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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 computationSun, 23 Nov 2014 14:15:18 +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/2014/Nov/23/t14167521515yuupnpz6gykvjk.htm/, Retrieved Tue, 28 May 2024 22:50:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=258005, Retrieved Tue, 28 May 2024 22:50:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70

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] [] [2014-11-23 14:15:18] [beda3c52974d0e45a2203fe962302ec0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
101.1
101.35
101.45
101.49
101.68
101.92
102.04
102.55
104.02
105.41
105.48
105.54
105.16
105.16
105.16
105.16
105.16
105.17
105.17
105.54
106.9
107.27
107.31
107.39
107.41
107.46
113.14
117
119.28
119.39
119.5
119.67
119.67
119.73
119.77
119.77
119.78
119.78
119.78
121.28
122.44
122.72
122.75
122.8
122.81
122.83
122.83
122.83
122.84
122.85
123.61
124.74
125.1
125.29
125.45
125.51
125.55
125.57
125.81
127.41
127.75
127.76
127.8
128.23
130.01
130.07
130.17
130.21
130.22
130.23
130.23
130.23
130.23
130.24
130.13
130.14
130.79
131.38
131.61
131.72
131.89
131.89
131.96
131.99
132
132.06
132.11
132.88
135.48
136.56
136.96
137.4
138.32
138.82
138.96
138.94
139
139.19
139.22
139.37
140.74
141.17
141.51
142.94
144.81
145.41
146.11
146.23

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' @ yule.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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' @ yule.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258005&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' @ yule.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258005&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258005&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' @ yule.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1102.8358333333331.762619220124284.44000000000001
2105.8791666666671.000603984268172.23
3116.8158333333334.7833925928121112.36
4121.8858333333331.341115264067613.05
5124.97751.311835112975854.56999999999999
6129.4091666666671.134143315726042.47999999999999
7131.1641666666670.7924927109883731.86000000000001
8135.8741666666672.866827382739366.96000000000001
9142.1416666666672.844611599413037.22999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 102.835833333333 & 1.76261922012428 & 4.44000000000001 \tabularnewline
2 & 105.879166666667 & 1.00060398426817 & 2.23 \tabularnewline
3 & 116.815833333333 & 4.78339259281211 & 12.36 \tabularnewline
4 & 121.885833333333 & 1.34111526406761 & 3.05 \tabularnewline
5 & 124.9775 & 1.31183511297585 & 4.56999999999999 \tabularnewline
6 & 129.409166666667 & 1.13414331572604 & 2.47999999999999 \tabularnewline
7 & 131.164166666667 & 0.792492710988373 & 1.86000000000001 \tabularnewline
8 & 135.874166666667 & 2.86682738273936 & 6.96000000000001 \tabularnewline
9 & 142.141666666667 & 2.84461159941303 & 7.22999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258005&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]102.835833333333[/C][C]1.76261922012428[/C][C]4.44000000000001[/C][/ROW]
[ROW][C]2[/C][C]105.879166666667[/C][C]1.00060398426817[/C][C]2.23[/C][/ROW]
[ROW][C]3[/C][C]116.815833333333[/C][C]4.78339259281211[/C][C]12.36[/C][/ROW]
[ROW][C]4[/C][C]121.885833333333[/C][C]1.34111526406761[/C][C]3.05[/C][/ROW]
[ROW][C]5[/C][C]124.9775[/C][C]1.31183511297585[/C][C]4.56999999999999[/C][/ROW]
[ROW][C]6[/C][C]129.409166666667[/C][C]1.13414331572604[/C][C]2.47999999999999[/C][/ROW]
[ROW][C]7[/C][C]131.164166666667[/C][C]0.792492710988373[/C][C]1.86000000000001[/C][/ROW]
[ROW][C]8[/C][C]135.874166666667[/C][C]2.86682738273936[/C][C]6.96000000000001[/C][/ROW]
[ROW][C]9[/C][C]142.141666666667[/C][C]2.84461159941303[/C][C]7.22999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258005&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258005&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
1102.8358333333331.762619220124284.44000000000001
2105.8791666666671.000603984268172.23
3116.8158333333334.7833925928121112.36
4121.8858333333331.341115264067613.05
5124.97751.311835112975854.56999999999999
6129.4091666666671.134143315726042.47999999999999
7131.1641666666670.7924927109883731.86000000000001
8135.8741666666672.866827382739366.96000000000001
9142.1416666666672.844611599413037.22999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.547681502670391
beta0.0116189930773771
S.D.0.0369397853510407
T-STAT0.31453872747124
p-value0.762279701356997

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.547681502670391 \tabularnewline
beta & 0.0116189930773771 \tabularnewline
S.D. & 0.0369397853510407 \tabularnewline
T-STAT & 0.31453872747124 \tabularnewline
p-value & 0.762279701356997 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258005&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.547681502670391[/C][/ROW]
[ROW][C]beta[/C][C]0.0116189930773771[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0369397853510407[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.31453872747124[/C][/ROW]
[ROW][C]p-value[/C][C]0.762279701356997[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258005&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258005&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)
alpha0.547681502670391
beta0.0116189930773771
S.D.0.0369397853510407
T-STAT0.31453872747124
p-value0.762279701356997






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.24273465011186
beta0.782396393174667
S.D.2.0150355300837
T-STAT0.388279204755346
p-value0.709347860945434
Lambda0.217603606825333

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.24273465011186 \tabularnewline
beta & 0.782396393174667 \tabularnewline
S.D. & 2.0150355300837 \tabularnewline
T-STAT & 0.388279204755346 \tabularnewline
p-value & 0.709347860945434 \tabularnewline
Lambda & 0.217603606825333 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258005&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.24273465011186[/C][/ROW]
[ROW][C]beta[/C][C]0.782396393174667[/C][/ROW]
[ROW][C]S.D.[/C][C]2.0150355300837[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.388279204755346[/C][/ROW]
[ROW][C]p-value[/C][C]0.709347860945434[/C][/ROW]
[ROW][C]Lambda[/C][C]0.217603606825333[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258005&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258005&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-3.24273465011186
beta0.782396393174667
S.D.2.0150355300837
T-STAT0.388279204755346
p-value0.709347860945434
Lambda0.217603606825333


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')