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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, 19 Dec 2009 07:50:47 -0700
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/Dec/19/t12612344133cxncxhc8o2d4fj.htm/, Retrieved Fri, 03 May 2024 22:39:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69614, Retrieved Fri, 03 May 2024 22:39:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109

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] [Standard Deviatio...] [2008-12-21 15:20:27] [005278dde49cfd8c32bf201feaeb19d6]
-  M D    [Standard Deviation-Mean Plot] [Standar Deviation...] [2009-12-19 14:50:47] [986e3c28a4248c495afaef9fd432264f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
67.8
66.9
71.5
75.9
71.9
70.7
73.5
76.1
82.5
87.1
83.2
86.1
85.9
77.4
74.4
69.9
73.8
69.2
69.7
71.0
71.2
75.8
73.0
66.4
58.6
55.5
52.6
54.9
54.6
51.2
50.9
49.6
53.4
52.0
47.5
42.1
44.5
43.2
51.4
59.4
60.3
61.4
68.8
73.6
81.8
79.6
85.8
88.1
89.1
95.0
96.2
84.2
96.9
103.1
99.3
103.5
112.4
111.1
113.7
92.0
93.0
98.4
92.6
94.6
99.5
97.6
91.3
93.6
93.1
78.4
70.2
69.3
71.1
73.5
85.9
91.5
91.8
88.3
91.3
94.0
99.3
96.7
88.0
96.7
106.8
114.3
105.7
90.1
91.6
97.7
100.8
104.6
95.9
102.7
104.0
107.9
113.8
113.8
123.1
125.1
137.6
134.0
140.3
152.1
150.6
167.3
153.2
142.0
154.4
158.5
180.9
181.3
172.4
192.0
199.3
215.4
214.3
201.5
190.5
196.0
215.7
209.4
214.1
237.8
239.0
237.8
251.5
248.8
215.4
201.2
203.1
214.2
188.9
203.0
213.3
228.5
228.2
240.9
258.8
248.5
269.2
289.6
323.4
317.2
322.8
340.9
368.2
388.5
441.2
474.3
483.9
417.9
365.9
263.0
199.4

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69614&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69614&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69614&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
176.17.0107709341347820.2
273.14166666666675.0606248865554419.5
351.90833333333334.2540800379984616.5
466.491666666666715.580317322788644.9
599.70833333333339.3783559649898529.5
689.310.569940225168630.2
789.00833333333338.7428368948355128.2
8101.8416666666677.0109600345502324.2
9137.74166666666716.633616472965153.5
10188.04166666666719.485400517652561
1122417.796526729571850.3
12250.79166666666742.8758982589887134.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 76.1 & 7.01077093413478 & 20.2 \tabularnewline
2 & 73.1416666666667 & 5.06062488655544 & 19.5 \tabularnewline
3 & 51.9083333333333 & 4.25408003799846 & 16.5 \tabularnewline
4 & 66.4916666666667 & 15.5803173227886 & 44.9 \tabularnewline
5 & 99.7083333333333 & 9.37835596498985 & 29.5 \tabularnewline
6 & 89.3 & 10.5699402251686 & 30.2 \tabularnewline
7 & 89.0083333333333 & 8.74283689483551 & 28.2 \tabularnewline
8 & 101.841666666667 & 7.01096003455023 & 24.2 \tabularnewline
9 & 137.741666666667 & 16.6336164729651 & 53.5 \tabularnewline
10 & 188.041666666667 & 19.4854005176525 & 61 \tabularnewline
11 & 224 & 17.7965267295718 & 50.3 \tabularnewline
12 & 250.791666666667 & 42.8758982589887 & 134.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69614&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]76.1[/C][C]7.01077093413478[/C][C]20.2[/C][/ROW]
[ROW][C]2[/C][C]73.1416666666667[/C][C]5.06062488655544[/C][C]19.5[/C][/ROW]
[ROW][C]3[/C][C]51.9083333333333[/C][C]4.25408003799846[/C][C]16.5[/C][/ROW]
[ROW][C]4[/C][C]66.4916666666667[/C][C]15.5803173227886[/C][C]44.9[/C][/ROW]
[ROW][C]5[/C][C]99.7083333333333[/C][C]9.37835596498985[/C][C]29.5[/C][/ROW]
[ROW][C]6[/C][C]89.3[/C][C]10.5699402251686[/C][C]30.2[/C][/ROW]
[ROW][C]7[/C][C]89.0083333333333[/C][C]8.74283689483551[/C][C]28.2[/C][/ROW]
[ROW][C]8[/C][C]101.841666666667[/C][C]7.01096003455023[/C][C]24.2[/C][/ROW]
[ROW][C]9[/C][C]137.741666666667[/C][C]16.6336164729651[/C][C]53.5[/C][/ROW]
[ROW][C]10[/C][C]188.041666666667[/C][C]19.4854005176525[/C][C]61[/C][/ROW]
[ROW][C]11[/C][C]224[/C][C]17.7965267295718[/C][C]50.3[/C][/ROW]
[ROW][C]12[/C][C]250.791666666667[/C][C]42.8758982589887[/C][C]134.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69614&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69614&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
176.17.0107709341347820.2
273.14166666666675.0606248865554419.5
351.90833333333334.2540800379984616.5
466.491666666666715.580317322788644.9
599.70833333333339.3783559649898529.5
689.310.569940225168630.2
789.00833333333338.7428368948355128.2
8101.8416666666677.0109600345502324.2
9137.74166666666716.633616472965153.5
10188.04166666666719.485400517652561
1122417.796526729571850.3
12250.79166666666742.8758982589887134.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-2.65567530594988
beta0.135536786389930
S.D.0.027417277922253
T-STAT4.94348077786099
p-value0.000584148403145762

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -2.65567530594988 \tabularnewline
beta & 0.135536786389930 \tabularnewline
S.D. & 0.027417277922253 \tabularnewline
T-STAT & 4.94348077786099 \tabularnewline
p-value & 0.000584148403145762 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69614&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.65567530594988[/C][/ROW]
[ROW][C]beta[/C][C]0.135536786389930[/C][/ROW]
[ROW][C]S.D.[/C][C]0.027417277922253[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.94348077786099[/C][/ROW]
[ROW][C]p-value[/C][C]0.000584148403145762[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69614&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69614&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-2.65567530594988
beta0.135536786389930
S.D.0.027417277922253
T-STAT4.94348077786099
p-value0.000584148403145762






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.70382616490284
beta1.09386516659573
S.D.0.227386918597505
T-STAT4.81058969153791
p-value0.000712213092876349
Lambda-0.093865166595726

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.70382616490284 \tabularnewline
beta & 1.09386516659573 \tabularnewline
S.D. & 0.227386918597505 \tabularnewline
T-STAT & 4.81058969153791 \tabularnewline
p-value & 0.000712213092876349 \tabularnewline
Lambda & -0.093865166595726 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69614&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.70382616490284[/C][/ROW]
[ROW][C]beta[/C][C]1.09386516659573[/C][/ROW]
[ROW][C]S.D.[/C][C]0.227386918597505[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.81058969153791[/C][/ROW]
[ROW][C]p-value[/C][C]0.000712213092876349[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.093865166595726[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69614&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69614&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-2.70382616490284
beta1.09386516659573
S.D.0.227386918597505
T-STAT4.81058969153791
p-value0.000712213092876349
Lambda-0.093865166595726


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')