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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, 30 Apr 2012 07:11:41 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Apr/30/t1335784330mk9gyfn5ep6iy36.htm/, Retrieved Sun, 28 Apr 2024 19:22:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=165213, Retrieved Sun, 28 Apr 2024 19:22:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W83
Estimated Impact157

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] [] [2012-04-30 11:11:41] [f846b3a26bb0d084da7285efcbdb2f3f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
105.32
106.93
107.99
109.41
111.79
112.7
113.41
115.14
115.6
116.21
116.9
117.31
117.62
118.66
120
120.41
120.8
120.93
121.54
122.04
122.5
123.01
123.79
123.99
124.58
125.77
127.6
130.97
131.79
132.29
132.29
132.65
133.88
134.79
135.9
136.33
136.33
137.91
138.92
140.12
141.92
142.57
143.69
144.61
145.02
146.07
146.77
147.55
148.14
148.62
151.16
152.56
154.55
156.17
158.8
159.39
162.44
166.48
168.3
170.32
170.64
172.85
174.38
177.2
178.96
179.62
180.27
183.38
190.81
193.72
196.86
197.73

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'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=165213&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=165213&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=165213&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1112.39254.1180183341019711.99
2121.2741666666671.948857279784676.36999999999999
3131.573.7897421356268411.75
4142.6233333333333.6491028370205611.22
5158.07757.5608502708479722.18
6183.0359.4582916966110727.09

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 112.3925 & 4.11801833410197 & 11.99 \tabularnewline
2 & 121.274166666667 & 1.94885727978467 & 6.36999999999999 \tabularnewline
3 & 131.57 & 3.78974213562684 & 11.75 \tabularnewline
4 & 142.623333333333 & 3.64910283702056 & 11.22 \tabularnewline
5 & 158.0775 & 7.56085027084797 & 22.18 \tabularnewline
6 & 183.035 & 9.45829169661107 & 27.09 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=165213&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]112.3925[/C][C]4.11801833410197[/C][C]11.99[/C][/ROW]
[ROW][C]2[/C][C]121.274166666667[/C][C]1.94885727978467[/C][C]6.36999999999999[/C][/ROW]
[ROW][C]3[/C][C]131.57[/C][C]3.78974213562684[/C][C]11.75[/C][/ROW]
[ROW][C]4[/C][C]142.623333333333[/C][C]3.64910283702056[/C][C]11.22[/C][/ROW]
[ROW][C]5[/C][C]158.0775[/C][C]7.56085027084797[/C][C]22.18[/C][/ROW]
[ROW][C]6[/C][C]183.035[/C][C]9.45829169661107[/C][C]27.09[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=165213&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=165213&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
1112.39254.1180183341019711.99
2121.2741666666671.948857279784676.36999999999999
3131.573.7897421356268411.75
4142.6233333333333.6491028370205611.22
5158.07757.5608502708479722.18
6183.0359.4582916966110727.09






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-8.63616004061515
beta0.0969899764688303
S.D.0.0247052891399341
T-STAT3.92587902612538
p-value0.0171624539070937

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -8.63616004061515 \tabularnewline
beta & 0.0969899764688303 \tabularnewline
S.D. & 0.0247052891399341 \tabularnewline
T-STAT & 3.92587902612538 \tabularnewline
p-value & 0.0171624539070937 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=165213&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-8.63616004061515[/C][/ROW]
[ROW][C]beta[/C][C]0.0969899764688303[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0247052891399341[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.92587902612538[/C][/ROW]
[ROW][C]p-value[/C][C]0.0171624539070937[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=165213&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=165213&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-8.63616004061515
beta0.0969899764688303
S.D.0.0247052891399341
T-STAT3.92587902612538
p-value0.0171624539070937






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-11.1411284457958
beta2.55887580071624
S.D.0.934253310968341
T-STAT2.73895288427075
p-value0.0519614979816472
Lambda-1.55887580071624

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -11.1411284457958 \tabularnewline
beta & 2.55887580071624 \tabularnewline
S.D. & 0.934253310968341 \tabularnewline
T-STAT & 2.73895288427075 \tabularnewline
p-value & 0.0519614979816472 \tabularnewline
Lambda & -1.55887580071624 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=165213&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.1411284457958[/C][/ROW]
[ROW][C]beta[/C][C]2.55887580071624[/C][/ROW]
[ROW][C]S.D.[/C][C]0.934253310968341[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.73895288427075[/C][/ROW]
[ROW][C]p-value[/C][C]0.0519614979816472[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.55887580071624[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=165213&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=165213&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-11.1411284457958
beta2.55887580071624
S.D.0.934253310968341
T-STAT2.73895288427075
p-value0.0519614979816472
Lambda-1.55887580071624


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')