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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 computationTue, 28 Dec 2010 15:13:13 +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/2010/Dec/28/t1293549415mpdswjzv0fbsut0.htm/, Retrieved Sun, 05 May 2024 03:23:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116386, Retrieved Sun, 05 May 2024 03:23:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact116

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] [StandardDev-MeanPlot] [2010-12-28 15:13:13] [a35bd1e3fb5b4b301d5250bc2f7eb297] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5
0
-2
6
11
9
17
21
21
41
57
65
68
73
71
71
70
69
65
57
57
57
55
65
65
64
60
43
47
40
31
27
24
23
17
16

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116386&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116386&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116386&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 time2 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
120.916666666666722.039049366288467
264.83333333333336.589707309451818
338.083333333333317.875622472738649

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 20.9166666666667 & 22.0390493662884 & 67 \tabularnewline
2 & 64.8333333333333 & 6.5897073094518 & 18 \tabularnewline
3 & 38.0833333333333 & 17.8756224727386 & 49 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116386&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]20.9166666666667[/C][C]22.0390493662884[/C][C]67[/C][/ROW]
[ROW][C]2[/C][C]64.8333333333333[/C][C]6.5897073094518[/C][C]18[/C][/ROW]
[ROW][C]3[/C][C]38.0833333333333[/C][C]17.8756224727386[/C][C]49[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116386&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116386&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
120.916666666666722.039049366288467
264.83333333333336.589707309451818
338.083333333333317.875622472738649






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha30.2749273934915
beta-0.357903658401040
S.D.0.0485444635350774
T-STAT-7.37269777721254
p-value0.0858245326423991

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 30.2749273934915 \tabularnewline
beta & -0.357903658401040 \tabularnewline
S.D. & 0.0485444635350774 \tabularnewline
T-STAT & -7.37269777721254 \tabularnewline
p-value & 0.0858245326423991 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116386&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]30.2749273934915[/C][/ROW]
[ROW][C]beta[/C][C]-0.357903658401040[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0485444635350774[/C][/ROW]
[ROW][C]T-STAT[/C][C]-7.37269777721254[/C][/ROW]
[ROW][C]p-value[/C][C]0.0858245326423991[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116386&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116386&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)
alpha30.2749273934915
beta-0.357903658401040
S.D.0.0485444635350774
T-STAT-7.37269777721254
p-value0.0858245326423991






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha6.42670130145786
beta-1.05217387096174
S.D.0.438518705084190
T-STAT-2.39938196196154
p-value0.251390048966931
Lambda2.05217387096174

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 6.42670130145786 \tabularnewline
beta & -1.05217387096174 \tabularnewline
S.D. & 0.438518705084190 \tabularnewline
T-STAT & -2.39938196196154 \tabularnewline
p-value & 0.251390048966931 \tabularnewline
Lambda & 2.05217387096174 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116386&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]6.42670130145786[/C][/ROW]
[ROW][C]beta[/C][C]-1.05217387096174[/C][/ROW]
[ROW][C]S.D.[/C][C]0.438518705084190[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.39938196196154[/C][/ROW]
[ROW][C]p-value[/C][C]0.251390048966931[/C][/ROW]
[ROW][C]Lambda[/C][C]2.05217387096174[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116386&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116386&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)
alpha6.42670130145786
beta-1.05217387096174
S.D.0.438518705084190
T-STAT-2.39938196196154
p-value0.251390048966931
Lambda2.05217387096174


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = 1 ; par3 = 0 ; par4 = 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')