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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 computationMon, 17 May 2010 22:00:22 +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/May/18/t1274133633gcfk4dhhx3msxje.htm/, Retrieved Sat, 04 May 2024 12:37:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76170, Retrieved Sat, 04 May 2024 12:37:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact203

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] [] [2010-05-17 22:00:22] [a1c0563c4f28de3d0d1958a3be552dbb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
66857.2
64722.8
68489.6
71342.9
63542.5
69425.0
58927.9
61009.0
66837.0
66147.6
65982.3
65527.5
65914.6
59189.9
66211.4
66400.8
60167.7
64547.9
57706.2
58642.6
60082.1
63414.8
66044.0
57628.5
62838.8
55758.6
61004.5
66173.4
57489.0
59552.2
57061.8
55895.3
56314.7
61232.8
60014.1
57685.4
60403.1
52349.7
55693.3
65676.1
54898.8
55518.2
53779.1
52340.9
55704.4
60330.3
52837.4
55388.1
60383.4
52070.3
54077.0
62887.8
49212.8
57722.0
53936.8
46991.0
54984.2
56485.1
51277.8
53596.4
54252.5
49413.0
53213.2
58695.3
48723.5
54510.0
49454.1
46136.6
54622.5
50583.0
53224.3
53056.4

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76170&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76170&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76170&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
167853.1252791.32174112916620.09999999999
263226.14542.9992229803410497.1
366123.6543.0827008844971309.5
464429.1753498.576903423267210.9
560266.13029.429762623106841.7
661792.353695.559209375498415.5
761443.8254352.3796053614910414.8
857499.5751525.202330566893656.89999999999
958811.752221.939966935804918.10000000001
1058530.555797.0746240381213326.4
1154134.251395.4796128933177.30000000000
1256065.053119.744210134337492.9
1357354.6255113.9163051259810817.5
1451965.654807.8520287130310731
1554085.8752212.701168820595207.3
1653893.53817.671741607279282.3
1749706.053504.653678087668373.4
1852871.551679.473041363474039.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 67853.125 & 2791.3217411291 & 6620.09999999999 \tabularnewline
2 & 63226.1 & 4542.99922298034 & 10497.1 \tabularnewline
3 & 66123.6 & 543.082700884497 & 1309.5 \tabularnewline
4 & 64429.175 & 3498.57690342326 & 7210.9 \tabularnewline
5 & 60266.1 & 3029.42976262310 & 6841.7 \tabularnewline
6 & 61792.35 & 3695.55920937549 & 8415.5 \tabularnewline
7 & 61443.825 & 4352.37960536149 & 10414.8 \tabularnewline
8 & 57499.575 & 1525.20233056689 & 3656.89999999999 \tabularnewline
9 & 58811.75 & 2221.93996693580 & 4918.10000000001 \tabularnewline
10 & 58530.55 & 5797.07462403812 & 13326.4 \tabularnewline
11 & 54134.25 & 1395.479612893 & 3177.30000000000 \tabularnewline
12 & 56065.05 & 3119.74421013433 & 7492.9 \tabularnewline
13 & 57354.625 & 5113.91630512598 & 10817.5 \tabularnewline
14 & 51965.65 & 4807.85202871303 & 10731 \tabularnewline
15 & 54085.875 & 2212.70116882059 & 5207.3 \tabularnewline
16 & 53893.5 & 3817.67174160727 & 9282.3 \tabularnewline
17 & 49706.05 & 3504.65367808766 & 8373.4 \tabularnewline
18 & 52871.55 & 1679.47304136347 & 4039.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76170&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]67853.125[/C][C]2791.3217411291[/C][C]6620.09999999999[/C][/ROW]
[ROW][C]2[/C][C]63226.1[/C][C]4542.99922298034[/C][C]10497.1[/C][/ROW]
[ROW][C]3[/C][C]66123.6[/C][C]543.082700884497[/C][C]1309.5[/C][/ROW]
[ROW][C]4[/C][C]64429.175[/C][C]3498.57690342326[/C][C]7210.9[/C][/ROW]
[ROW][C]5[/C][C]60266.1[/C][C]3029.42976262310[/C][C]6841.7[/C][/ROW]
[ROW][C]6[/C][C]61792.35[/C][C]3695.55920937549[/C][C]8415.5[/C][/ROW]
[ROW][C]7[/C][C]61443.825[/C][C]4352.37960536149[/C][C]10414.8[/C][/ROW]
[ROW][C]8[/C][C]57499.575[/C][C]1525.20233056689[/C][C]3656.89999999999[/C][/ROW]
[ROW][C]9[/C][C]58811.75[/C][C]2221.93996693580[/C][C]4918.10000000001[/C][/ROW]
[ROW][C]10[/C][C]58530.55[/C][C]5797.07462403812[/C][C]13326.4[/C][/ROW]
[ROW][C]11[/C][C]54134.25[/C][C]1395.479612893[/C][C]3177.30000000000[/C][/ROW]
[ROW][C]12[/C][C]56065.05[/C][C]3119.74421013433[/C][C]7492.9[/C][/ROW]
[ROW][C]13[/C][C]57354.625[/C][C]5113.91630512598[/C][C]10817.5[/C][/ROW]
[ROW][C]14[/C][C]51965.65[/C][C]4807.85202871303[/C][C]10731[/C][/ROW]
[ROW][C]15[/C][C]54085.875[/C][C]2212.70116882059[/C][C]5207.3[/C][/ROW]
[ROW][C]16[/C][C]53893.5[/C][C]3817.67174160727[/C][C]9282.3[/C][/ROW]
[ROW][C]17[/C][C]49706.05[/C][C]3504.65367808766[/C][C]8373.4[/C][/ROW]
[ROW][C]18[/C][C]52871.55[/C][C]1679.47304136347[/C][C]4039.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76170&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76170&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
167853.1252791.32174112916620.09999999999
263226.14542.9992229803410497.1
366123.6543.0827008844971309.5
464429.1753498.576903423267210.9
560266.13029.429762623106841.7
661792.353695.559209375498415.5
761443.8254352.3796053614910414.8
857499.5751525.202330566893656.89999999999
958811.752221.939966935804918.10000000001
1058530.555797.0746240381213326.4
1154134.251395.4796128933177.30000000000
1256065.053119.744210134337492.9
1357354.6255113.9163051259810817.5
1451965.654807.8520287130310731
1554085.8752212.701168820595207.3
1653893.53817.671741607279282.3
1749706.053504.653678087668373.4
1852871.551679.473041363474039.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha4121.92702787809
beta-0.0157569507204182
S.D.0.0694943139168478
T-STAT-0.226737265717479
p-value0.823499510618175

