FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationFri, 23 Dec 2016 08:49:58 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/23/t1482479679cytjb7dj84c8ag7.htm/, Retrieved Tue, 07 May 2024 07:22:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302761, Retrieved Tue, 07 May 2024 07:22:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118

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] [] [2016-12-23 07:49:58] [0b5bf205c55efce49027552c8371b570] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3996.1
3984.2
4049
4032.8
4074.1
4114.4
4091.4
4166.6
4152.5
4112.7
4145.9
4174.4
4183.6
4172.5
4280.3
4327.4
4251.2
4256.5
4285.7
4257.4
4231.9
4274.3
4248.3
4310.5
4301.9
4336.5
4385.1
4310.4
4378.8
4338
4304.2
4266.9
4230.1
4230.6
4353.2
4371.2
4393.2
4250.2
4129.5
4124.9
4177.1
4156.9
4111.9
4167.4
4190.7
4165
4209.8
4250
4224.8
4322.7
4311.7
4373.8
4358.9
4441.2
4538.9
4444.8
4537.8
4490.2
4517.3
4561.9
4567
4588.3
4656.8
4677.7
4684.2
4752.8
4738.9
4785.6
4742.7
4711.4
4758.1
4800.5
4877.3
4885
4941.4
5009.4
5017.5
4984.1
4903.9
4968.6
4937.3
4987.1
5001.9
5094.6
5177.8
5206.1
5253.1
5284.3
5266.8
5225.1
5272.8
5529.8
5535.2
5715.9
5672.2
5475.7
5435.3
5458.5
5373.3
5395.3
5515
5410.9
5400.2
5424.2
5388.5
5482.1
5506.9
5377.2
5353.5
5401.1
5438.1
5510.2
5499
5606.5
5644
5440.7

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302761&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302761&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302761&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
14091.17564.9016896404232190.2
24256.6333333333345.4774936011476154.9
34317.2416666666753.5023102021744155
44193.8833333333376.9424204233664281.3
54427107.951310573543337.099999999999
64705.3333333333373.5435842740806233.5
74967.3416666666762.4022939312234217.3
85384.56666666667190.294796820537538.099999999999
95430.6166666666749.455541712336141.7

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4091.175 & 64.9016896404232 & 190.2 \tabularnewline
2 & 4256.63333333333 & 45.4774936011476 & 154.9 \tabularnewline
3 & 4317.24166666667 & 53.5023102021744 & 155 \tabularnewline
4 & 4193.88333333333 & 76.9424204233664 & 281.3 \tabularnewline
5 & 4427 & 107.951310573543 & 337.099999999999 \tabularnewline
6 & 4705.33333333333 & 73.5435842740806 & 233.5 \tabularnewline
7 & 4967.34166666667 & 62.4022939312234 & 217.3 \tabularnewline
8 & 5384.56666666667 & 190.294796820537 & 538.099999999999 \tabularnewline
9 & 5430.61666666667 & 49.455541712336 & 141.7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302761&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]4091.175[/C][C]64.9016896404232[/C][C]190.2[/C][/ROW]
[ROW][C]2[/C][C]4256.63333333333[/C][C]45.4774936011476[/C][C]154.9[/C][/ROW]
[ROW][C]3[/C][C]4317.24166666667[/C][C]53.5023102021744[/C][C]155[/C][/ROW]
[ROW][C]4[/C][C]4193.88333333333[/C][C]76.9424204233664[/C][C]281.3[/C][/ROW]
[ROW][C]5[/C][C]4427[/C][C]107.951310573543[/C][C]337.099999999999[/C][/ROW]
[ROW][C]6[/C][C]4705.33333333333[/C][C]73.5435842740806[/C][C]233.5[/C][/ROW]
[ROW][C]7[/C][C]4967.34166666667[/C][C]62.4022939312234[/C][C]217.3[/C][/ROW]
[ROW][C]8[/C][C]5384.56666666667[/C][C]190.294796820537[/C][C]538.099999999999[/C][/ROW]
[ROW][C]9[/C][C]5430.61666666667[/C][C]49.455541712336[/C][C]141.7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302761&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302761&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
14091.17564.9016896404232190.2
24256.6333333333345.4774936011476154.9
34317.2416666666753.5023102021744155
44193.8833333333376.9424204233664281.3
54427107.951310573543337.099999999999
64705.3333333333373.5435842740806233.5
74967.3416666666762.4022939312234217.3
85384.56666666667190.294796820537538.099999999999
95430.6166666666749.455541712336141.7






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-91.298989556886
beta0.0370127365868146
S.D.0.0303941192341167
T-STAT1.21775980089164
p-value0.262766506967356

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -91.298989556886 \tabularnewline
beta & 0.0370127365868146 \tabularnewline
S.D. & 0.0303941192341167 \tabularnewline
T-STAT & 1.21775980089164 \tabularnewline
p-value & 0.262766506967356 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302761&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-91.298989556886[/C][/ROW]
[ROW][C]beta[/C][C]0.0370127365868146[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0303941192341167[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.21775980089164[/C][/ROW]
[ROW][C]p-value[/C][C]0.262766506967356[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302761&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302761&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)
alpha-91.298989556886
beta0.0370127365868146
S.D.0.0303941192341167
T-STAT1.21775980089164
p-value0.262766506967356






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-7.11075569522291
beta1.35073550196118
S.D.1.47908896338871
T-STAT0.913221270251749
p-value0.391493897052878
Lambda-0.35073550196118

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -7.11075569522291 \tabularnewline
beta & 1.35073550196118 \tabularnewline
S.D. & 1.47908896338871 \tabularnewline
T-STAT & 0.913221270251749 \tabularnewline
p-value & 0.391493897052878 \tabularnewline
Lambda & -0.35073550196118 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302761&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-7.11075569522291[/C][/ROW]
[ROW][C]beta[/C][C]1.35073550196118[/C][/ROW]
[ROW][C]S.D.[/C][C]1.47908896338871[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.913221270251749[/C][/ROW]
[ROW][C]p-value[/C][C]0.391493897052878[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.35073550196118[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302761&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302761&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)
alpha-7.11075569522291
beta1.35073550196118
S.D.1.47908896338871
T-STAT0.913221270251749
p-value0.391493897052878
Lambda-0.35073550196118


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')