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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 computationThu, 19 Nov 2015 19:01:27 +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/2015/Nov/19/t1447959726b3l4cyuj8m3t0ii.htm/, Retrieved Wed, 22 May 2024 00:04:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283687, Retrieved Wed, 22 May 2024 00:04:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74

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] [] [2015-11-19 19:01:27] [237b8e3b7b7bc12136ba0893525d9132] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
71.83
71.39
73.71
74.13
74.45
74.95
75.09
75.23
76.11
76.64
76.97
78.23
77.15
76.33
70.19
68.42
66.49
63.41
62.92
65.53
65.26
68.25
74.39
78.71
82.15
86.05
89.46
89.32
88.94
93.35
94.72
96.11
104.06
104.11
103.9
110.75
110.82
107.59
96.03
95.69
90.63
75.87
75.57
78.78
74.93
75.85
75.49
76.87
78.18
79.37
80.59
81.18
81.02
82.75
83.63
85.35
90.52
90.66
90.69
92.56
92.87
93.82
96.32
96.03
96.53
102.96
102.38
102.66
106.83
106.5
106.78
108.49
108.77
110.43
110.84
110.52
110.11
109.42
109.06
108.98
108.36
108.11
108.44
107.76
106.27
101.07
100.79
100.97
99.33
99.35
99.23
98.14
98.17
98.48
99
99.19
99.1
100.13
100.07
95.26
94.72
94.25
89.46
88.38
88.57
93.82
93.94
93.92

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=283687&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=283687&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283687&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
174.89416666666671.999297414472186.84
269.75416666666675.5556727083607315.79
395.24333333333338.7416103502244728.6
486.176666666666713.418557254335535.89
584.70833333333335.1005076990314214.38
6101.0141666666675.6123248437269915.62
7109.2333333333331.027170281831983.08
899.99916666666672.221017204850618.13
994.30166666666674.0813496727816811.75

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 74.8941666666667 & 1.99929741447218 & 6.84 \tabularnewline
2 & 69.7541666666667 & 5.55567270836073 & 15.79 \tabularnewline
3 & 95.2433333333333 & 8.74161035022447 & 28.6 \tabularnewline
4 & 86.1766666666667 & 13.4185572543355 & 35.89 \tabularnewline
5 & 84.7083333333333 & 5.10050769903142 & 14.38 \tabularnewline
6 & 101.014166666667 & 5.61232484372699 & 15.62 \tabularnewline
7 & 109.233333333333 & 1.02717028183198 & 3.08 \tabularnewline
8 & 99.9991666666667 & 2.22101720485061 & 8.13 \tabularnewline
9 & 94.3016666666667 & 4.08134967278168 & 11.75 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283687&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]74.8941666666667[/C][C]1.99929741447218[/C][C]6.84[/C][/ROW]
[ROW][C]2[/C][C]69.7541666666667[/C][C]5.55567270836073[/C][C]15.79[/C][/ROW]
[ROW][C]3[/C][C]95.2433333333333[/C][C]8.74161035022447[/C][C]28.6[/C][/ROW]
[ROW][C]4[/C][C]86.1766666666667[/C][C]13.4185572543355[/C][C]35.89[/C][/ROW]
[ROW][C]5[/C][C]84.7083333333333[/C][C]5.10050769903142[/C][C]14.38[/C][/ROW]
[ROW][C]6[/C][C]101.014166666667[/C][C]5.61232484372699[/C][C]15.62[/C][/ROW]
[ROW][C]7[/C][C]109.233333333333[/C][C]1.02717028183198[/C][C]3.08[/C][/ROW]
[ROW][C]8[/C][C]99.9991666666667[/C][C]2.22101720485061[/C][C]8.13[/C][/ROW]
[ROW][C]9[/C][C]94.3016666666667[/C][C]4.08134967278168[/C][C]11.75[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283687&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283687&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
174.89416666666671.999297414472186.84
269.75416666666675.5556727083607315.79
395.24333333333338.7416103502244728.6
486.176666666666713.418557254335535.89
584.70833333333335.1005076990314214.38
6101.0141666666675.6123248437269915.62
7109.2333333333331.027170281831983.08
899.99916666666672.221017204850618.13
994.30166666666674.0813496727816811.75






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha10.9605744028503
beta-0.0624139603177105
S.D.0.110783947235146
T-STAT-0.563384514411937
p-value0.590754866713971

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 10.9605744028503 \tabularnewline
beta & -0.0624139603177105 \tabularnewline
S.D. & 0.110783947235146 \tabularnewline
T-STAT & -0.563384514411937 \tabularnewline
p-value & 0.590754866713971 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283687&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]10.9605744028503[/C][/ROW]
[ROW][C]beta[/C][C]-0.0624139603177105[/C][/ROW]
[ROW][C]S.D.[/C][C]0.110783947235146[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.563384514411937[/C][/ROW]
[ROW][C]p-value[/C][C]0.590754866713971[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283687&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283687&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)
alpha10.9605744028503
beta-0.0624139603177105
S.D.0.110783947235146
T-STAT-0.563384514411937
p-value0.590754866713971






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha8.33359076905023
beta-1.53790624103719
S.D.1.96147796546818
T-STAT-0.784054813825097
p-value0.458712675828402
Lambda2.53790624103719

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 8.33359076905023 \tabularnewline
beta & -1.53790624103719 \tabularnewline
S.D. & 1.96147796546818 \tabularnewline
T-STAT & -0.784054813825097 \tabularnewline
p-value & 0.458712675828402 \tabularnewline
Lambda & 2.53790624103719 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283687&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]8.33359076905023[/C][/ROW]
[ROW][C]beta[/C][C]-1.53790624103719[/C][/ROW]
[ROW][C]S.D.[/C][C]1.96147796546818[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.784054813825097[/C][/ROW]
[ROW][C]p-value[/C][C]0.458712675828402[/C][/ROW]
[ROW][C]Lambda[/C][C]2.53790624103719[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283687&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283687&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)
alpha8.33359076905023
beta-1.53790624103719
S.D.1.96147796546818
T-STAT-0.784054813825097
p-value0.458712675828402
Lambda2.53790624103719


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')