حساب داخل وبين الفروق وفترات الثقة في R
https://stackoverflow.com/questions/1401894
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05-07-2019 - |
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وأحتاج لحساب داخل وبين المدى الفروق من بعض البيانات كجزء من تطوير طريقة جديدة الكيمياء التحليلية. ولست بحاجة أيضا فترات الثقة من هذه البيانات باستخدام لغة R
وأفترض أنا بحاجة إلى استخدام أنوفا أو شيء من هذا؟
وبياناتي مثل
> 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
المحلول 4
ولقد تم النظر في مشكلة مماثلة. لقد وجدت إشارة إلى caluclating فترات الثقة بورديك وGraybill (بورديك، R. وGraybill، F. 1992، فترات الثقة على مكونات التباين، CRC الصحافة)
<ع> استخدام بعض الرموز لقد كنت أحاول أن أحصل على هذه القيم
> 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
وهنا أقل فترة الثقة لمدة تتراوح بين المدى CV أقل من الصفر، لذلك كما ذكرت نان.
وأنا أحب أن يكون طريقة أفضل للقيام بذلك. إذا كنت تحصل على الوقت الذي قد يحاول إنشاء دالة للقيام بذلك.
وبول.
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وتحرير: أنا لم نهاية المطاف كتابة دالة، ومن هنا (مسؤولية المشتري)
#' 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)
}
نصائح أخرى
لديك أربع مجموعات من ثلاث ملاحظات:
> 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
تأكد بعض التسميات:
> n = rep(3, 4)
> group = rep(1:4, n)
> group
[1] 1 1 1 2 2 2 3 3 3 4 4 4
واحسب احصائيات تشغيل في غضون:
> 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
ويمكنك القيام ببعض ANOVA هنا:
> 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
خطأ أو داخل مجموعة الفرق:
> anova(fit)["Residuals", "Mean Sq"]
[1] 0.2422917
ومن ضروب المعاملة أو بين-مجموعة الفرق:
> anova(fit)["group", "Mean Sq"]
[1] 0.8586111
وهذا يجب أن يعطيك ما يكفي من الثقة للقيام فترات الثقة.
إذا كنت ترغب في تطبيق وظيفة (مثل var) عبر عامل مثل Run أو Rep، يمكنك استخدام tapply:
> 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
وانا ذاهب الى اتخاذ الكراك في هذا عندما يكون لدي المزيد من الوقت، ولكن في الوقت نفسه، وهنا dput() لبنية بيانات Kiar ل:
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")
... في حال كنت ترغب في أخذ لقطة سريعة على ذلك.
لا تنتمي إلى StackOverflow
