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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationTue, 10 Mar 2015 13:25:39 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Mar/10/t1425993967v00hr92mnuxv6oa.htm/, Retrieved Sun, 19 May 2024 08:51:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278132, Retrieved Sun, 19 May 2024 08:51:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact155

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Standard Deviation-Mean Plot] [] [2015-03-10 13:25:39] [aed7930eb470b174eb4d45bdfa14c6e0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100.8
100.9
101.5
101.8
102.3
102.7
103.3
104.3
103.9
104.1
104.5
104
105.3
105.3
105.7
105.7
105.3
105.6
106.5
107
106.6
106.4
105.6
105.8
106.3
105.2
104.1
103.4
102.6
101.6
101.7
101
100.7
100.8
100.3
99.8
100
100.3
100.1
100.8
100.1
99.9
100.5
100.6
99.9
99.5
99.2
98.9
98.8
98.4
98.9
98.4
98.3
98.1
98.2
97.6
96.8
96.6
96
94.9
95.2
95
93.7
92.9
92.3
93.2
89.6
89.2
88.7
88.4
88.9
88.3
85.8
86.8
86.9
85.7
84.5
84
85
85.2
85
84.8
84.5
85

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278132&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278132&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278132&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1102.8416666666671.357443006225863.7
2105.90.5768251665169211.7
3102.2916666666672.057119934335976.5
499.98333333333330.5621926769894841.89999999999999
597.58333333333331.243041236303734
691.28333333333332.680852419841446.90000000000001
785.26666666666670.8896713727636472.90000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 102.841666666667 & 1.35744300622586 & 3.7 \tabularnewline
2 & 105.9 & 0.576825166516921 & 1.7 \tabularnewline
3 & 102.291666666667 & 2.05711993433597 & 6.5 \tabularnewline
4 & 99.9833333333333 & 0.562192676989484 & 1.89999999999999 \tabularnewline
5 & 97.5833333333333 & 1.24304123630373 & 4 \tabularnewline
6 & 91.2833333333333 & 2.68085241984144 & 6.90000000000001 \tabularnewline
7 & 85.2666666666667 & 0.889671372763647 & 2.90000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278132&T=1

[TABLE]
[ROW][C]Standard Deviation-Mean Plot[/C][/ROW]
[ROW][C]Section[/C][C]Mean[/C][C]Standard Deviation[/C][C]Range[/C][/ROW]
[ROW][C]1[/C][C]102.841666666667[/C][C]1.35744300622586[/C][C]3.7[/C][/ROW]
[ROW][C]2[/C][C]105.9[/C][C]0.576825166516921[/C][C]1.7[/C][/ROW]
[ROW][C]3[/C][C]102.291666666667[/C][C]2.05711993433597[/C][C]6.5[/C][/ROW]
[ROW][C]4[/C][C]99.9833333333333[/C][C]0.562192676989484[/C][C]1.89999999999999[/C][/ROW]
[ROW][C]5[/C][C]97.5833333333333[/C][C]1.24304123630373[/C][C]4[/C][/ROW]
[ROW][C]6[/C][C]91.2833333333333[/C][C]2.68085241984144[/C][C]6.90000000000001[/C][/ROW]
[ROW][C]7[/C][C]85.2666666666667[/C][C]0.889671372763647[/C][C]2.90000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278132&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278132&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1102.8416666666671.357443006225863.7
2105.90.5768251665169211.7
3102.2916666666672.057119934335976.5
499.98333333333330.5621926769894841.89999999999999
597.58333333333331.243041236303734
691.28333333333332.680852419841446.90000000000001
785.26666666666670.8896713727636472.90000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha3.70898326003986
beta-0.024222049196967
S.D.0.0472819851995731
T-STAT-0.512289175142032
p-value0.630267616417341

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3.70898326003986 \tabularnewline
beta & -0.024222049196967 \tabularnewline
S.D. & 0.0472819851995731 \tabularnewline
T-STAT & -0.512289175142032 \tabularnewline
p-value & 0.630267616417341 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278132&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.70898326003986[/C][/ROW]
[ROW][C]beta[/C][C]-0.024222049196967[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0472819851995731[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.512289175142032[/C][/ROW]
[ROW][C]p-value[/C][C]0.630267616417341[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278132&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278132&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha3.70898326003986
beta-0.024222049196967
S.D.0.0472819851995731
T-STAT-0.512289175142032
p-value0.630267616417341






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha7.95897519725637
beta-1.70648574993236
S.D.3.41908835854445
T-STAT-0.499105483971416
p-value0.638885678285609
Lambda2.70648574993236

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 7.95897519725637 \tabularnewline
beta & -1.70648574993236 \tabularnewline
S.D. & 3.41908835854445 \tabularnewline
T-STAT & -0.499105483971416 \tabularnewline
p-value & 0.638885678285609 \tabularnewline
Lambda & 2.70648574993236 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278132&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.95897519725637[/C][/ROW]
[ROW][C]beta[/C][C]-1.70648574993236[/C][/ROW]
[ROW][C]S.D.[/C][C]3.41908835854445[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.499105483971416[/C][/ROW]
[ROW][C]p-value[/C][C]0.638885678285609[/C][/ROW]
[ROW][C]Lambda[/C][C]2.70648574993236[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278132&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278132&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha7.95897519725637
beta-1.70648574993236
S.D.3.41908835854445
T-STAT-0.499105483971416
p-value0.638885678285609
Lambda2.70648574993236


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
(n <- length(x))
(np <- floor(n / par1))
arr <- array(NA,dim=c(par1,np))
j <- 0
k <- 1
for (i in 1:(np*par1))
{
j = j + 1
arr[j,k] <- x[i]
if (j == par1) {
j = 0
k=k+1
}
}
arr
arr.mean <- array(NA,dim=np)
arr.sd <- array(NA,dim=np)
arr.range <- array(NA,dim=np)
for (j in 1:np)
{
arr.mean[j] <- mean(arr[,j],na.rm=TRUE)
arr.sd[j] <- sd(arr[,j],na.rm=TRUE)
arr.range[j] <- max(arr[,j],na.rm=TRUE) - min(arr[,j],na.rm=TRUE)
}
arr.mean
arr.sd
arr.range
(lm1 <- lm(arr.sd~arr.mean))
(lnlm1 <- lm(log(arr.sd)~log(arr.mean)))
(lm2 <- lm(arr.range~arr.mean))
bitmap(file='test1.png')
plot(arr.mean,arr.sd,main='Standard Deviation-Mean Plot',xlab='mean',ylab='standard deviation')
dev.off()
bitmap(file='test2.png')
plot(arr.mean,arr.range,main='Range-Mean Plot',xlab='mean',ylab='range')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Standard Deviation-Mean Plot',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Section',header=TRUE)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,'Standard Deviation',header=TRUE)
a<-table.element(a,'Range',header=TRUE)
a<-table.row.end(a)
for (j in 1:np) {
a<-table.row.start(a)
a<-table.element(a,j,header=TRUE)
a<-table.element(a,arr.mean[j])
a<-table.element(a,arr.sd[j] )
a<-table.element(a,arr.range[j] )
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: S.E.(k) = alpha + beta * Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: ln S.E.(k) = alpha + beta * ln Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Lambda',header=TRUE)
a<-table.element(a,1-lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')