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 computationSat, 19 Mar 2016 18:49:38 +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/2016/Mar/19/t1458413403bhh3mu1lxu2l8wc.htm/, Retrieved Tue, 07 May 2024 18:30:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294345, Retrieved Tue, 07 May 2024 18:30:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75

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] [] [2016-03-19 18:49:38] [56edb0d8f6220d107203045c2c4d5731] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
37.43
38.39
38.99
39.83
41.21
41.72
42.12
43.18
43.43
43.77
44.19
44.38
44.57
45.13
45.84
46.11
46.35
46.41
46.78
47.09
47.34
47.64
48.17
48.24
48.59
49.29
50.44
52.42
52.9
53.19
53.19
53.38
54.17
54.69
55.39
55.64
55.64
56.57
57.16
57.87
58.89
59.28
59.94
60.35
60.59
61.2
61.62
62.07
62.38
62.62
64.15
64.97
66.12
67.08
68.66
69.04
70.8
73.2
74.19
75.36
75.54
76.81
77.69
79.34
80.36
80.74
81.12
82.95
87.31
88.93
90.8
91.29
91.36
92.72
95.75
97.19
98.73
99.03
99.4
99.66
100.5
101.21
101.26
101.44
101.97
102.23
102.58
101.91
101.63
101.1
100.71
100.75
100.14
97.72
94.91
94.34
97.11
96.51
95.8
95.25
95.09
94.97
95.21
95.46
95.33
95.14
95.6
95.66
95.66
96.33
97.66
98.27
99.53
100.86
101.26
101.29
101.38
101.49
101.29
101.26

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'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294345&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294345&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294345&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'Herman Ole Andreas Wold' @ wold.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
141.55333333333332.393921595637716.95
246.63916666666671.137616793870843.67
352.77416666666672.26883012839557.05
459.2652.077330017113316.43
568.21416666666674.4440510968614112.98
682.745.507576599558115.75
798.18753.3383368886045910.08
899.99916666666672.816404730513828.23999999999999
995.59416666666670.6315271293867872.14
1099.692.157612316680395.83

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 41.5533333333333 & 2.39392159563771 & 6.95 \tabularnewline
2 & 46.6391666666667 & 1.13761679387084 & 3.67 \tabularnewline
3 & 52.7741666666667 & 2.2688301283955 & 7.05 \tabularnewline
4 & 59.265 & 2.07733001711331 & 6.43 \tabularnewline
5 & 68.2141666666667 & 4.44405109686141 & 12.98 \tabularnewline
6 & 82.74 & 5.5075765995581 & 15.75 \tabularnewline
7 & 98.1875 & 3.33833688860459 & 10.08 \tabularnewline
8 & 99.9991666666667 & 2.81640473051382 & 8.23999999999999 \tabularnewline
9 & 95.5941666666667 & 0.631527129386787 & 2.14 \tabularnewline
10 & 99.69 & 2.15761231668039 & 5.83 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294345&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]41.5533333333333[/C][C]2.39392159563771[/C][C]6.95[/C][/ROW]
[ROW][C]2[/C][C]46.6391666666667[/C][C]1.13761679387084[/C][C]3.67[/C][/ROW]
[ROW][C]3[/C][C]52.7741666666667[/C][C]2.2688301283955[/C][C]7.05[/C][/ROW]
[ROW][C]4[/C][C]59.265[/C][C]2.07733001711331[/C][C]6.43[/C][/ROW]
[ROW][C]5[/C][C]68.2141666666667[/C][C]4.44405109686141[/C][C]12.98[/C][/ROW]
[ROW][C]6[/C][C]82.74[/C][C]5.5075765995581[/C][C]15.75[/C][/ROW]
[ROW][C]7[/C][C]98.1875[/C][C]3.33833688860459[/C][C]10.08[/C][/ROW]
[ROW][C]8[/C][C]99.9991666666667[/C][C]2.81640473051382[/C][C]8.23999999999999[/C][/ROW]
[ROW][C]9[/C][C]95.5941666666667[/C][C]0.631527129386787[/C][C]2.14[/C][/ROW]
[ROW][C]10[/C][C]99.69[/C][C]2.15761231668039[/C][C]5.83[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294345&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294345&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
141.55333333333332.393921595637716.95
246.63916666666671.137616793870843.67
352.77416666666672.26883012839557.05
459.2652.077330017113316.43
568.21416666666674.4440510968614112.98
682.745.507576599558115.75
798.18753.3383368886045910.08
899.99916666666672.816404730513828.23999999999999
995.59416666666670.6315271293867872.14
1099.692.157612316680395.83






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.99590282564328
beta0.00915076617885156
S.D.0.0216450624412844
T-STAT0.422764600641575
p-value0.68360150886142

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.99590282564328 \tabularnewline
beta & 0.00915076617885156 \tabularnewline
S.D. & 0.0216450624412844 \tabularnewline
T-STAT & 0.422764600641575 \tabularnewline
p-value & 0.68360150886142 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294345&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.99590282564328[/C][/ROW]
[ROW][C]beta[/C][C]0.00915076617885156[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0216450624412844[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.422764600641575[/C][/ROW]
[ROW][C]p-value[/C][C]0.68360150886142[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294345&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294345&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)
alpha1.99590282564328
beta0.00915076617885156
S.D.0.0216450624412844
T-STAT0.422764600641575
p-value0.68360150886142






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.0559163095103802
beta0.181672376420061
S.D.0.652333854466396
T-STAT0.278496011170028
p-value0.787694650248557
Lambda0.818327623579939

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.0559163095103802 \tabularnewline
beta & 0.181672376420061 \tabularnewline
S.D. & 0.652333854466396 \tabularnewline
T-STAT & 0.278496011170028 \tabularnewline
p-value & 0.787694650248557 \tabularnewline
Lambda & 0.818327623579939 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294345&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.0559163095103802[/C][/ROW]
[ROW][C]beta[/C][C]0.181672376420061[/C][/ROW]
[ROW][C]S.D.[/C][C]0.652333854466396[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.278496011170028[/C][/ROW]
[ROW][C]p-value[/C][C]0.787694650248557[/C][/ROW]
[ROW][C]Lambda[/C][C]0.818327623579939[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294345&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294345&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)
alpha0.0559163095103802
beta0.181672376420061
S.D.0.652333854466396
T-STAT0.278496011170028
p-value0.787694650248557
Lambda0.818327623579939


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')