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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, 05 Dec 2013 10:48:29 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/05/t13862585170i1kjkf19s9jwi7.htm/, Retrieved Fri, 19 Apr 2024 05:55:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=231165, Retrieved Fri, 19 Apr 2024 05:55:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72

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] [] [2013-12-05 15:48:29] [ffc6217b42a6800413892efb2ef7f057] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
59.8
60.7
59.7
60.2
61.3
59.8
61.2
59.3
59.4
63.1
68
69.4
70.2
72.6
72.1
69.7
71.5
75.7
76
76.4
83.8
86.2
88.5
95.9
103.1
113.5
115.7
113.1
112.7
121.9
120.3
108.7
102.8
83.4
79.4
77.8
85.7
83.2
82
86.9
95.7
97.9
89.3
91.5
86.8
91
93.8
96.8
95.7
91.4
88.7
88.2
87.7
89.5
95.6
100.5
106.3
112
117.7
125
132.4
138.1
134.7
136.7
134.3
131.6
129.8
131.9
129.8
119.4
116.7
112.8
116
117.5
118.8
118.7
116.3
115.2
131.7
133.7
132.5
126.9
122.2
120.2

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 4 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231165&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231165&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231165&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 time4 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
161.8253.3936103060149610.1
278.21666666666678.4141475378007726.2
3104.36666666666715.697210715360444.1
490.055.290385791053615.9
599.858333333333312.657262258434437.3
6129.0166666666678.1830015979171825.3
7122.4756.8882145727321818.5

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 61.825 & 3.39361030601496 & 10.1 \tabularnewline
2 & 78.2166666666667 & 8.41414753780077 & 26.2 \tabularnewline
3 & 104.366666666667 & 15.6972107153604 & 44.1 \tabularnewline
4 & 90.05 & 5.2903857910536 & 15.9 \tabularnewline
5 & 99.8583333333333 & 12.6572622584344 & 37.3 \tabularnewline
6 & 129.016666666667 & 8.18300159791718 & 25.3 \tabularnewline
7 & 122.475 & 6.88821457273218 & 18.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231165&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]61.825[/C][C]3.39361030601496[/C][C]10.1[/C][/ROW]
[ROW][C]2[/C][C]78.2166666666667[/C][C]8.41414753780077[/C][C]26.2[/C][/ROW]
[ROW][C]3[/C][C]104.366666666667[/C][C]15.6972107153604[/C][C]44.1[/C][/ROW]
[ROW][C]4[/C][C]90.05[/C][C]5.2903857910536[/C][C]15.9[/C][/ROW]
[ROW][C]5[/C][C]99.8583333333333[/C][C]12.6572622584344[/C][C]37.3[/C][/ROW]
[ROW][C]6[/C][C]129.016666666667[/C][C]8.18300159791718[/C][C]25.3[/C][/ROW]
[ROW][C]7[/C][C]122.475[/C][C]6.88821457273218[/C][C]18.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231165&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231165&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
161.8253.3936103060149610.1
278.21666666666678.4141475378007726.2
3104.36666666666715.697210715360444.1
490.055.290385791053615.9
599.858333333333312.657262258434437.3
6129.0166666666678.1830015979171825.3
7122.4756.8882145727321818.5






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2.3566607059307
beta0.0641975398925334
S.D.0.0747627558358573
T-STAT0.858683433680268
p-value0.429748241625164

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.3566607059307 \tabularnewline
beta & 0.0641975398925334 \tabularnewline
S.D. & 0.0747627558358573 \tabularnewline
T-STAT & 0.858683433680268 \tabularnewline
p-value & 0.429748241625164 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231165&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.3566607059307[/C][/ROW]
[ROW][C]beta[/C][C]0.0641975398925334[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0747627558358573[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.858683433680268[/C][/ROW]
[ROW][C]p-value[/C][C]0.429748241625164[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231165&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231165&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)
alpha2.3566607059307
beta0.0641975398925334
S.D.0.0747627558358573
T-STAT0.858683433680268
p-value0.429748241625164






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.99476103095112
beta1.10660045300459
S.D.0.748981457285794
T-STAT1.47747376419005
p-value0.199592512200866
Lambda-0.106600453004591

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.99476103095112 \tabularnewline
beta & 1.10660045300459 \tabularnewline
S.D. & 0.748981457285794 \tabularnewline
T-STAT & 1.47747376419005 \tabularnewline
p-value & 0.199592512200866 \tabularnewline
Lambda & -0.106600453004591 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231165&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.99476103095112[/C][/ROW]
[ROW][C]beta[/C][C]1.10660045300459[/C][/ROW]
[ROW][C]S.D.[/C][C]0.748981457285794[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.47747376419005[/C][/ROW]
[ROW][C]p-value[/C][C]0.199592512200866[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.106600453004591[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231165&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231165&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-2.99476103095112
beta1.10660045300459
S.D.0.748981457285794
T-STAT1.47747376419005
p-value0.199592512200866
Lambda-0.106600453004591


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')