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 4121.92702787809 \tabularnewline
beta & -0.0157569507204182 \tabularnewline
S.D. & 0.0694943139168478 \tabularnewline
T-STAT & -0.226737265717479 \tabularnewline
p-value & 0.823499510618175 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76170&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4121.92702787809[/C][/ROW]
[ROW][C]beta[/C][C]-0.0157569507204182[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0694943139168478[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.226737265717479[/C][/ROW]
[ROW][C]p-value[/C][C]0.823499510618175[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76170&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76170&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)
alpha4121.92702787809
beta-0.0157569507204182
S.D.0.0694943139168478
T-STAT-0.226737265717479
p-value0.823499510618175






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha17.3169577209064
beta-0.854524551978274
S.D.1.65792916860907
T-STAT-0.515416803176932
p-value0.61330968440998
Lambda1.85452455197827

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 17.3169577209064 \tabularnewline
beta & -0.854524551978274 \tabularnewline
S.D. & 1.65792916860907 \tabularnewline
T-STAT & -0.515416803176932 \tabularnewline
p-value & 0.61330968440998 \tabularnewline
Lambda & 1.85452455197827 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76170&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]17.3169577209064[/C][/ROW]
[ROW][C]beta[/C][C]-0.854524551978274[/C][/ROW]
[ROW][C]S.D.[/C][C]1.65792916860907[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.515416803176932[/C][/ROW]
[ROW][C]p-value[/C][C]0.61330968440998[/C][/ROW]
[ROW][C]Lambda[/C][C]1.85452455197827[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76170&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76170&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)
alpha17.3169577209064
beta-0.854524551978274
S.D.1.65792916860907
T-STAT-0.515416803176932
p-value0.61330968440998
Lambda1.85452455197827


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')