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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 computationSat, 10 Dec 2016 15:36:41 +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/10/t148138061069mcxkmh7u05uli.htm/, Retrieved Mon, 06 May 2024 04:17:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298690, Retrieved Mon, 06 May 2024 04:17:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68

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] [stand dev] [2016-12-10 14:36:41] [f0fcaf0884a2ab8e55345d70fdb8db2d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2888.9
2916.2
2939.5
2968.3
2986.7
3008.4
3035.3
3059
3078.4
3096.8
3125.2
3157.6
3186
3215.2
3257.8
3296
3330.6
3366.2
3402.9
3426.1
3461.3
3488
3509.5
3536
3561
3593.2
3620.4
3630.4
3643.1
3672.5
3692.2
3719.4
3744.1
3768.3
3803.5
3838.9
3860.4
3879.8
3905.5
3932.4
3959.7
3980.7
4012.8
4037.7
4065
4086.4
4106.9
4137.5
4166.3
4177.8
4176.4
4189.8
4218
4235.9
4237.9
4264.6
4295.5
4327.8
4340.1
4340.2
4375.3
4405.2
4433.3
4472
4507.4
4525.5
4562.5
4581.6
4591
4614
4643.3
4674.6
4687.4
4703.2
4728.3
4757.1
4765.2
4785.4
4810.1
4830.2
4843.3
4861.1
4875.6
4897.3
4901.5
4900.4
4914.6
4930.2
4917
4936.1
4942.3
4951.1
4975.6
4973.5
4963.4
4974.8
5001.8
5013.4
5007.9
4985.6
4967.1
4988.9
4999.8
4988.3
4975.5
4981.1
4993.4
4992.9
4994.1
5014.4
5028.6
5025.4
5021.7
5026.9
5026.6

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=298690&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=298690&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298690&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
13021.6916666666784.9537784309619268.7
23372.96666666667117.105479518822350
33690.5833333333386.281619588345277.9
43997.0666666666791.9181882618088277.1
54247.52565.4672315673339173.9
64532.1416666666795.7932665913551299.3
74795.3568.7550527068905209.900000000001
84940.0416666666727.98133983189375.2000000000007
94991.3083333333313.280228525780946.2999999999993

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3021.69166666667 & 84.9537784309619 & 268.7 \tabularnewline
2 & 3372.96666666667 & 117.105479518822 & 350 \tabularnewline
3 & 3690.58333333333 & 86.281619588345 & 277.9 \tabularnewline
4 & 3997.06666666667 & 91.9181882618088 & 277.1 \tabularnewline
5 & 4247.525 & 65.4672315673339 & 173.9 \tabularnewline
6 & 4532.14166666667 & 95.7932665913551 & 299.3 \tabularnewline
7 & 4795.35 & 68.7550527068905 & 209.900000000001 \tabularnewline
8 & 4940.04166666667 & 27.981339831893 & 75.2000000000007 \tabularnewline
9 & 4991.30833333333 & 13.2802285257809 & 46.2999999999993 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298690&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]3021.69166666667[/C][C]84.9537784309619[/C][C]268.7[/C][/ROW]
[ROW][C]2[/C][C]3372.96666666667[/C][C]117.105479518822[/C][C]350[/C][/ROW]
[ROW][C]3[/C][C]3690.58333333333[/C][C]86.281619588345[/C][C]277.9[/C][/ROW]
[ROW][C]4[/C][C]3997.06666666667[/C][C]91.9181882618088[/C][C]277.1[/C][/ROW]
[ROW][C]5[/C][C]4247.525[/C][C]65.4672315673339[/C][C]173.9[/C][/ROW]
[ROW][C]6[/C][C]4532.14166666667[/C][C]95.7932665913551[/C][C]299.3[/C][/ROW]
[ROW][C]7[/C][C]4795.35[/C][C]68.7550527068905[/C][C]209.900000000001[/C][/ROW]
[ROW][C]8[/C][C]4940.04166666667[/C][C]27.981339831893[/C][C]75.2000000000007[/C][/ROW]
[ROW][C]9[/C][C]4991.30833333333[/C][C]13.2802285257809[/C][C]46.2999999999993[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298690&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298690&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
13021.6916666666784.9537784309619268.7
23372.96666666667117.105479518822350
33690.5833333333386.281619588345277.9
43997.0666666666791.9181882618088277.1
54247.52565.4672315673339173.9
64532.1416666666795.7932665913551299.3
74795.3568.7550527068905209.900000000001
84940.0416666666727.98133983189375.2000000000007
94991.3083333333313.280228525780946.2999999999993






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha215.308609367913
beta-0.0342188518027844
S.D.0.0121054491767334
T-STAT-2.82673127640342
p-value0.0255255701286602

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 215.308609367913 \tabularnewline
beta & -0.0342188518027844 \tabularnewline
S.D. & 0.0121054491767334 \tabularnewline
T-STAT & -2.82673127640342 \tabularnewline
p-value & 0.0255255701286602 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298690&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]215.308609367913[/C][/ROW]
[ROW][C]beta[/C][C]-0.0342188518027844[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0121054491767334[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.82673127640342[/C][/ROW]
[ROW][C]p-value[/C][C]0.0255255701286602[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298690&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298690&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)
alpha215.308609367913
beta-0.0342188518027844
S.D.0.0121054491767334
T-STAT-2.82673127640342
p-value0.0255255701286602






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha25.7340476774313
beta-2.59675383050061
S.D.1.13647775350817
T-STAT-2.28491391273147
p-value0.0562274825764601
Lambda3.59675383050061

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 25.7340476774313 \tabularnewline
beta & -2.59675383050061 \tabularnewline
S.D. & 1.13647775350817 \tabularnewline
T-STAT & -2.28491391273147 \tabularnewline
p-value & 0.0562274825764601 \tabularnewline
Lambda & 3.59675383050061 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298690&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]25.7340476774313[/C][/ROW]
[ROW][C]beta[/C][C]-2.59675383050061[/C][/ROW]
[ROW][C]S.D.[/C][C]1.13647775350817[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.28491391273147[/C][/ROW]
[ROW][C]p-value[/C][C]0.0562274825764601[/C][/ROW]
[ROW][C]Lambda[/C][C]3.59675383050061[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298690&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298690&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)
alpha25.7340476774313
beta-2.59675383050061
S.D.1.13647775350817
T-STAT-2.28491391273147
p-value0.0562274825764601
Lambda3.59675383050061


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')