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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 computationWed, 08 Dec 2010 13:10:23 +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/08/t1291813732jurazrtxkglil6p.htm/, Retrieved Fri, 03 May 2024 10:51:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106885, Retrieved Fri, 03 May 2024 10:51:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact120

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] [] [2010-12-08 13:10:23] [5815de052410d7754c978b0de903e641] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100.4
97.7
97
96.5
98.4
106.3
103.1
102.4
95
98.1
106.1
99.1
101.2
95.5
99.8
97.1
97.5
96.8
97.7
100.9
94.3
99.5
100.8
97
99.2
101
102.3
97
91.2
97.6
95.7
100.5
94.4
102.9
105.1
98.8
100.7
99.6
107.7
102.9
101.6
102.7
110.5
109.8
94.3
102.5
105
102.3
107.7
100.3
99.5
95
97.7
96.3
97.8
106.4
96.1
106.2
114.7
111.9
121
117.7
115.4
114.3
109.5
108.1
108.2
99.1
101.2
98.1
95.5
97.9
98.2
98.7
95.6
95.8
94.4
96.5
103.3
104.3
104.5
102.3
103.8
103.1
102.2
106.3
102.1
94
102.6
102.6
106.7
107.9
109.3
105.9
109.1
108.5
111.7
109.8
109.1
108.5
108.5
106.2
117.1
109.8
115.2
115.9
119.2
121
118.6
117.6
114.6
110.6
102.5
101.6
107.4
105.8
102.8
104
100.4
100.6

