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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 14:52:26 -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/t138610035730e57f98pciabkg.htm/, Retrieved Fri, 19 Apr 2024 07:47:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230400, Retrieved Fri, 19 Apr 2024 07:47:38 +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] [] [2013-12-03 19:52:26] [da6056b86d6cc6ac74ca244744435ec9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
86.86
86.79
82.52
86.87
81.62
82.66
89.87
92.04
79.74
77.75
79.12
76.37
75.01
77.6
77.81
81.7
76.47
74.72
84.43
86.72
70.99
75.43
74.14
73.3
71.97
69.27
74.13
76.4
72.26
72.1
87.82
91.62
82.69
85.76
86.87
93.09
83.73
84.49
87.37
89.13
83.2
83.77
93.68
93.09
88.59
87.88
87.89
89.38
89.13
89.58
90.22
91.44
91.04
92.1
97.54
99.12
100
99.68
100.08
99.9
99.63
99.45
99.63
99.46
96.91
97.65
102.1
103.57
104.59
104.79
101.31
104.8
104.56
104.15
102.73
101.86
101.9
102.33
105.71
106.1
102.81
103.23
102.35
104.11

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230400&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230400&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230400&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
183.51754.9488035744189615.67
277.364.6819595742109415.73
380.33166666666678.5448749481070823.82
487.68333333333333.4694231465327210.48
594.98583333333334.7057922882981210.95
6101.15752.792587998125177.89
7103.4866666666671.43473363592714.23999999999999

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 83.5175 & 4.94880357441896 & 15.67 \tabularnewline
2 & 77.36 & 4.68195957421094 & 15.73 \tabularnewline
3 & 80.3316666666667 & 8.54487494810708 & 23.82 \tabularnewline
4 & 87.6833333333333 & 3.46942314653272 & 10.48 \tabularnewline
5 & 94.9858333333333 & 4.70579228829812 & 10.95 \tabularnewline
6 & 101.1575 & 2.79258799812517 & 7.89 \tabularnewline
7 & 103.486666666667 & 1.4347336359271 & 4.23999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230400&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]83.5175[/C][C]4.94880357441896[/C][C]15.67[/C][/ROW]
[ROW][C]2[/C][C]77.36[/C][C]4.68195957421094[/C][C]15.73[/C][/ROW]
[ROW][C]3[/C][C]80.3316666666667[/C][C]8.54487494810708[/C][C]23.82[/C][/ROW]
[ROW][C]4[/C][C]87.6833333333333[/C][C]3.46942314653272[/C][C]10.48[/C][/ROW]
[ROW][C]5[/C][C]94.9858333333333[/C][C]4.70579228829812[/C][C]10.95[/C][/ROW]
[ROW][C]6[/C][C]101.1575[/C][C]2.79258799812517[/C][C]7.89[/C][/ROW]
[ROW][C]7[/C][C]103.486666666667[/C][C]1.4347336359271[/C][C]4.23999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230400&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230400&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
183.51754.9488035744189615.67
277.364.6819595742109415.73
380.33166666666678.5448749481070823.82
487.68333333333333.4694231465327210.48
594.98583333333334.7057922882981210.95
6101.15752.792587998125177.89
7103.4866666666671.43473363592714.23999999999999






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha18.7968387583494
beta-0.160693843327527
S.D.0.0655805990637256
T-STAT-2.4503259442839
p-value0.0579131848215028

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 18.7968387583494 \tabularnewline
beta & -0.160693843327527 \tabularnewline
S.D. & 0.0655805990637256 \tabularnewline
T-STAT & -2.4503259442839 \tabularnewline
p-value & 0.0579131848215028 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230400&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]18.7968387583494[/C][/ROW]
[ROW][C]beta[/C][C]-0.160693843327527[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0655805990637256[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.4503259442839[/C][/ROW]
[ROW][C]p-value[/C][C]0.0579131848215028[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230400&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230400&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)
alpha18.7968387583494
beta-0.160693843327527
S.D.0.0655805990637256
T-STAT-2.4503259442839
p-value0.0579131848215028






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha18.7249278877597
beta-3.86745928527383
S.D.1.34509900477042
T-STAT-2.87522276914771
p-value0.0347816394159876
Lambda4.86745928527383

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 18.7249278877597 \tabularnewline
beta & -3.86745928527383 \tabularnewline
S.D. & 1.34509900477042 \tabularnewline
T-STAT & -2.87522276914771 \tabularnewline
p-value & 0.0347816394159876 \tabularnewline
Lambda & 4.86745928527383 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230400&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]18.7249278877597[/C][/ROW]
[ROW][C]beta[/C][C]-3.86745928527383[/C][/ROW]
[ROW][C]S.D.[/C][C]1.34509900477042[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.87522276914771[/C][/ROW]
[ROW][C]p-value[/C][C]0.0347816394159876[/C][/ROW]
[ROW][C]Lambda[/C][C]4.86745928527383[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230400&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230400&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)
alpha18.7249278877597
beta-3.86745928527383
S.D.1.34509900477042
T-STAT-2.87522276914771
p-value0.0347816394159876
Lambda4.86745928527383


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')