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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 computationTue, 03 Dec 2013 04:42:52 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/03/t1386063785ay4frkoawadpacl.htm/, Retrieved Thu, 25 Apr 2024 10:21:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230191, Retrieved Thu, 25 Apr 2024 10:21:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107

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] [] [2013-12-03 09:42:52] [1b8ce37c5679a09a5286ac5230bb7f24] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
96.86
96.77
96.5
96.01
96.07
95.93
95.93
95.83
96.24
96.25
96.59
96.62
96.62
96.81
96.71
96.45
96.63
96.56
96.56
96.65
97.04
97.14
97.2
97.26
97.26
97.24
97.35
97.36
97.28
97.31
97.31
97.31
97.23
97.78
97.64
97.68
97.68
97.81
97.75
97.63
97.6
97.65
97.65
97.65
97.86
98.41
98.79
98.75
98.74
98.55
98.65
98.86
98.94
99.05
99.05
99.05
99.17
98.99
98.91
98.89
98.89
98.72
98.89
98.97
99.16
99.54
99.54
99.55
100.01
99.52
99.44
99.39
99.39
99.4
100.43
100.62
101.05
100.95
100.95
100.91
101.13
100.81
100.47
100.56

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' @ 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230191&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230191&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230191&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' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
196.30.3566001070718231.03
296.80250.2819453525387190.810000000000002
397.39583333333330.1899980063691270.549999999999997
497.93583333333330.4462257547950641.19000000000001
598.90416666666670.1814816962137120.620000000000005
699.30166666666670.3764628035068581.29000000000001
7100.5558333333330.5875288516448791.73999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 96.3 & 0.356600107071823 & 1.03 \tabularnewline
2 & 96.8025 & 0.281945352538719 & 0.810000000000002 \tabularnewline
3 & 97.3958333333333 & 0.189998006369127 & 0.549999999999997 \tabularnewline
4 & 97.9358333333333 & 0.446225754795064 & 1.19000000000001 \tabularnewline
5 & 98.9041666666667 & 0.181481696213712 & 0.620000000000005 \tabularnewline
6 & 99.3016666666667 & 0.376462803506858 & 1.29000000000001 \tabularnewline
7 & 100.555833333333 & 0.587528851644879 & 1.73999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230191&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]96.3[/C][C]0.356600107071823[/C][C]1.03[/C][/ROW]
[ROW][C]2[/C][C]96.8025[/C][C]0.281945352538719[/C][C]0.810000000000002[/C][/ROW]
[ROW][C]3[/C][C]97.3958333333333[/C][C]0.189998006369127[/C][C]0.549999999999997[/C][/ROW]
[ROW][C]4[/C][C]97.9358333333333[/C][C]0.446225754795064[/C][C]1.19000000000001[/C][/ROW]
[ROW][C]5[/C][C]98.9041666666667[/C][C]0.181481696213712[/C][C]0.620000000000005[/C][/ROW]
[ROW][C]6[/C][C]99.3016666666667[/C][C]0.376462803506858[/C][C]1.29000000000001[/C][/ROW]
[ROW][C]7[/C][C]100.555833333333[/C][C]0.587528851644879[/C][C]1.73999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230191&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230191&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
196.30.3566001070718231.03
296.80250.2819453525387190.810000000000002
397.39583333333330.1899980063691270.549999999999997
497.93583333333330.4462257547950641.19000000000001
598.90416666666670.1814816962137120.620000000000005
699.30166666666670.3764628035068581.29000000000001
7100.5558333333330.5875288516448791.73999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-4.40584088443095
beta0.0484012375363503
S.D.0.0371177232500395
T-STAT1.30399262935123
p-value0.249038098809131

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -4.40584088443095 \tabularnewline
beta & 0.0484012375363503 \tabularnewline
S.D. & 0.0371177232500395 \tabularnewline
T-STAT & 1.30399262935123 \tabularnewline
p-value & 0.249038098809131 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230191&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.40584088443095[/C][/ROW]
[ROW][C]beta[/C][C]0.0484012375363503[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0371177232500395[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.30399262935123[/C][/ROW]
[ROW][C]p-value[/C][C]0.249038098809131[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230191&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230191&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-4.40584088443095
beta0.0484012375363503
S.D.0.0371177232500395
T-STAT1.30399262935123
p-value0.249038098809131






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-51.1655129844514
beta10.906855155168
S.D.11.7231711633739
T-STAT0.930367304475064
p-value0.394883871340126
Lambda-9.90685515516802

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -51.1655129844514 \tabularnewline
beta & 10.906855155168 \tabularnewline
S.D. & 11.7231711633739 \tabularnewline
T-STAT & 0.930367304475064 \tabularnewline
p-value & 0.394883871340126 \tabularnewline
Lambda & -9.90685515516802 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230191&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-51.1655129844514[/C][/ROW]
[ROW][C]beta[/C][C]10.906855155168[/C][/ROW]
[ROW][C]S.D.[/C][C]11.7231711633739[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.930367304475064[/C][/ROW]
[ROW][C]p-value[/C][C]0.394883871340126[/C][/ROW]
[ROW][C]Lambda[/C][C]-9.90685515516802[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230191&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230191&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-51.1655129844514
beta10.906855155168
S.D.11.7231711633739
T-STAT0.930367304475064
p-value0.394883871340126
Lambda-9.90685515516802


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')