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=106885&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=106885&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106885&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
197.91.737814719698283.90000000000001
2102.553.246023207967977.89999999999999
399.5754.68712776299811.1
498.42.575525836277585.7
598.2251.824600412875844.10000000000001
697.92.871701005791986.5
799.8752.299818833444645.3
896.253.902563260217579.3
9100.34.7208756249944410.7
10102.7253.589219970968628.10000000000001
11106.154.64937271754668.9
12101.0254.6485660871570610.7
13100.6255.262049664025112.7
1499.554.6177194948733510.1
15107.2258.2168018920583318.6
16117.12.960855732160336.7
17106.2254.7926158480173110.4
1898.1752.337199178504055.7
1997.0751.602862023589893.10000000000001
2099.6254.913501806247769.9
21103.4250.942956343987712.2
22101.155.152669211195312.3
23104.952.757414247684485.30000000000001
24108.21.570562531918633.39999999999999
25109.7751.388944443333383.2
26110.44.7081489639418410.9
27117.8252.742717630380495.8
28115.353.59397644214138
29104.3252.731757675929555.80000000000001
30101.951.74642491965733.59999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 97.9 & 1.73781471969828 & 3.90000000000001 \tabularnewline
2 & 102.55 & 3.24602320796797 & 7.89999999999999 \tabularnewline
3 & 99.575 & 4.687127762998 & 11.1 \tabularnewline
4 & 98.4 & 2.57552583627758 & 5.7 \tabularnewline
5 & 98.225 & 1.82460041287584 & 4.10000000000001 \tabularnewline
6 & 97.9 & 2.87170100579198 & 6.5 \tabularnewline
7 & 99.875 & 2.29981883344464 & 5.3 \tabularnewline
8 & 96.25 & 3.90256326021757 & 9.3 \tabularnewline
9 & 100.3 & 4.72087562499444 & 10.7 \tabularnewline
10 & 102.725 & 3.58921997096862 & 8.10000000000001 \tabularnewline
11 & 106.15 & 4.6493727175466 & 8.9 \tabularnewline
12 & 101.025 & 4.64856608715706 & 10.7 \tabularnewline
13 & 100.625 & 5.2620496640251 & 12.7 \tabularnewline
14 & 99.55 & 4.61771949487335 & 10.1 \tabularnewline
15 & 107.225 & 8.21680189205833 & 18.6 \tabularnewline
16 & 117.1 & 2.96085573216033 & 6.7 \tabularnewline
17 & 106.225 & 4.79261584801731 & 10.4 \tabularnewline
18 & 98.175 & 2.33719917850405 & 5.7 \tabularnewline
19 & 97.075 & 1.60286202358989 & 3.10000000000001 \tabularnewline
20 & 99.625 & 4.91350180624776 & 9.9 \tabularnewline
21 & 103.425 & 0.94295634398771 & 2.2 \tabularnewline
22 & 101.15 & 5.1526692111953 & 12.3 \tabularnewline
23 & 104.95 & 2.75741424768448 & 5.30000000000001 \tabularnewline
24 & 108.2 & 1.57056253191863 & 3.39999999999999 \tabularnewline
25 & 109.775 & 1.38894444333338 & 3.2 \tabularnewline
26 & 110.4 & 4.70814896394184 & 10.9 \tabularnewline
27 & 117.825 & 2.74271763038049 & 5.8 \tabularnewline
28 & 115.35 & 3.5939764421413 & 8 \tabularnewline
29 & 104.325 & 2.73175767592955 & 5.80000000000001 \tabularnewline
30 & 101.95 & 1.7464249196573 & 3.59999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106885&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]97.9[/C][C]1.73781471969828[/C][C]3.90000000000001[/C][/ROW]
[ROW][C]2[/C][C]102.55[/C][C]3.24602320796797[/C][C]7.89999999999999[/C][/ROW]
[ROW][C]3[/C][C]99.575[/C][C]4.687127762998[/C][C]11.1[/C][/ROW]
[ROW][C]4[/C][C]98.4[/C][C]2.57552583627758[/C][C]5.7[/C][/ROW]
[ROW][C]5[/C][C]98.225[/C][C]1.82460041287584[/C][C]4.10000000000001[/C][/ROW]
[ROW][C]6[/C][C]97.9[/C][C]2.87170100579198[/C][C]6.5[/C][/ROW]
[ROW][C]7[/C][C]99.875[/C][C]2.29981883344464[/C][C]5.3[/C][/ROW]
[ROW][C]8[/C][C]96.25[/C][C]3.90256326021757[/C][C]9.3[/C][/ROW]
[ROW][C]9[/C][C]100.3[/C][C]4.72087562499444[/C][C]10.7[/C][/ROW]
[ROW][C]10[/C][C]102.725[/C][C]3.58921997096862[/C][C]8.10000000000001[/C][/ROW]
[ROW][C]11[/C][C]106.15[/C][C]4.6493727175466[/C][C]8.9[/C][/ROW]
[ROW][C]12[/C][C]101.025[/C][C]4.64856608715706[/C][C]10.7[/C][/ROW]
[ROW][C]13[/C][C]100.625[/C][C]5.2620496640251[/C][C]12.7[/C][/ROW]
[ROW][C]14[/C][C]99.55[/C][C]4.61771949487335[/C][C]10.1[/C][/ROW]
[ROW][C]15[/C][C]107.225[/C][C]8.21680189205833[/C][C]18.6[/C][/ROW]
[ROW][C]16[/C][C]117.1[/C][C]2.96085573216033[/C][C]6.7[/C][/ROW]
[ROW][C]17[/C][C]106.225[/C][C]4.79261584801731[/C][C]10.4[/C][/ROW]
[ROW][C]18[/C][C]98.175[/C][C]2.33719917850405[/C][C]5.7[/C][/ROW]
[ROW][C]19[/C][C]97.075[/C][C]1.60286202358989[/C][C]3.10000000000001[/C][/ROW]
[ROW][C]20[/C][C]99.625[/C][C]4.91350180624776[/C][C]9.9[/C][/ROW]
[ROW][C]21[/C][C]103.425[/C][C]0.94295634398771[/C][C]2.2[/C][/ROW]
[ROW][C]22[/C][C]101.15[/C][C]5.1526692111953[/C][C]12.3[/C][/ROW]
[ROW][C]23[/C][C]104.95[/C][C]2.75741424768448[/C][C]5.30000000000001[/C][/ROW]
[ROW][C]24[/C][C]108.2[/C][C]1.57056253191863[/C][C]3.39999999999999[/C][/ROW]
[ROW][C]25[/C][C]109.775[/C][C]1.38894444333338[/C][C]3.2[/C][/ROW]
[ROW][C]26[/C][C]110.4[/C][C]4.70814896394184[/C][C]10.9[/C][/ROW]
[ROW][C]27[/C][C]117.825[/C][C]2.74271763038049[/C][C]5.8[/C][/ROW]
[ROW][C]28[/C][C]115.35[/C][C]3.5939764421413[/C][C]8[/C][/ROW]
[ROW][C]29[/C][C]104.325[/C][C]2.73175767592955[/C][C]5.80000000000001[/C][/ROW]
[ROW][C]30[/C][C]101.95[/C][C]1.7464249196573[/C][C]3.59999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106885&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106885&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
197.91.737814719698283.90000000000001
2102.553.246023207967977.89999999999999
399.5754.68712776299811.1
498.42.575525836277585.7
598.2251.824600412875844.10000000000001
697.92.871701005791986.5
799.8752.299818833444645.3
896.253.902563260217579.3
9100.34.7208756249944410.7
10102.7253.589219970968628.10000000000001
11106.154.64937271754668.9
12101.0254.6485660871570610.7
13100.6255.262049664025112.7
1499.554.6177194948733510.1
15107.2258.2168018920583318.6
16117.12.960855732160336.7
17106.2254.7926158480173110.4
1898.1752.337199178504055.7
1997.0751.602862023589893.10000000000001
2099.6254.913501806247769.9
21103.4250.942956343987712.2
22101.155.152669211195312.3
23104.952.757414247684485.30000000000001
24108.21.570562531918633.39999999999999
25109.7751.388944443333383.2
26110.44.7081489639418410.9
27117.8252.742717630380495.8
28115.353.59397644214138
29104.3252.731757675929555.80000000000001
30101.951.74642491965733.59999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2.30391985044529
beta0.0108494493008549
S.D.0.0511017686065783
T-STAT0.212310642012853
p-value0.833402716248396

