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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 computationFri, 14 Dec 2012 06:55:10 -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/2012/Dec/14/t1355486143oz2oq1z4sg1pwkk.htm/, Retrieved Wed, 24 Apr 2024 22:18:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=199505, Retrieved Wed, 24 Apr 2024 22:18:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97

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] [] [2012-12-08 16:17:08] [8e0cd02157c87b7abb8ec068a7f6eed6]
- RM D    [Standard Deviation-Mean Plot] [] [2012-12-14 11:55:10] [c881bea568ce57c3f1ac16d86b52731a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1855.87
1868.53
1865.71
1872.59
1875.95
1875.95
1875.95
1878.08
1878.26
1876.39
1876.77
1876.88
1876.88
1876.68
1865.52
1858.99
1856.87
1858.22
1858.22
1859.32
1859.52
1852.48
1850.07
1850.07
1850.07
1841.55
1845
1844.01
1842.67
1842.67
1842.67
1842.9
1840.37
1841.59
1844.33
1844.33
1844.33
1845.39
1861.84
1862.85
1869.46
1870.8
1870.8
1871.52
1875.52
1880.38
1885.05
1886.42
1886.42
1891.65
1903.11
1905.29
1904.26
1905.37
1905.37
1905.12
1908.62
1915.08
1916.36
1916.68
1916.24
1922.05
1922.63
1922.47
1920.64
1920.66
1920.66
1921.19
1921.44
1921.73
1921.81
1921.81

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199505&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199505&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199505&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 time3 seconds
R Server'George Udny Yule' @ yule.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11873.07756.6537673880701522.3900000000001
21860.236666666678.8654685907364326.8100000000002
31843.513333333332.462904173876239.70000000000005
41868.6966666666713.48447142816442.0900000000001
51905.27759.0813976947884230.26
61921.110833333331.675114423952386.3900000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1873.0775 & 6.65376738807015 & 22.3900000000001 \tabularnewline
2 & 1860.23666666667 & 8.86546859073643 & 26.8100000000002 \tabularnewline
3 & 1843.51333333333 & 2.46290417387623 & 9.70000000000005 \tabularnewline
4 & 1868.69666666667 & 13.484471428164 & 42.0900000000001 \tabularnewline
5 & 1905.2775 & 9.08139769478842 & 30.26 \tabularnewline
6 & 1921.11083333333 & 1.67511442395238 & 6.3900000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199505&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]1873.0775[/C][C]6.65376738807015[/C][C]22.3900000000001[/C][/ROW]
[ROW][C]2[/C][C]1860.23666666667[/C][C]8.86546859073643[/C][C]26.8100000000002[/C][/ROW]
[ROW][C]3[/C][C]1843.51333333333[/C][C]2.46290417387623[/C][C]9.70000000000005[/C][/ROW]
[ROW][C]4[/C][C]1868.69666666667[/C][C]13.484471428164[/C][C]42.0900000000001[/C][/ROW]
[ROW][C]5[/C][C]1905.2775[/C][C]9.08139769478842[/C][C]30.26[/C][/ROW]
[ROW][C]6[/C][C]1921.11083333333[/C][C]1.67511442395238[/C][C]6.3900000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199505&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199505&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
11873.07756.6537673880701522.3900000000001
21860.236666666678.8654685907364326.8100000000002
31843.513333333332.462904173876239.70000000000005
41868.6966666666713.48447142816442.0900000000001
51905.27759.0813976947884230.26
61921.110833333331.675114423952386.3900000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha55.2638812658087
beta-0.0256709022444297
S.D.0.0755044733139045
T-STAT-0.339991806017966
p-value0.750966214135331

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 55.2638812658087 \tabularnewline
beta & -0.0256709022444297 \tabularnewline
S.D. & 0.0755044733139045 \tabularnewline
T-STAT & -0.339991806017966 \tabularnewline
p-value & 0.750966214135331 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199505&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]55.2638812658087[/C][/ROW]
[ROW][C]beta[/C][C]-0.0256709022444297[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0755044733139045[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.339991806017966[/C][/ROW]
[ROW][C]p-value[/C][C]0.750966214135331[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199505&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199505&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)
alpha55.2638812658087
beta-0.0256709022444297
S.D.0.0755044733139045
T-STAT-0.339991806017966
p-value0.750966214135331






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha92.8907469975237
beta-12.0948717513664
S.D.25.9655595750288
T-STAT-0.465804394333105
p-value0.665588449163854
Lambda13.0948717513664

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 92.8907469975237 \tabularnewline
beta & -12.0948717513664 \tabularnewline
S.D. & 25.9655595750288 \tabularnewline
T-STAT & -0.465804394333105 \tabularnewline
p-value & 0.665588449163854 \tabularnewline
Lambda & 13.0948717513664 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199505&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]92.8907469975237[/C][/ROW]
[ROW][C]beta[/C][C]-12.0948717513664[/C][/ROW]
[ROW][C]S.D.[/C][C]25.9655595750288[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.465804394333105[/C][/ROW]
[ROW][C]p-value[/C][C]0.665588449163854[/C][/ROW]
[ROW][C]Lambda[/C][C]13.0948717513664[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199505&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199505&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)
alpha92.8907469975237
beta-12.0948717513664
S.D.25.9655595750288
T-STAT-0.465804394333105
p-value0.665588449163854
Lambda13.0948717513664


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')