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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationTue, 21 Dec 2010 19:35:28 +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/2010/Dec/21/t1292959999eiiv2ks0eijyvoe.htm/, Retrieved Sun, 19 May 2024 19:19:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113883, Retrieved Sun, 19 May 2024 19:19:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88

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] [standard deviatio...] [2010-12-21 19:35:28] [06510e00f8d0c95cc2ff019b83c7c2eb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2350.44
2440.25
2408.64
2472.81
2407.6
2454.62
2448.05
2497.84
2645.64
2756.76
2849.27
2921.44
2981.85
3080.58
3106.22
3119.31
3061.26
3097.31
3161.69
3257.16
3277.01
3295.32
3363.99
3494.17
3667.03
3813.06
3917.96
3895.51
3801.06
3570.12
3701.61
3862.27
3970.1
4138.52
4199.75
4290.89
4443.91
4502.64
4356.98
4591.27
4696.96
4621.4
4562.84
4202.52
4296.49
4435.23
4105.18
4116.68
3844.49
3720.98
3674.4
3857.62
3801.06
3504.37
3032.6
3047.03
2962.34
2197.82
2014.45
1862.83
1905.41
1810.99
1670.07
1864.44
2052.02
2029.6
2070.83
2293.41
2443.27
2513.17
2466.92
2502.66
2539.91

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113883&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113883&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113883&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 time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
12554.44666666667190.570772791696571
23191.3225147.471609663753512.32
33902.32333333333218.664223632879720.77
44411.00833333333198.014401580626591.78
53126.66583333333740.9765292376411994.79
62135.2325298.12292754759843.1

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2554.44666666667 & 190.570772791696 & 571 \tabularnewline
2 & 3191.3225 & 147.471609663753 & 512.32 \tabularnewline
3 & 3902.32333333333 & 218.664223632879 & 720.77 \tabularnewline
4 & 4411.00833333333 & 198.014401580626 & 591.78 \tabularnewline
5 & 3126.66583333333 & 740.976529237641 & 1994.79 \tabularnewline
6 & 2135.2325 & 298.12292754759 & 843.1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113883&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]2554.44666666667[/C][C]190.570772791696[/C][C]571[/C][/ROW]
[ROW][C]2[/C][C]3191.3225[/C][C]147.471609663753[/C][C]512.32[/C][/ROW]
[ROW][C]3[/C][C]3902.32333333333[/C][C]218.664223632879[/C][C]720.77[/C][/ROW]
[ROW][C]4[/C][C]4411.00833333333[/C][C]198.014401580626[/C][C]591.78[/C][/ROW]
[ROW][C]5[/C][C]3126.66583333333[/C][C]740.976529237641[/C][C]1994.79[/C][/ROW]
[ROW][C]6[/C][C]2135.2325[/C][C]298.12292754759[/C][C]843.1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113883&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113883&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
12554.44666666667190.570772791696571
23191.3225147.471609663753512.32
33902.32333333333218.664223632879720.77
44411.00833333333198.014401580626591.78
53126.66583333333740.9765292376411994.79
62135.2325298.12292754759843.1






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha426.262186621946
beta-0.0395296665917335
S.D.0.131015801285613
T-STAT-0.301716786859619
p-value0.777903890660371

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 426.262186621946 \tabularnewline
beta & -0.0395296665917335 \tabularnewline
S.D. & 0.131015801285613 \tabularnewline
T-STAT & -0.301716786859619 \tabularnewline
p-value & 0.777903890660371 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113883&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]426.262186621946[/C][/ROW]
[ROW][C]beta[/C][C]-0.0395296665917335[/C][/ROW]
[ROW][C]S.D.[/C][C]0.131015801285613[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.301716786859619[/C][/ROW]
[ROW][C]p-value[/C][C]0.777903890660371[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113883&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113883&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)
alpha426.262186621946
beta-0.0395296665917335
S.D.0.131015801285613
T-STAT-0.301716786859619
p-value0.777903890660371






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha8.55951744171207
beta-0.375491013364173
S.D.1.05743785098486
T-STAT-0.355095113168546
p-value0.740450735587472
Lambda1.37549101336417

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 8.55951744171207 \tabularnewline
beta & -0.375491013364173 \tabularnewline
S.D. & 1.05743785098486 \tabularnewline
T-STAT & -0.355095113168546 \tabularnewline
p-value & 0.740450735587472 \tabularnewline
Lambda & 1.37549101336417 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113883&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]8.55951744171207[/C][/ROW]
[ROW][C]beta[/C][C]-0.375491013364173[/C][/ROW]
[ROW][C]S.D.[/C][C]1.05743785098486[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.355095113168546[/C][/ROW]
[ROW][C]p-value[/C][C]0.740450735587472[/C][/ROW]
[ROW][C]Lambda[/C][C]1.37549101336417[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113883&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113883&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)
alpha8.55951744171207
beta-0.375491013364173
S.D.1.05743785098486
T-STAT-0.355095113168546
p-value0.740450735587472
Lambda1.37549101336417


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')