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.30391985044529 \tabularnewline
beta & 0.0108494493008549 \tabularnewline
S.D. & 0.0511017686065783 \tabularnewline
T-STAT & 0.212310642012853 \tabularnewline
p-value & 0.833402716248396 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106885&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.30391985044529[/C][/ROW]
[ROW][C]beta[/C][C]0.0108494493008549[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0511017686065783[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.212310642012853[/C][/ROW]
[ROW][C]p-value[/C][C]0.833402716248396[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106885&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106885&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)
alpha2.30391985044529
beta0.0108494493008549
S.D.0.0511017686065783
T-STAT0.212310642012853
p-value0.833402716248396






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.487824329572515
beta0.346771771561808
S.D.1.69540390713622
T-STAT0.204536376318464
p-value0.839413890024644
Lambda0.653228228438192

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.487824329572515 \tabularnewline
beta & 0.346771771561808 \tabularnewline
S.D. & 1.69540390713622 \tabularnewline
T-STAT & 0.204536376318464 \tabularnewline
p-value & 0.839413890024644 \tabularnewline
Lambda & 0.653228228438192 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106885&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.487824329572515[/C][/ROW]
[ROW][C]beta[/C][C]0.346771771561808[/C][/ROW]
[ROW][C]S.D.[/C][C]1.69540390713622[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.204536376318464[/C][/ROW]
[ROW][C]p-value[/C][C]0.839413890024644[/C][/ROW]
[ROW][C]Lambda[/C][C]0.653228228438192[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106885&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106885&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-0.487824329572515
beta0.346771771561808
S.D.1.69540390713622
T-STAT0.204536376318464
p-value0.839413890024644
Lambda0.653228228438192


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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')