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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 computationThu, 14 Dec 2017 13:57:20 +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/14/t1513256358rlttg3ptu6j9v2f.htm/, Retrieved Tue, 14 May 2024 10:12:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309492, Retrieved Tue, 14 May 2024 10:12:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70

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] [SD - Mean Plot] [2017-12-14 12:57:20] [76161aa76684ab75eda7753df0aa1ca0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
63.2
68.6
77.7
68.1
75.1
73.3
60.5
65.9
77.7
77.1
77.7
71.3
76
75.3
81.7
72.5
77.4
81.1
65.1
68.7
75.6
79.7
75.3
67.7
73.2
72.2
79.3
77.5
75.6
77.4
69.2
67.1
77.9
82.7
75.7
70.1
76.4
74.3
80.5
78
73.5
78.8
71.2
66.2
82.7
83.8
75
80.4
74.6
77.7
89.8
82.4
77
89.6
75.7
75.1
89.9
88.8
86.5
90
84
82.7
91.7
87.5
82
92.2
73.1
75.6
91.6
87.5
90.1
91.3
87.6
88.4
100.7
85.3
92
96.8
77.9
80.9
95.3
99.3
96.1
92.5
93.7
92.1
103.6
92.5
95.7
103.4
89
89.1
98.7
109.4
101.1
95.4
101.4
102.1
103.6
106
98.4
106.6
95.8
87.2
108.5
107
92
94.9
84.4
85
94
84.5
88.2
92.1
81.1
81.2
96.1
95.3
92.1
91.7
90.3
96.1
108.7
95.9
95.1
109.4
91.2
91.4
107.4
105.6
105.3
103.7
99.5
103.2
123.1
102.2
110
106.2
91.3
99.3
111.8
104.4
102.4
101
100.6
104.5
117.4
97.4
99.5
106.4
95.2
94
104.1
105.8
101.1
93.5
97.9
96.8
108.4
103.5
101.3
107.4
100.7
91.1
105
112.8
105.6
101
101.9
103.5
109.5
105
102.9
108.5
96.9
88.4
112.4
111.3
101.6
101.2
101.8
98.8
114.4
104.5
97.6
109.1
94.5
90.4
111.8
110.5
106.8
101.8
103.7
107.4
117.5
109.6
102.8
115.5
97.8
100.2
112.9
108.7
109
113.9
106.9
109.6
124.5
104.2
110.8
118.7
102.1
105.1

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=309492&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=309492&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309492&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
171.356.0593278955222917.2
274.6755.2868834263331716.6
374.8254.5708811563477115.6
476.73333333333335.0462106995489617.6
583.09166666666676.6257703954584315.4
685.7756.4423492327227719.1
791.06666666666677.1905662102676222.8
896.9756.3516819533383220.4
9100.2916666666676.6957867802119121.3
1088.80833333333335.4143678105461915
11100.0083333333337.3451849823025219.1
12104.5333333333337.8757779798492831.8
13101.6256.6919388412137723.9
14102.6255.816297635250321.7
15103.5916666666676.65096825942524
16103.57.3561353489945624
17108.256.1746549406718819.7

