MeanLCB=meanLCB, MeanUCB=meanUCB, Within=withinCV,WithinLCB=sqrt(withinLCB)/grandmean*100, WithinUCB=sqrt(withinUCB)/grandmean*100,
Between=betweenCV, BetweenLCB=sqrt(betweenLCB)/grandmean*100, BetweenUCB=sqrt(betweenUCB)/grandmean*100,
Total=totalCV, TotalLCB=sqrt(totalLCB)/grandmean*100, TotalUCB=sqrt(totalUCB)/grandmean*100)
if(!digits=="NA"){
result$Mean<-signif(result$Mean,digits=digits)
result$MeanLCB<-signif(result$MeanLCB,digits=digits)
result$MeanUCB<-signif(result$MeanUCB,digits=digits)
result$Within<-signif(result$Within,digits=digits)
result$WithinLCB<-signif(result$WithinLCB,digits=digits)
result$WithinUCB<-signif(result$WithinUCB,digits=digits)
result$Between<-signif(result$Between,digits=digits)
result$BetweenLCB<-signif(result$BetweenLCB,digits=digits)
result$BetweenUCB<-signif(result$BetweenUCB,digits=digits)
result$Total<-signif(result$Total,digits=digits)
result$TotalLCB<-signif(result$TotalLCB,digits=digits)
result$TotalUCB<-signif(result$TotalUCB,digits=digits)
}
return(result)
}
assayvar<-function(adata, aresponse, afactor, anominal, aconfidence=95, digits=3, debug=FALSE){
result<-ddply(adata,anominal,function(df){
resul<-avar(dataf=df,afactor=afactor,aresponse=aresponse,aconfidence=aconfidence, digits=digits, debug=debug)
resul$n<-nrow(subset(df, !is.na(with(df, get(aresponse)))))
return(resul)
})
return(result)
}
Andere Tipps
Sie haben vier Gruppen von drei Beobachtungen:
> run1 = c(9.85, 9.95, 10.00)
> run2 = c(9.90, 8.80, 9.50)
> run3 = c(11.20, 11.10, 9.80)
> run4 = c(9.70, 10.10, 10.00)
> runs = c(run1, run2, run3, run4)
> runs
[1] 9.85 9.95 10.00 9.90 8.80 9.50 11.20 11.10 9.80 9.70 10.10 10.00
einige Labels:
> n = rep(3, 4)
> group = rep(1:4, n)
> group
[1] 1 1 1 2 2 2 3 3 3 4 4 4
Berechnen innerhalb geführte Statistik:
> withinRunStats = function(x) c(sum = sum(x), mean = mean(x), var = var(x), n = length(x))
> tapply(runs, group, withinRunStats)
$`1`
sum mean var n
29.800000000 9.933333333 0.005833333 3.000000000
$`2`
sum mean var n
28.20 9.40 0.31 3.00
$`3`
sum mean var n
32.10 10.70 0.61 3.00
$`4`
sum mean var n
29.80000000 9.93333333 0.04333333 3.00000000
Sie können einige ANOVA tun hier:
> data = data.frame(y = runs, group = factor(group))
> data
y group
1 9.85 1
2 9.95 1
3 10.00 1
4 9.90 2
5 8.80 2
6 9.50 2
7 11.20 3
8 11.10 3
9 9.80 3
10 9.70 4
11 10.10 4
12 10.00 4
> fit = lm(runs ~ group, data)
> fit
Call:
lm(formula = runs ~ group, data = data)
Coefficients:
(Intercept) group2 group3 group4
9.933e+00 -5.333e-01 7.667e-01 -2.448e-15
> anova(fit)
Analysis of Variance Table
Response: runs
Df Sum Sq Mean Sq F value Pr(>F)
group 3 2.57583 0.85861 3.5437 0.06769 .
Residuals 8 1.93833 0.24229
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> degreesOfFreedom = anova(fit)[, "Df"]
> names(degreesOfFreedom) = c("treatment", "error")
> degreesOfFreedom
treatment error
3 8
Fehler oder innerhalb der Gruppe Varianz:
> anova(fit)["Residuals", "Mean Sq"]
[1] 0.2422917
Behandlung oder zwischen den Gruppen Varianz:
> anova(fit)["group", "Mean Sq"]
[1] 0.8586111
Das sollten Sie genug Vertrauen geben Konfidenzintervall zu tun.
Wenn Sie eine Funktion (wie var) über einen Faktor wie Run oder Rep anwenden möchten, können Sie tapply verwenden:
> with(variance, tapply(Value, Run, var))
1 2 3 4
0.005833333 0.310000000 0.610000000 0.043333333
> with(variance, tapply(Value, Rep, var))
1 2 3
0.48562500 0.88729167 0.05583333
Ich werde einen Riss an diese nehmen, wenn ich mehr Zeit habe, aber in der Zwischenzeit, hier ist die dput() für Kiar der Datenstruktur:
structure(list(Run = c(1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4), Rep = c(1,
2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3), Value = c(9.85, 9.95, 10, 9.9,
8.8, 9.5, 11.2, 11.1, 9.8, 9.7, 10.1, 10)), .Names = c("Run",
"Rep", "Value"), row.names = c(NA, -12L), class = "data.frame")
... für den Fall, Sie möchten einen schnellen Schuss auf ihn nehmen.
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