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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 computationMon, 18 Dec 2017 11:12:46 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/18/t1513591972dgg9ls78h6y0cqy.htm/, Retrieved Tue, 14 May 2024 18:22:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310110, Retrieved Tue, 14 May 2024 18:22:20 +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] [] [2017-12-18 10:12:46] [29a87998297b2697efa2253fad859704] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
52
54.9
60.5
54.8
60.1
60.3
49.8
53.8
64.8
62
65.2
60.1
61.2
63.6
68.6
63.1
66.5
71.9
58.1
61.5
66.2
72.3
67
62.9
66.4
65.6
70.9
68.4
66.4
67.6
64.1
62.1
70
74.4
67
64.8
70.7
64
72.5
70.4
63.6
69.8
67.7
66.4
78.9
79.9
69.1
81.2
66
71.8
86.1
76.1
70.5
83.3
74.8
73.4
86.5
82
80.8
91.5
77
72.3
83.5
79
76.7
83.1
71.1
75.5
90.9
85.4
84.8
83.8
79.3
79.9
93
78.1
82.3
87.3
74.6
80
91.3
94.2
90.9
88
81.6
77.4
91
79.9
83.4
91.6
85.2
84.1
87
92.8
89.2
87.3
89.5
86.8
92
92.2
86.4
92.9
91.2
80.3
102
99
89.2
103
80.4
83.4
97.6
87
84.4
94.1
88.9
82.3
94.7
94.5
91.6
96.8
87.9
99.9
109.5
91.2
89.4
109.7
96.9
94.1
104.4
100.8
107.4
108.9
95.2
102.7
130.9
104
106.5
106.1
97.8
112.2
114.5
105.8
101
101.2
96.5
99.5
123.8
94.6
95.8
105.4
104.4
105.2
112.7
114.8
108.9
103.8
102.5
98.1
118.2
114.8
109.9
116.7
116.9
104.4
113.5
123.8
116.4
114.1
102.8
112.7
121.1
120.8
117.8
130.4
110.9
105.4
137.6
133.3
123.3
122.8
110.2
101.4
128.7
120.6
110.1
121.6
113
115.9
131.1
127.4
123.9
120.8
108.5
112.9
129.6
121.3
119.1
140.8
127.4
128.1
136.6
126.5
120.8
144.3
116
123.4
138.6
118.3
124.2
136
127.4
131.6