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 71.35 & 6.05932789552229 & 17.2 \tabularnewline
2 & 74.675 & 5.28688342633317 & 16.6 \tabularnewline
3 & 74.825 & 4.57088115634771 & 15.6 \tabularnewline
4 & 76.7333333333333 & 5.04621069954896 & 17.6 \tabularnewline
5 & 83.0916666666667 & 6.62577039545843 & 15.4 \tabularnewline
6 & 85.775 & 6.44234923272277 & 19.1 \tabularnewline
7 & 91.0666666666667 & 7.19056621026762 & 22.8 \tabularnewline
8 & 96.975 & 6.35168195333832 & 20.4 \tabularnewline
9 & 100.291666666667 & 6.69578678021191 & 21.3 \tabularnewline
10 & 88.8083333333333 & 5.41436781054619 & 15 \tabularnewline
11 & 100.008333333333 & 7.34518498230252 & 19.1 \tabularnewline
12 & 104.533333333333 & 7.87577797984928 & 31.8 \tabularnewline
13 & 101.625 & 6.69193884121377 & 23.9 \tabularnewline
14 & 102.625 & 5.8162976352503 & 21.7 \tabularnewline
15 & 103.591666666667 & 6.650968259425 & 24 \tabularnewline
16 & 103.5 & 7.35613534899456 & 24 \tabularnewline
17 & 108.25 & 6.17465494067188 & 19.7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309492&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]71.35[/C][C]6.05932789552229[/C][C]17.2[/C][/ROW]
[ROW][C]2[/C][C]74.675[/C][C]5.28688342633317[/C][C]16.6[/C][/ROW]
[ROW][C]3[/C][C]74.825[/C][C]4.57088115634771[/C][C]15.6[/C][/ROW]
[ROW][C]4[/C][C]76.7333333333333[/C][C]5.04621069954896[/C][C]17.6[/C][/ROW]
[ROW][C]5[/C][C]83.0916666666667[/C][C]6.62577039545843[/C][C]15.4[/C][/ROW]
[ROW][C]6[/C][C]85.775[/C][C]6.44234923272277[/C][C]19.1[/C][/ROW]
[ROW][C]7[/C][C]91.0666666666667[/C][C]7.19056621026762[/C][C]22.8[/C][/ROW]
[ROW][C]8[/C][C]96.975[/C][C]6.35168195333832[/C][C]20.4[/C][/ROW]
[ROW][C]9[/C][C]100.291666666667[/C][C]6.69578678021191[/C][C]21.3[/C][/ROW]
[ROW][C]10[/C][C]88.8083333333333[/C][C]5.41436781054619[/C][C]15[/C][/ROW]
[ROW][C]11[/C][C]100.008333333333[/C][C]7.34518498230252[/C][C]19.1[/C][/ROW]
[ROW][C]12[/C][C]104.533333333333[/C][C]7.87577797984928[/C][C]31.8[/C][/ROW]
[ROW][C]13[/C][C]101.625[/C][C]6.69193884121377[/C][C]23.9[/C][/ROW]
[ROW][C]14[/C][C]102.625[/C][C]5.8162976352503[/C][C]21.7[/C][/ROW]
[ROW][C]15[/C][C]103.591666666667[/C][C]6.650968259425[/C][C]24[/C][/ROW]
[ROW][C]16[/C][C]103.5[/C][C]7.35613534899456[/C][C]24[/C][/ROW]
[ROW][C]17[/C][C]108.25[/C][C]6.17465494067188[/C][C]19.7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309492&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309492&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
171.356.0593278955222917.2
274.6755.2868834263331716.6
374.8254.5708811563477115.6
476.73333333333335.0462106995489617.6
583.09166666666676.6257703954584315.4
685.7756.4423492327227719.1
791.06666666666677.1905662102676222.8
896.9756.3516819533383220.4
9100.2916666666676.6957867802119121.3
1088.80833333333335.4143678105461915
11100.0083333333337.3451849823025219.1
12104.5333333333337.8757779798492831.8
13101.6256.6919388412137723.9
14102.6255.816297635250321.7
15103.5916666666676.65096825942524
16103.57.3561353489945624
17108.256.1746549406718819.7






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha2.01243237187714
beta0.0468088684087409
S.D.0.0142171892527917
T-STAT3.29241368152636
p-value0.00493507507676751

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.01243237187714 \tabularnewline
beta & 0.0468088684087409 \tabularnewline
S.D. & 0.0142171892527917 \tabularnewline
T-STAT & 3.29241368152636 \tabularnewline
p-value & 0.00493507507676751 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309492&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.01243237187714[/C][/ROW]
[ROW][C]beta[/C][C]0.0468088684087409[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0142171892527917[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.29241368152636[/C][/ROW]
[ROW][C]p-value[/C][C]0.00493507507676751[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309492&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309492&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)
alpha2.01243237187714
beta0.0468088684087409
S.D.0.0142171892527917
T-STAT3.29241368152636
p-value0.00493507507676751






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.30886657385067
beta0.696350479602915
S.D.0.20336954934655
T-STAT3.42406462442569
p-value0.00376709238878874
Lambda0.303649520397085

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.30886657385067 \tabularnewline
beta & 0.696350479602915 \tabularnewline
S.D. & 0.20336954934655 \tabularnewline
T-STAT & 3.42406462442569 \tabularnewline
p-value & 0.00376709238878874 \tabularnewline
Lambda & 0.303649520397085 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309492&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.30886657385067[/C][/ROW]
[ROW][C]beta[/C][C]0.696350479602915[/C][/ROW]
[ROW][C]S.D.[/C][C]0.20336954934655[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.42406462442569[/C][/ROW]
[ROW][C]p-value[/C][C]0.00376709238878874[/C][/ROW]
[ROW][C]Lambda[/C][C]0.303649520397085[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309492&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309492&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-1.30886657385067
beta0.696350479602915
S.D.0.20336954934655
T-STAT3.42406462442569
p-value0.00376709238878874
Lambda0.303649520397085


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')