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Description of Statistical Computation

Author's title

Spreidings- en gemiddeldegrafieken - Eigen reeks: Faxtoestellen - Kirsten W...

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationFri, 16 May 2008 03:18:27 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/16/t1210929562n4tpwxw2jrvbwq1.htm/, Retrieved Sun, 19 May 2024 20:28:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=12595, Retrieved Sun, 19 May 2024 20:28:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact226

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] [Spreidings- en ge...] [2008-05-16 09:18:27] [d9cff6fe3aecfbbd189e6e236f7b17ac] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
77.5
77.7
76.6
77
76.5
77.6
77.8
76.9
76.9
77
77
76.3
76.5
77.1
76.4
75.4
75.4
75.5
75.5
75.8
75.7
75.9
76.1
76
76
75.89
74.87
74.9
74.79
74.64
74.09
74.33
73.93
73.78
72.85
71.51
71.5
71.5
71.31
70.85
70.62
70.07
68.83
68.82
68.4
68.21
67.75
67.7
67.42
66.27
64.8
62.69
62.75
62.31
62.4
61.75
61.69
60.39
59.9
59.62
58.97
58.54
58.32
56.03
53.63
53.61
53.48
53.48
52.81
52.8
52.57
52.36

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12595&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12595&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12595&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
177.20.4966554808583811.10000000000001
277.20.6055300708194951.30000000000000
376.80.3366501646120710.700000000000003
476.350.7047458170621951.69999999999999
575.550.1732050807568850.399999999999991
675.9250.170782512765990.399999999999991
775.4150.6137589103222831.13000000000000
874.46250.313621321554090.700000000000003
973.01751.112755588617732.42
1071.290.3067028964106280.650000000000006
1169.5850.905851349100211.80000000000001
1268.0150.3443351080948130.700000000000003
1365.2952.041020986336664.73
1462.30250.4143569314813821
1560.40.9169878225291032.07
1657.9651.317940312254952.94
1753.550.08124038404636210.150000000000006
1852.6350.2142428528562860.450000000000003

