FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationTue, 22 Dec 2009 07:16:19 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/22/t1261493186oh4vt7m4x09e95i.htm/, Retrieved Sat, 04 May 2024 15:05:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70452, Retrieved Sat, 04 May 2024 15:05:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordspaper
Estimated Impact135

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] [SMP s=6] [2009-12-22 14:16:19] [b08f24ccf7d7e0757793cda532be96b3] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
83.87
84.23
84.61
84.82
85.04
85.06
84.93
84.98
85.23
85.30
85.33
85.55
85.70
85.88
86.04
86.07
86.31
86.38
86.35
86.55
86.70
86.74
86.85
86.95
86.80
87.01
87.17
87.43
87.66
87.68
87.59
87.65
87.72
87.70
87.71
87.80
87.62
87.84
88.17
88.47
88.58
88.57
88.55
88.68
88.79
88.85
88.95
89.27
89.09
89.42
89.72
89.85
89.96
90.25
90.20
90.27
90.78
90.79
90.98
91.25
90.75
91.01
91.50
92.09
92.56
92.66
92.38
92.38
92.66
92.69
92.59
92.98
92.98
93.15
93.65
94.06
94.24
94.24
94.11
94.16
94.43
94.67
94.60
95.00
94.84
95.26
95.81
95.92
95.85
95.90
95.80
96.00
96.34
96.43
96.48
96.75
96.51
96.69
97.28
97.69
98.08
98.09
97.92
98.06
98.23
98.57
98.53
98.92
98.42
98.73
99.32
99.73
100.00
100.08
100.02
100.26
100.71
100.95
100.75
101.03
100.64
100.93
101.41
102.07
102.42
102.53
102.43
102.60
102.65
102.74
102.82
103.21
102.75
103.09
103.71
104.30
104.58
104.71
104.44
104.57
104.95
105.49
106.03
106.48
106.25
106.70
107.60
108.05
108.72
109.17
109.08
109.04
109.34
109.37
108.96
108.77
108.11
108.67
109.05
109.43
109.62
109.85
109.34
109.65
109.69
109.91
110.09

