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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 computationSun, 22 Nov 2015 17:32:07 +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/22/t1448213587pvebf4zrke7k3jw.htm/, Retrieved Wed, 15 May 2024 23:03:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283853, Retrieved Wed, 15 May 2024 23:03:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72

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] [s] [2015-11-22 17:32:07] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
88.83
89.01
88.21
87.78
87.93
88.11
88.2
88.12
88.38
87.65
88.24
87.83
87.75
87.88
87.61
88.05
87.77
87.79
88.34
88.48
88.75
87.95
89.09
88.73
89.24
89.77
89.84
90.97
91.53
92.2
92.27
92.42
92.07
91.73
92.1
91.68
92.63
93.02
92.66
93.23
93.79
93.92
94.04
94.23
94.37
94.29
94.38
94
94.11
93.98
93.42
93.3
93.32
93.75
93.82
94.06
94.09
93.64
93.9
93.18
93.54
93.55
93.8
93.39
93.27
93.58
93.47
93.75
93.3
92.65
92.96
92.84
93.29
93.57
93.54
94.38
93.98
94.48
94.63
95.45
95.59
94.76
95.66
95.03
96.45
97.15
97.5
98.54
99.54
100.33
100.28
101.81
101.91
101.92
102.68
101.9
102.14
102.3
102.06
102.4
102.99
102.99
102.83
103.01
102.6
102.18
102.6
101.44

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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283853&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283853&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283853&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'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
188.19083333333330.4033148630882311.36
288.18250.4824958784562561.48
391.31833333333331.10541504614443.18000000000001
493.71333333333330.6543606641508051.75
593.71416666666670.3356799973279030.929999999999993
693.34166666666670.3590095803566781.14999999999999
794.530.8161216486863612.36999999999999
8100.0008333333332.151289077964586.23
9102.4616666666670.4720137388858171.57000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 88.1908333333333 & 0.403314863088231 & 1.36 \tabularnewline
2 & 88.1825 & 0.482495878456256 & 1.48 \tabularnewline
3 & 91.3183333333333 & 1.1054150461444 & 3.18000000000001 \tabularnewline
4 & 93.7133333333333 & 0.654360664150805 & 1.75 \tabularnewline
5 & 93.7141666666667 & 0.335679997327903 & 0.929999999999993 \tabularnewline
6 & 93.3416666666667 & 0.359009580356678 & 1.14999999999999 \tabularnewline
7 & 94.53 & 0.816121648686361 & 2.36999999999999 \tabularnewline
8 & 100.000833333333 & 2.15128907796458 & 6.23 \tabularnewline
9 & 102.461666666667 & 0.472013738885817 & 1.57000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283853&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]88.1908333333333[/C][C]0.403314863088231[/C][C]1.36[/C][/ROW]
[ROW][C]2[/C][C]88.1825[/C][C]0.482495878456256[/C][C]1.48[/C][/ROW]
[ROW][C]3[/C][C]91.3183333333333[/C][C]1.1054150461444[/C][C]3.18000000000001[/C][/ROW]
[ROW][C]4[/C][C]93.7133333333333[/C][C]0.654360664150805[/C][C]1.75[/C][/ROW]
[ROW][C]5[/C][C]93.7141666666667[/C][C]0.335679997327903[/C][C]0.929999999999993[/C][/ROW]
[ROW][C]6[/C][C]93.3416666666667[/C][C]0.359009580356678[/C][C]1.14999999999999[/C][/ROW]
[ROW][C]7[/C][C]94.53[/C][C]0.816121648686361[/C][C]2.36999999999999[/C][/ROW]
[ROW][C]8[/C][C]100.000833333333[/C][C]2.15128907796458[/C][C]6.23[/C][/ROW]
[ROW][C]9[/C][C]102.461666666667[/C][C]0.472013738885817[/C][C]1.57000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283853&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283853&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
188.19083333333330.4033148630882311.36
288.18250.4824958784562561.48
391.31833333333331.10541504614443.18000000000001
493.71333333333330.6543606641508051.75
593.71416666666670.3356799973279030.929999999999993
693.34166666666670.3590095803566781.14999999999999
794.530.8161216486863612.36999999999999
8100.0008333333332.151289077964586.23
9102.4616666666670.4720137388858171.57000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-3.91906970731922
beta0.0497382010372353
S.D.0.0418233813136862
T-STAT1.18924389838751
p-value0.273114806960974

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -3.91906970731922 \tabularnewline
beta & 0.0497382010372353 \tabularnewline
S.D. & 0.0418233813136862 \tabularnewline
T-STAT & 1.18924389838751 \tabularnewline
p-value & 0.273114806960974 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283853&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.91906970731922[/C][/ROW]
[ROW][C]beta[/C][C]0.0497382010372353[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0418233813136862[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.18924389838751[/C][/ROW]
[ROW][C]p-value[/C][C]0.273114806960974[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283853&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283853&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-3.91906970731922
beta0.0497382010372353
S.D.0.0418233813136862
T-STAT1.18924389838751
p-value0.273114806960974






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-19.9986817088559
beta4.29919426001576
S.D.4.26075137983171
T-STAT1.00902255887683
p-value0.346562689684856
Lambda-3.29919426001576

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -19.9986817088559 \tabularnewline
beta & 4.29919426001576 \tabularnewline
S.D. & 4.26075137983171 \tabularnewline
T-STAT & 1.00902255887683 \tabularnewline
p-value & 0.346562689684856 \tabularnewline
Lambda & -3.29919426001576 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283853&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-19.9986817088559[/C][/ROW]
[ROW][C]beta[/C][C]4.29919426001576[/C][/ROW]
[ROW][C]S.D.[/C][C]4.26075137983171[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.00902255887683[/C][/ROW]
[ROW][C]p-value[/C][C]0.346562689684856[/C][/ROW]
[ROW][C]Lambda[/C][C]-3.29919426001576[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283853&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283853&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-19.9986817088559
beta4.29919426001576
S.D.4.26075137983171
T-STAT1.00902255887683
p-value0.346562689684856
Lambda-3.29919426001576


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')