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310110&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=310110&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310110&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
158.19166666666674.997537272285115.4
265.24166666666674.318345291961514.2
367.30833333333333.3041181833731312.3
471.18333333333335.9453317566784917.6
578.56666666666677.6389353533940425.5
680.25833333333335.9249025052712719.8
784.90833333333336.6324900484225619.6
885.8754.8324894770143615.4
992.04166666666676.6116231445886722.7
1089.64166666666676.0358713061365417.2
11100.0083333333338.0844922630623621.8
12106.4916666666679.4142501592323435.7
13105.458.6279145273298329.2
14112.4416666666677.3912058720092725.7
15119.90833333333310.724776609950134.8
16118.7258.8355814749228629.7
17126.32510.699203453783635.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 58.1916666666667 & 4.9975372722851 & 15.4 \tabularnewline
2 & 65.2416666666667 & 4.3183452919615 & 14.2 \tabularnewline
3 & 67.3083333333333 & 3.30411818337313 & 12.3 \tabularnewline
4 & 71.1833333333333 & 5.94533175667849 & 17.6 \tabularnewline
5 & 78.5666666666667 & 7.63893535339404 & 25.5 \tabularnewline
6 & 80.2583333333333 & 5.92490250527127 & 19.8 \tabularnewline
7 & 84.9083333333333 & 6.63249004842256 & 19.6 \tabularnewline
8 & 85.875 & 4.83248947701436 & 15.4 \tabularnewline
9 & 92.0416666666667 & 6.61162314458867 & 22.7 \tabularnewline
10 & 89.6416666666667 & 6.03587130613654 & 17.2 \tabularnewline
11 & 100.008333333333 & 8.08449226306236 & 21.8 \tabularnewline
12 & 106.491666666667 & 9.41425015923234 & 35.7 \tabularnewline
13 & 105.45 & 8.62791452732983 & 29.2 \tabularnewline
14 & 112.441666666667 & 7.39120587200927 & 25.7 \tabularnewline
15 & 119.908333333333 & 10.7247766099501 & 34.8 \tabularnewline
16 & 118.725 & 8.83558147492286 & 29.7 \tabularnewline
17 & 126.325 & 10.6992034537836 & 35.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310110&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]58.1916666666667[/C][C]4.9975372722851[/C][C]15.4[/C][/ROW]
[ROW][C]2[/C][C]65.2416666666667[/C][C]4.3183452919615[/C][C]14.2[/C][/ROW]
[ROW][C]3[/C][C]67.3083333333333[/C][C]3.30411818337313[/C][C]12.3[/C][/ROW]
[ROW][C]4[/C][C]71.1833333333333[/C][C]5.94533175667849[/C][C]17.6[/C][/ROW]
[ROW][C]5[/C][C]78.5666666666667[/C][C]7.63893535339404[/C][C]25.5[/C][/ROW]
[ROW][C]6[/C][C]80.2583333333333[/C][C]5.92490250527127[/C][C]19.8[/C][/ROW]
[ROW][C]7[/C][C]84.9083333333333[/C][C]6.63249004842256[/C][C]19.6[/C][/ROW]
[ROW][C]8[/C][C]85.875[/C][C]4.83248947701436[/C][C]15.4[/C][/ROW]
[ROW][C]9[/C][C]92.0416666666667[/C][C]6.61162314458867[/C][C]22.7[/C][/ROW]
[ROW][C]10[/C][C]89.6416666666667[/C][C]6.03587130613654[/C][C]17.2[/C][/ROW]
[ROW][C]11[/C][C]100.008333333333[/C][C]8.08449226306236[/C][C]21.8[/C][/ROW]
[ROW][C]12[/C][C]106.491666666667[/C][C]9.41425015923234[/C][C]35.7[/C][/ROW]
[ROW][C]13[/C][C]105.45[/C][C]8.62791452732983[/C][C]29.2[/C][/ROW]
[ROW][C]14[/C][C]112.441666666667[/C][C]7.39120587200927[/C][C]25.7[/C][/ROW]
[ROW][C]15[/C][C]119.908333333333[/C][C]10.7247766099501[/C][C]34.8[/C][/ROW]
[ROW][C]16[/C][C]118.725[/C][C]8.83558147492286[/C][C]29.7[/C][/ROW]
[ROW][C]17[/C][C]126.325[/C][C]10.6992034537836[/C][C]35.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310110&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310110&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
158.19166666666674.997537272285115.4
265.24166666666674.318345291961514.2
367.30833333333333.3041181833731312.3
471.18333333333335.9453317566784917.6
578.56666666666677.6389353533940425.5
680.25833333333335.9249025052712719.8
784.90833333333336.6324900484225619.6
885.8754.8324894770143615.4
992.04166666666676.6116231445886722.7
1089.64166666666676.0358713061365417.2
11100.0083333333338.0844922630623621.8
12106.4916666666679.4142501592323435.7
13105.458.6279145273298329.2
14112.4416666666677.3912058720092725.7
15119.90833333333310.724776609950134.8
16118.7258.8355814749228629.7
17126.32510.699203453783635.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.36364505214813
beta0.0916447519589143
S.D.0.0126756008867152
T-STAT7.23001242923036
p-value2.92577487293383e-06

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.36364505214813 \tabularnewline
beta & 0.0916447519589143 \tabularnewline
S.D. & 0.0126756008867152 \tabularnewline
T-STAT & 7.23001242923036 \tabularnewline
p-value & 2.92577487293383e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310110&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.36364505214813[/C][/ROW]
[ROW][C]beta[/C][C]0.0916447519589143[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0126756008867152[/C][/ROW]
[ROW][C]T-STAT[/C][C]7.23001242923036[/C][/ROW]
[ROW][C]p-value[/C][C]2.92577487293383e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310110&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310110&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-1.36364505214813
beta0.0916447519589143
S.D.0.0126756008867152
T-STAT7.23001242923036
p-value2.92577487293383e-06






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.4571463222645
beta1.19313110606952
S.D.0.18937556659061
T-STAT6.30034342629226
p-value1.42286657005399e-05
Lambda-0.193131106069518

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.4571463222645 \tabularnewline
beta & 1.19313110606952 \tabularnewline
S.D. & 0.18937556659061 \tabularnewline
T-STAT & 6.30034342629226 \tabularnewline
p-value & 1.42286657005399e-05 \tabularnewline
Lambda & -0.193131106069518 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310110&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.4571463222645[/C][/ROW]
[ROW][C]beta[/C][C]1.19313110606952[/C][/ROW]
[ROW][C]S.D.[/C][C]0.18937556659061[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.30034342629226[/C][/ROW]
[ROW][C]p-value[/C][C]1.42286657005399e-05[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.193131106069518[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310110&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310110&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-3.4571463222645
beta1.19313110606952
S.D.0.18937556659061
T-STAT6.30034342629226
p-value1.42286657005399e-05
Lambda-0.193131106069518


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 <- '12'
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')