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70452&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70452&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70452&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
184.6050.4739936708438191.19000000000000
285.220.2320344801963670.61999999999999
386.06333333333330.2558645474986060.679999999999993
486.690.2149418526020490.600000000000009
587.29166666666670.3581852407158450.88000000000001
687.6950.07063993204979460.209999999999994
788.20833333333330.4051378366268250.959999999999994
888.84833333333330.2485491232466250.719999999999999
989.7150.4104022417092751.16000000000000
1090.71166666666670.4073041451626381.05000000000000
1191.76166666666670.8011346120763131.91000000000000
1292.61333333333330.2244697455486330.600000000000009
1393.720.5538591878808151.25999999999999
1494.4950.3350671574475780.89
1595.59666666666670.4454510822376181.08000000000000
1696.30.3444996371551080.950000000000003
1797.390.6830226936200581.58000000000000
1898.37166666666670.3704816684623761
1999.380.6847773360735581.66000000000000
20100.620.3978944583680461.01000000000001
21101.6666666666670.7922289231444811.89
22102.7416666666670.2649842762630730.779999999999987
23103.8566666666670.8101769354077311.95999999999999
24105.3266666666670.8187958638553762.04000000000001
25107.7483333333331.133338725477372.92
26109.0933333333330.2292305971432880.600000000000009
27109.1216666666670.6490736989484841.73999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 84.605 & 0.473993670843819 & 1.19000000000000 \tabularnewline
2 & 85.22 & 0.232034480196367 & 0.61999999999999 \tabularnewline
3 & 86.0633333333333 & 0.255864547498606 & 0.679999999999993 \tabularnewline
4 & 86.69 & 0.214941852602049 & 0.600000000000009 \tabularnewline
5 & 87.2916666666667 & 0.358185240715845 & 0.88000000000001 \tabularnewline
6 & 87.695 & 0.0706399320497946 & 0.209999999999994 \tabularnewline
7 & 88.2083333333333 & 0.405137836626825 & 0.959999999999994 \tabularnewline
8 & 88.8483333333333 & 0.248549123246625 & 0.719999999999999 \tabularnewline
9 & 89.715 & 0.410402241709275 & 1.16000000000000 \tabularnewline
10 & 90.7116666666667 & 0.407304145162638 & 1.05000000000000 \tabularnewline
11 & 91.7616666666667 & 0.801134612076313 & 1.91000000000000 \tabularnewline
12 & 92.6133333333333 & 0.224469745548633 & 0.600000000000009 \tabularnewline
13 & 93.72 & 0.553859187880815 & 1.25999999999999 \tabularnewline
14 & 94.495 & 0.335067157447578 & 0.89 \tabularnewline
15 & 95.5966666666667 & 0.445451082237618 & 1.08000000000000 \tabularnewline
16 & 96.3 & 0.344499637155108 & 0.950000000000003 \tabularnewline
17 & 97.39 & 0.683022693620058 & 1.58000000000000 \tabularnewline
18 & 98.3716666666667 & 0.370481668462376 & 1 \tabularnewline
19 & 99.38 & 0.684777336073558 & 1.66000000000000 \tabularnewline
20 & 100.62 & 0.397894458368046 & 1.01000000000001 \tabularnewline
21 & 101.666666666667 & 0.792228923144481 & 1.89 \tabularnewline
22 & 102.741666666667 & 0.264984276263073 & 0.779999999999987 \tabularnewline
23 & 103.856666666667 & 0.810176935407731 & 1.95999999999999 \tabularnewline
24 & 105.326666666667 & 0.818795863855376 & 2.04000000000001 \tabularnewline
25 & 107.748333333333 & 1.13333872547737 & 2.92 \tabularnewline
26 & 109.093333333333 & 0.229230597143288 & 0.600000000000009 \tabularnewline
27 & 109.121666666667 & 0.649073698948484 & 1.73999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70452&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]84.605[/C][C]0.473993670843819[/C][C]1.19000000000000[/C][/ROW]
[ROW][C]2[/C][C]85.22[/C][C]0.232034480196367[/C][C]0.61999999999999[/C][/ROW]
[ROW][C]3[/C][C]86.0633333333333[/C][C]0.255864547498606[/C][C]0.679999999999993[/C][/ROW]
[ROW][C]4[/C][C]86.69[/C][C]0.214941852602049[/C][C]0.600000000000009[/C][/ROW]
[ROW][C]5[/C][C]87.2916666666667[/C][C]0.358185240715845[/C][C]0.88000000000001[/C][/ROW]
[ROW][C]6[/C][C]87.695[/C][C]0.0706399320497946[/C][C]0.209999999999994[/C][/ROW]
[ROW][C]7[/C][C]88.2083333333333[/C][C]0.405137836626825[/C][C]0.959999999999994[/C][/ROW]
[ROW][C]8[/C][C]88.8483333333333[/C][C]0.248549123246625[/C][C]0.719999999999999[/C][/ROW]
[ROW][C]9[/C][C]89.715[/C][C]0.410402241709275[/C][C]1.16000000000000[/C][/ROW]
[ROW][C]10[/C][C]90.7116666666667[/C][C]0.407304145162638[/C][C]1.05000000000000[/C][/ROW]
[ROW][C]11[/C][C]91.7616666666667[/C][C]0.801134612076313[/C][C]1.91000000000000[/C][/ROW]
[ROW][C]12[/C][C]92.6133333333333[/C][C]0.224469745548633[/C][C]0.600000000000009[/C][/ROW]
[ROW][C]13[/C][C]93.72[/C][C]0.553859187880815[/C][C]1.25999999999999[/C][/ROW]
[ROW][C]14[/C][C]94.495[/C][C]0.335067157447578[/C][C]0.89[/C][/ROW]
[ROW][C]15[/C][C]95.5966666666667[/C][C]0.445451082237618[/C][C]1.08000000000000[/C][/ROW]
[ROW][C]16[/C][C]96.3[/C][C]0.344499637155108[/C][C]0.950000000000003[/C][/ROW]
[ROW][C]17[/C][C]97.39[/C][C]0.683022693620058[/C][C]1.58000000000000[/C][/ROW]
[ROW][C]18[/C][C]98.3716666666667[/C][C]0.370481668462376[/C][C]1[/C][/ROW]
[ROW][C]19[/C][C]99.38[/C][C]0.684777336073558[/C][C]1.66000000000000[/C][/ROW]
[ROW][C]20[/C][C]100.62[/C][C]0.397894458368046[/C][C]1.01000000000001[/C][/ROW]
[ROW][C]21[/C][C]101.666666666667[/C][C]0.792228923144481[/C][C]1.89[/C][/ROW]
[ROW][C]22[/C][C]102.741666666667[/C][C]0.264984276263073[/C][C]0.779999999999987[/C][/ROW]
[ROW][C]23[/C][C]103.856666666667[/C][C]0.810176935407731[/C][C]1.95999999999999[/C][/ROW]
[ROW][C]24[/C][C]105.326666666667[/C][C]0.818795863855376[/C][C]2.04000000000001[/C][/ROW]
[ROW][C]25[/C][C]107.748333333333[/C][C]1.13333872547737[/C][C]2.92[/C][/ROW]
[ROW][C]26[/C][C]109.093333333333[/C][C]0.229230597143288[/C][C]0.600000000000009[/C][/ROW]
[ROW][C]27[/C][C]109.121666666667[/C][C]0.649073698948484[/C][C]1.73999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70452&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70452&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
184.6050.4739936708438191.19000000000000
285.220.2320344801963670.61999999999999
386.06333333333330.2558645474986060.679999999999993
486.690.2149418526020490.600000000000009
587.29166666666670.3581852407158450.88000000000001
687.6950.07063993204979460.209999999999994
788.20833333333330.4051378366268250.959999999999994
888.84833333333330.2485491232466250.719999999999999
989.7150.4104022417092751.16000000000000
1090.71166666666670.4073041451626381.05000000000000
1191.76166666666670.8011346120763131.91000000000000
1292.61333333333330.2244697455486330.600000000000009
1393.720.5538591878808151.25999999999999
1494.4950.3350671574475780.89
1595.59666666666670.4454510822376181.08000000000000
1696.30.3444996371551080.950000000000003
1797.390.6830226936200581.58000000000000
1898.37166666666670.3704816684623761
1999.380.6847773360735581.66000000000000
20100.620.3978944583680461.01000000000001
21101.6666666666670.7922289231444811.89
22102.7416666666670.2649842762630730.779999999999987
23103.8566666666670.8101769354077311.95999999999999
24105.3266666666670.8187958638553762.04000000000001
25107.7483333333331.133338725477372.92
26109.0933333333330.2292305971432880.600000000000009
27109.1216666666670.6490736989484841.73999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-1.23336138591695
beta0.017832598935286
S.D.0.00547092083016779
T-STAT3.25952421701177
p-value0.00321036434607795

