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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 computationThu, 10 Dec 2009 07:55:39 -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/10/t12604570135b1p6dm6q1xewaa.htm/, Retrieved Thu, 25 Apr 2024 03:31:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=65444, Retrieved Thu, 25 Apr 2024 03:31:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125

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 Mannen] [2008-12-23 19:26:32] [ab2167f62c8fd37f7bb79fc194eace61]
-  M D    [Standard Deviation-Mean Plot] [Paper - 2] [2009-12-10 14:55:39] [64da8748fbb01eed936684060058da39] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
55
43
55
50
44
59
41
25
46
47
50
51
41
54
55
43
53
59
54
49
62
57
60
55
69
62
65
55
66
67
59
54
60
65
59
68
58
75
61
59
69
64
62
60
59
54
58
59
69
81
74
54
68
74
51
61
46
56
50
59
53

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=65444&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=65444&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65444&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
147.16666666666678.7991046376459534
253.56.3889108475687621
362.41666666666675.0173939873446715
461.55.6165340331430921
561.916666666666711.139269874338035

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 47.1666666666667 & 8.79910463764595 & 34 \tabularnewline
2 & 53.5 & 6.38891084756876 & 21 \tabularnewline
3 & 62.4166666666667 & 5.01739398734467 & 15 \tabularnewline
4 & 61.5 & 5.61653403314309 & 21 \tabularnewline
5 & 61.9166666666667 & 11.1392698743380 & 35 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65444&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]47.1666666666667[/C][C]8.79910463764595[/C][C]34[/C][/ROW]
[ROW][C]2[/C][C]53.5[/C][C]6.38891084756876[/C][C]21[/C][/ROW]
[ROW][C]3[/C][C]62.4166666666667[/C][C]5.01739398734467[/C][C]15[/C][/ROW]
[ROW][C]4[/C][C]61.5[/C][C]5.61653403314309[/C][C]21[/C][/ROW]
[ROW][C]5[/C][C]61.9166666666667[/C][C]11.1392698743380[/C][C]35[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65444&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65444&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
147.16666666666678.7991046376459534
253.56.3889108475687621
362.41666666666675.0173939873446715
461.55.6165340331430921
561.916666666666711.139269874338035






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha11.4019746788347
beta-0.0699778709044788
S.D.0.213514817580168
T-STAT-0.327742456929035
p-value0.764646495202212

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 11.4019746788347 \tabularnewline
beta & -0.0699778709044788 \tabularnewline
S.D. & 0.213514817580168 \tabularnewline
T-STAT & -0.327742456929035 \tabularnewline
p-value & 0.764646495202212 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65444&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]11.4019746788347[/C][/ROW]
[ROW][C]beta[/C][C]-0.0699778709044788[/C][/ROW]
[ROW][C]S.D.[/C][C]0.213514817580168[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.327742456929035[/C][/ROW]
[ROW][C]p-value[/C][C]0.764646495202212[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65444&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65444&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)
alpha11.4019746788347
beta-0.0699778709044788
S.D.0.213514817580168
T-STAT-0.327742456929035
p-value0.764646495202212






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha5.01873091369895
beta-0.757733894060469
S.D.1.48264619819342
T-STAT-0.511068584658805
p-value0.644538730387465
Lambda1.75773389406047

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 5.01873091369895 \tabularnewline
beta & -0.757733894060469 \tabularnewline
S.D. & 1.48264619819342 \tabularnewline
T-STAT & -0.511068584658805 \tabularnewline
p-value & 0.644538730387465 \tabularnewline
Lambda & 1.75773389406047 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65444&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.01873091369895[/C][/ROW]
[ROW][C]beta[/C][C]-0.757733894060469[/C][/ROW]
[ROW][C]S.D.[/C][C]1.48264619819342[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.511068584658805[/C][/ROW]
[ROW][C]p-value[/C][C]0.644538730387465[/C][/ROW]
[ROW][C]Lambda[/C][C]1.75773389406047[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65444&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65444&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)
alpha5.01873091369895
beta-0.757733894060469
S.D.1.48264619819342
T-STAT-0.511068584658805
p-value0.644538730387465
Lambda1.75773389406047


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')