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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 computationThu, 28 May 2009 12:55:19 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/May/28/t1243536934to47dj88ll2cj9t.htm/, Retrieved Sun, 05 May 2024 23:55:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40694, Retrieved Sun, 05 May 2024 23:55:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation Plot] [] [2009-05-28 18:32:45] [96b01d8cb0304fe86f721affdc70b94f]
- RMPD    [Standard Deviation-Mean Plot] [] [2009-05-28 18:55:19] [5ece983fa688b54e830000b964b580e8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3851.3
3851.8
3854.1
3858.4
3861.6
3856.3
3855.8
3860.4
3855.1
3839.5
3833
3833.6
3826.8
3818.2
3811.4
3806.8
3810.3
3818.2
3858.9
3867.8
3872.3
3873.3
3876.7
3882.6
3883.5
3882.2
3888.1
3893.7
3901.9
3914.3
3930.3
3948.3
3971.5
3990.1
3993
3998
4015.8
4041.2
4060.7
4076.7
4103
4125.3
4139.7
4146.7
4158
4155.1
4144.8
4148.2
4142.5
4142.1
4145.4
4146.3
4143.5
4149.2
4158.9
4166.1
4179.1
4194.4
4211.7
4226.3
4235.8
4243.6
4258.7
4278.2
4298
4315.1
4334.3
4356
4374
4395.5
4417.8
4432.8
4446.3

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'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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40694&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40694&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40694&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
13853.93.238312317653507.09999999999991
23858.5252.906745029524605.79999999999973
33840.310.293363557814022.0999999999999
43815.88.7009578016828920
53838.828.761200716706457.5
63876.2254.6485660871569210.2999999999997
73886.8755.2066463934730911.5
83923.720.102404499628146.4000000000001
93988.1511.569644189285426.5
104048.626.2463965780760.8999999999996
114128.67519.296351123118143.6999999999998
124151.5256.082420022765113.1999999999998
134144.0752.088659857420424.19999999999982
144154.42510.049668319568322.6000000000004
154202.87520.523868218897447.1999999999998
164254.07518.682500724831442.3999999999996
174325.8524.97738977555558
184405.02525.741843368337258.8000000000002