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -1.23336138591695 \tabularnewline
beta & 0.017832598935286 \tabularnewline
S.D. & 0.00547092083016779 \tabularnewline
T-STAT & 3.25952421701177 \tabularnewline
p-value & 0.00321036434607795 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70452&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.23336138591695[/C][/ROW]
[ROW][C]beta[/C][C]0.017832598935286[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00547092083016779[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.25952421701177[/C][/ROW]
[ROW][C]p-value[/C][C]0.00321036434607795[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70452&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70452&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-1.23336138591695
beta0.017832598935286
S.D.0.00547092083016779
T-STAT3.25952421701177
p-value0.00321036434607795






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-17.7048508289648
beta3.6874265359002
S.D.1.2784120927241
T-STAT2.88438020641909
p-value0.00795735650360938
Lambda-2.6874265359002

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -17.7048508289648 \tabularnewline
beta & 3.6874265359002 \tabularnewline
S.D. & 1.2784120927241 \tabularnewline
T-STAT & 2.88438020641909 \tabularnewline
p-value & 0.00795735650360938 \tabularnewline
Lambda & -2.6874265359002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70452&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-17.7048508289648[/C][/ROW]
[ROW][C]beta[/C][C]3.6874265359002[/C][/ROW]
[ROW][C]S.D.[/C][C]1.2784120927241[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.88438020641909[/C][/ROW]
[ROW][C]p-value[/C][C]0.00795735650360938[/C][/ROW]
[ROW][C]Lambda[/C][C]-2.6874265359002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70452&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70452&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-17.7048508289648
beta3.6874265359002
S.D.1.2784120927241
T-STAT2.88438020641909
p-value0.00795735650360938
Lambda-2.6874265359002


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 6 ;
Parameters (R input):
par1 = 6 ;
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')