FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationWed, 26 Dec 2012 18:12:14 -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/26/t1356563546ajzgreyrrt3xq6y.htm/, Retrieved Fri, 19 Apr 2024 13:14:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204747, Retrieved Fri, 19 Apr 2024 13:14:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138

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] [] [2012-12-26 23:12:14] [4fb632b17dd9b46a28f1faaf764882b5] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
33.7
34.59
35.1
35.87
37.15
37.61
37.97
38.94
39.18
39.49
39.86
40.02
40.2
40.85
41.45
41.7
41.92
41.97
42.31
42.61
42.82
43.07
43.51
43.57
43.86
44.49
45.99
48.22
49.46
50.39
50.4
50.59
51.32
51.86
52.47
52.73
52.73
53.59
54.11
54.8
55.72
56.06
56.66
57.05
57.31
57.89
58.32
58.72
59.02
59.54
61.49
62.26
63.49
64.36
65.93
66.82
68.85
71.27
72.27
73.4
73.58
74.84
75.74
77.81
78.74
79.06
79.48
81.19
85.11
86.64
88.48
89.2

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' @ 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204747&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204747&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204747&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' @ yule.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
137.45666666666672.183284986742076.32
242.1651.029832289964993.37
349.3153.035922804144948.87
456.081.933564771936215.99
565.7254.8944077550534414.38
680.82255.3391983140134115.62

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 37.4566666666667 & 2.18328498674207 & 6.32 \tabularnewline
2 & 42.165 & 1.02983228996499 & 3.37 \tabularnewline
3 & 49.315 & 3.03592280414494 & 8.87 \tabularnewline
4 & 56.08 & 1.93356477193621 & 5.99 \tabularnewline
5 & 65.725 & 4.89440775505344 & 14.38 \tabularnewline
6 & 80.8225 & 5.33919831401341 & 15.62 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204747&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]37.4566666666667[/C][C]2.18328498674207[/C][C]6.32[/C][/ROW]
[ROW][C]2[/C][C]42.165[/C][C]1.02983228996499[/C][C]3.37[/C][/ROW]
[ROW][C]3[/C][C]49.315[/C][C]3.03592280414494[/C][C]8.87[/C][/ROW]
[ROW][C]4[/C][C]56.08[/C][C]1.93356477193621[/C][C]5.99[/C][/ROW]
[ROW][C]5[/C][C]65.725[/C][C]4.89440775505344[/C][C]14.38[/C][/ROW]
[ROW][C]6[/C][C]80.8225[/C][C]5.33919831401341[/C][C]15.62[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204747&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204747&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
137.45666666666672.183284986742076.32
242.1651.029832289964993.37
349.3153.035922804144948.87
456.081.933564771936215.99
565.7254.8944077550534414.38
680.82255.3391983140134115.62






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-2.03308183517279
beta0.0923341694027807
S.D.0.0269599780718871
T-STAT3.42486070116887
p-value0.0266609817103058

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -2.03308183517279 \tabularnewline
beta & 0.0923341694027807 \tabularnewline
S.D. & 0.0269599780718871 \tabularnewline
T-STAT & 3.42486070116887 \tabularnewline
p-value & 0.0266609817103058 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204747&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.03308183517279[/C][/ROW]
[ROW][C]beta[/C][C]0.0923341694027807[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0269599780718871[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.42486070116887[/C][/ROW]
[ROW][C]p-value[/C][C]0.0266609817103058[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204747&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204747&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-2.03308183517279
beta0.0923341694027807
S.D.0.0269599780718871
T-STAT3.42486070116887
p-value0.0266609817103058






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-5.73598664686293
beta1.68677768914967
S.D.0.686136194338839
T-STAT2.45837153478697
p-value0.069813568452616
Lambda-0.686777689149666

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.73598664686293 \tabularnewline
beta & 1.68677768914967 \tabularnewline
S.D. & 0.686136194338839 \tabularnewline
T-STAT & 2.45837153478697 \tabularnewline
p-value & 0.069813568452616 \tabularnewline
Lambda & -0.686777689149666 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204747&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.73598664686293[/C][/ROW]
[ROW][C]beta[/C][C]1.68677768914967[/C][/ROW]
[ROW][C]S.D.[/C][C]0.686136194338839[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.45837153478697[/C][/ROW]
[ROW][C]p-value[/C][C]0.069813568452616[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.686777689149666[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204747&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204747&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-5.73598664686293
beta1.68677768914967
S.D.0.686136194338839
T-STAT2.45837153478697
p-value0.069813568452616
Lambda-0.686777689149666


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')