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3853.9 & 3.23831231765350 & 7.09999999999991 \tabularnewline
2 & 3858.525 & 2.90674502952460 & 5.79999999999973 \tabularnewline
3 & 3840.3 & 10.2933635578140 & 22.0999999999999 \tabularnewline
4 & 3815.8 & 8.70095780168289 & 20 \tabularnewline
5 & 3838.8 & 28.7612007167064 & 57.5 \tabularnewline
6 & 3876.225 & 4.64856608715692 & 10.2999999999997 \tabularnewline
7 & 3886.875 & 5.20664639347309 & 11.5 \tabularnewline
8 & 3923.7 & 20.1024044996281 & 46.4000000000001 \tabularnewline
9 & 3988.15 & 11.5696441892854 & 26.5 \tabularnewline
10 & 4048.6 & 26.24639657807 & 60.8999999999996 \tabularnewline
11 & 4128.675 & 19.2963511231181 & 43.6999999999998 \tabularnewline
12 & 4151.525 & 6.0824200227651 & 13.1999999999998 \tabularnewline
13 & 4144.075 & 2.08865985742042 & 4.19999999999982 \tabularnewline
14 & 4154.425 & 10.0496683195683 & 22.6000000000004 \tabularnewline
15 & 4202.875 & 20.5238682188974 & 47.1999999999998 \tabularnewline
16 & 4254.075 & 18.6825007248314 & 42.3999999999996 \tabularnewline
17 & 4325.85 & 24.977389775555 & 58 \tabularnewline
18 & 4405.025 & 25.7418433683372 & 58.8000000000002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40694&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]3853.9[/C][C]3.23831231765350[/C][C]7.09999999999991[/C][/ROW]
[ROW][C]2[/C][C]3858.525[/C][C]2.90674502952460[/C][C]5.79999999999973[/C][/ROW]
[ROW][C]3[/C][C]3840.3[/C][C]10.2933635578140[/C][C]22.0999999999999[/C][/ROW]
[ROW][C]4[/C][C]3815.8[/C][C]8.70095780168289[/C][C]20[/C][/ROW]
[ROW][C]5[/C][C]3838.8[/C][C]28.7612007167064[/C][C]57.5[/C][/ROW]
[ROW][C]6[/C][C]3876.225[/C][C]4.64856608715692[/C][C]10.2999999999997[/C][/ROW]
[ROW][C]7[/C][C]3886.875[/C][C]5.20664639347309[/C][C]11.5[/C][/ROW]
[ROW][C]8[/C][C]3923.7[/C][C]20.1024044996281[/C][C]46.4000000000001[/C][/ROW]
[ROW][C]9[/C][C]3988.15[/C][C]11.5696441892854[/C][C]26.5[/C][/ROW]
[ROW][C]10[/C][C]4048.6[/C][C]26.24639657807[/C][C]60.8999999999996[/C][/ROW]
[ROW][C]11[/C][C]4128.675[/C][C]19.2963511231181[/C][C]43.6999999999998[/C][/ROW]
[ROW][C]12[/C][C]4151.525[/C][C]6.0824200227651[/C][C]13.1999999999998[/C][/ROW]
[ROW][C]13[/C][C]4144.075[/C][C]2.08865985742042[/C][C]4.19999999999982[/C][/ROW]
[ROW][C]14[/C][C]4154.425[/C][C]10.0496683195683[/C][C]22.6000000000004[/C][/ROW]
[ROW][C]15[/C][C]4202.875[/C][C]20.5238682188974[/C][C]47.1999999999998[/C][/ROW]
[ROW][C]16[/C][C]4254.075[/C][C]18.6825007248314[/C][C]42.3999999999996[/C][/ROW]
[ROW][C]17[/C][C]4325.85[/C][C]24.977389775555[/C][C]58[/C][/ROW]
[ROW][C]18[/C][C]4405.025[/C][C]25.7418433683372[/C][C]58.8000000000002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40694&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40694&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
13853.93.238312317653507.09999999999991
23858.5252.906745029524605.79999999999973
33840.310.293363557814022.0999999999999
43815.88.7009578016828920
53838.828.761200716706457.5
63876.2254.6485660871569210.2999999999997
73886.8755.2066463934730911.5
83923.720.102404499628146.4000000000001
93988.1511.569644189285426.5
104048.626.2463965780760.8999999999996
114128.67519.296351123118143.6999999999998
124151.5256.082420022765113.1999999999998
134144.0752.088659857420424.19999999999982
144154.42510.049668319568322.6000000000004
154202.87520.523868218897447.1999999999998
164254.07518.682500724831442.3999999999996
174325.8524.97738977555558
184405.02525.741843368337258.8000000000002






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-72.5499066673058
beta0.0213902458491362
S.D.0.0109996780427497
T-STAT1.94462472137858
p-value0.0696146167564626

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -72.5499066673058 \tabularnewline
beta & 0.0213902458491362 \tabularnewline
S.D. & 0.0109996780427497 \tabularnewline
T-STAT & 1.94462472137858 \tabularnewline
p-value & 0.0696146167564626 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40694&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-72.5499066673058[/C][/ROW]
[ROW][C]beta[/C][C]0.0213902458491362[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0109996780427497[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.94462472137858[/C][/ROW]
[ROW][C]p-value[/C][C]0.0696146167564626[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40694&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40694&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-72.5499066673058
beta0.0213902458491362
S.D.0.0109996780427497
T-STAT1.94462472137858
p-value0.0696146167564626






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-59.068778859312
beta7.39695169633005
S.D.4.19892027951013
T-STAT1.76163184912694
p-value0.0972245123617093
Lambda-6.39695169633005

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -59.068778859312 \tabularnewline
beta & 7.39695169633005 \tabularnewline
S.D. & 4.19892027951013 \tabularnewline
T-STAT & 1.76163184912694 \tabularnewline
p-value & 0.0972245123617093 \tabularnewline
Lambda & -6.39695169633005 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40694&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-59.068778859312[/C][/ROW]
[ROW][C]beta[/C][C]7.39695169633005[/C][/ROW]
[ROW][C]S.D.[/C][C]4.19892027951013[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.76163184912694[/C][/ROW]
[ROW][C]p-value[/C][C]0.0972245123617093[/C][/ROW]
[ROW][C]Lambda[/C][C]-6.39695169633005[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40694&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40694&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-59.068778859312
beta7.39695169633005
S.D.4.19892027951013
T-STAT1.76163184912694
p-value0.0972245123617093
Lambda-6.39695169633005


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')