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 computationThu, 19 Nov 2015 17:44:10 +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/t1447955107f3q25t12vnsj9gq.htm/, Retrieved Tue, 14 May 2024 07:56:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283666, Retrieved Tue, 14 May 2024 07:56:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66

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 17:44:10] [0bbe3141369311cb51cf1cd235842853] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
76.93
79.32
79.35
80.94
80.13
81.38
81.1
81.53
80.46
79.71
78.66
79.96
80.64
81.8
81.06
81.67
79.72
81.28
81.36
85.26
90
93
95.62
102.15
105.73
109.79
113.77
114.3
114.76
113.69
113.88
114.47
112.57
114.43
112.7
113.48
113.05
112.22
111.44
111.67
111.91
111.7
104.26
101.13
98.55
97.06
96.22
95.15
94.54
94.29
93.98
93.76
94.16
93.83
93.97
94.19
94.14
94.24
94.27
94.21
93.45
95.84
98.59
97
96.45
96.48
96.1
95.49
95.85
95.85
98.52
101.77
101.2
102.85
102.98
102.87
100.48
97.59
97.55
99.06
100.43
102.93
104.22
105.26
105.44
106.97
105.82
104.4
102.03
100.17
98.01
96.49
95.63
95.4
94.97
94.68
95.87
94.99
94.65
94.35
94.1
94.21
95.2
95.55
95.68
95.27
95.3
95.93

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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283666&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283666&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283666&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
179.95583333333331.30506327490864.59999999999999
286.137.3328662385677922.43
3112.79752.593821767900869.03
4105.3633333333337.3126842893120617.9
594.13166666666670.2156104793090510.780000000000001
696.78252.073201849577348.31999999999999
7101.4516666666672.496582512640887.71000000000001
8100.0008333333334.7261082554702712.29
995.09166666666670.6373215733668461.83000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 79.9558333333333 & 1.3050632749086 & 4.59999999999999 \tabularnewline
2 & 86.13 & 7.33286623856779 & 22.43 \tabularnewline
3 & 112.7975 & 2.59382176790086 & 9.03 \tabularnewline
4 & 105.363333333333 & 7.31268428931206 & 17.9 \tabularnewline
5 & 94.1316666666667 & 0.215610479309051 & 0.780000000000001 \tabularnewline
6 & 96.7825 & 2.07320184957734 & 8.31999999999999 \tabularnewline
7 & 101.451666666667 & 2.49658251264088 & 7.71000000000001 \tabularnewline
8 & 100.000833333333 & 4.72610825547027 & 12.29 \tabularnewline
9 & 95.0916666666667 & 0.637321573366846 & 1.83000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283666&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]79.9558333333333[/C][C]1.3050632749086[/C][C]4.59999999999999[/C][/ROW]
[ROW][C]2[/C][C]86.13[/C][C]7.33286623856779[/C][C]22.43[/C][/ROW]
[ROW][C]3[/C][C]112.7975[/C][C]2.59382176790086[/C][C]9.03[/C][/ROW]
[ROW][C]4[/C][C]105.363333333333[/C][C]7.31268428931206[/C][C]17.9[/C][/ROW]
[ROW][C]5[/C][C]94.1316666666667[/C][C]0.215610479309051[/C][C]0.780000000000001[/C][/ROW]
[ROW][C]6[/C][C]96.7825[/C][C]2.07320184957734[/C][C]8.31999999999999[/C][/ROW]
[ROW][C]7[/C][C]101.451666666667[/C][C]2.49658251264088[/C][C]7.71000000000001[/C][/ROW]
[ROW][C]8[/C][C]100.000833333333[/C][C]4.72610825547027[/C][C]12.29[/C][/ROW]
[ROW][C]9[/C][C]95.0916666666667[/C][C]0.637321573366846[/C][C]1.83000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283666&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283666&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
179.95583333333331.30506327490864.59999999999999
286.137.3328662385677922.43
3112.79752.593821767900869.03
4105.3633333333337.3126842893120617.9
594.13166666666670.2156104793090510.780000000000001
696.78252.073201849577348.31999999999999
7101.4516666666672.496582512640887.71000000000001
8100.0008333333334.7261082554702712.29
995.09166666666670.6373215733668461.83000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.254294137278719
beta0.0355417342754282
S.D.0.102512283748947
T-STAT0.346707077197403
p-value0.739000181609893

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.254294137278719 \tabularnewline
beta & 0.0355417342754282 \tabularnewline
S.D. & 0.102512283748947 \tabularnewline
T-STAT & 0.346707077197403 \tabularnewline
p-value & 0.739000181609893 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283666&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.254294137278719[/C][/ROW]
[ROW][C]beta[/C][C]0.0355417342754282[/C][/ROW]
[ROW][C]S.D.[/C][C]0.102512283748947[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.346707077197403[/C][/ROW]
[ROW][C]p-value[/C][C]0.739000181609893[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283666&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283666&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-0.254294137278719
beta0.0355417342754282
S.D.0.102512283748947
T-STAT0.346707077197403
p-value0.739000181609893






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-10.1077002936005
beta2.36843089658615
S.D.4.14057003540459
T-STAT0.572005998288765
p-value0.585210274535254
Lambda-1.36843089658615

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -10.1077002936005 \tabularnewline
beta & 2.36843089658615 \tabularnewline
S.D. & 4.14057003540459 \tabularnewline
T-STAT & 0.572005998288765 \tabularnewline
p-value & 0.585210274535254 \tabularnewline
Lambda & -1.36843089658615 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283666&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-10.1077002936005[/C][/ROW]
[ROW][C]beta[/C][C]2.36843089658615[/C][/ROW]
[ROW][C]S.D.[/C][C]4.14057003540459[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.572005998288765[/C][/ROW]
[ROW][C]p-value[/C][C]0.585210274535254[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.36843089658615[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283666&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283666&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-10.1077002936005
beta2.36843089658615
S.D.4.14057003540459
T-STAT0.572005998288765
p-value0.585210274535254
Lambda-1.36843089658615


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')