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 77.2 & 0.496655480858381 & 1.10000000000001 \tabularnewline
2 & 77.2 & 0.605530070819495 & 1.30000000000000 \tabularnewline
3 & 76.8 & 0.336650164612071 & 0.700000000000003 \tabularnewline
4 & 76.35 & 0.704745817062195 & 1.69999999999999 \tabularnewline
5 & 75.55 & 0.173205080756885 & 0.399999999999991 \tabularnewline
6 & 75.925 & 0.17078251276599 & 0.399999999999991 \tabularnewline
7 & 75.415 & 0.613758910322283 & 1.13000000000000 \tabularnewline
8 & 74.4625 & 0.31362132155409 & 0.700000000000003 \tabularnewline
9 & 73.0175 & 1.11275558861773 & 2.42 \tabularnewline
10 & 71.29 & 0.306702896410628 & 0.650000000000006 \tabularnewline
11 & 69.585 & 0.90585134910021 & 1.80000000000001 \tabularnewline
12 & 68.015 & 0.344335108094813 & 0.700000000000003 \tabularnewline
13 & 65.295 & 2.04102098633666 & 4.73 \tabularnewline
14 & 62.3025 & 0.414356931481382 & 1 \tabularnewline
15 & 60.4 & 0.916987822529103 & 2.07 \tabularnewline
16 & 57.965 & 1.31794031225495 & 2.94 \tabularnewline
17 & 53.55 & 0.0812403840463621 & 0.150000000000006 \tabularnewline
18 & 52.635 & 0.214242852856286 & 0.450000000000003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12595&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]77.2[/C][C]0.496655480858381[/C][C]1.10000000000001[/C][/ROW]
[ROW][C]2[/C][C]77.2[/C][C]0.605530070819495[/C][C]1.30000000000000[/C][/ROW]
[ROW][C]3[/C][C]76.8[/C][C]0.336650164612071[/C][C]0.700000000000003[/C][/ROW]
[ROW][C]4[/C][C]76.35[/C][C]0.704745817062195[/C][C]1.69999999999999[/C][/ROW]
[ROW][C]5[/C][C]75.55[/C][C]0.173205080756885[/C][C]0.399999999999991[/C][/ROW]
[ROW][C]6[/C][C]75.925[/C][C]0.17078251276599[/C][C]0.399999999999991[/C][/ROW]
[ROW][C]7[/C][C]75.415[/C][C]0.613758910322283[/C][C]1.13000000000000[/C][/ROW]
[ROW][C]8[/C][C]74.4625[/C][C]0.31362132155409[/C][C]0.700000000000003[/C][/ROW]
[ROW][C]9[/C][C]73.0175[/C][C]1.11275558861773[/C][C]2.42[/C][/ROW]
[ROW][C]10[/C][C]71.29[/C][C]0.306702896410628[/C][C]0.650000000000006[/C][/ROW]
[ROW][C]11[/C][C]69.585[/C][C]0.90585134910021[/C][C]1.80000000000001[/C][/ROW]
[ROW][C]12[/C][C]68.015[/C][C]0.344335108094813[/C][C]0.700000000000003[/C][/ROW]
[ROW][C]13[/C][C]65.295[/C][C]2.04102098633666[/C][C]4.73[/C][/ROW]
[ROW][C]14[/C][C]62.3025[/C][C]0.414356931481382[/C][C]1[/C][/ROW]
[ROW][C]15[/C][C]60.4[/C][C]0.916987822529103[/C][C]2.07[/C][/ROW]
[ROW][C]16[/C][C]57.965[/C][C]1.31794031225495[/C][C]2.94[/C][/ROW]
[ROW][C]17[/C][C]53.55[/C][C]0.0812403840463621[/C][C]0.150000000000006[/C][/ROW]
[ROW][C]18[/C][C]52.635[/C][C]0.214242852856286[/C][C]0.450000000000003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12595&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12595&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
177.20.4966554808583811.10000000000001
277.20.6055300708194951.30000000000000
376.80.3366501646120710.700000000000003
476.350.7047458170621951.69999999999999
575.550.1732050807568850.399999999999991
675.9250.170782512765990.399999999999991
775.4150.6137589103222831.13000000000000
874.46250.313621321554090.700000000000003
973.01751.112755588617732.42
1071.290.3067028964106280.650000000000006
1169.5850.905851349100211.80000000000001
1268.0150.3443351080948130.700000000000003
1365.2952.041020986336664.73
1462.30250.4143569314813821
1560.40.9169878225291032.07
1657.9651.317940312254952.94
1753.550.08124038404636210.150000000000006
1852.6350.2142428528562860.450000000000003






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.07407696673553
beta-0.00664785546630519
S.D.0.0147088279484839
T-STAT-0.451963643166442
p-value0.65736204254348

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.07407696673553 \tabularnewline
beta & -0.00664785546630519 \tabularnewline
S.D. & 0.0147088279484839 \tabularnewline
T-STAT & -0.451963643166442 \tabularnewline
p-value & 0.65736204254348 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12595&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.07407696673553[/C][/ROW]
[ROW][C]beta[/C][C]-0.00664785546630519[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0147088279484839[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.451963643166442[/C][/ROW]
[ROW][C]p-value[/C][C]0.65736204254348[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12595&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12595&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)
alpha1.07407696673553
beta-0.00664785546630519
S.D.0.0147088279484839
T-STAT-0.451963643166442
p-value0.65736204254348






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.9105141588852
beta0.740039132606585
S.D.1.58328833278472
T-STAT0.467406420727542
p-value0.646511624868787
Lambda0.259960867393415

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.9105141588852 \tabularnewline
beta & 0.740039132606585 \tabularnewline
S.D. & 1.58328833278472 \tabularnewline
T-STAT & 0.467406420727542 \tabularnewline
p-value & 0.646511624868787 \tabularnewline
Lambda & 0.259960867393415 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=12595&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.9105141588852[/C][/ROW]
[ROW][C]beta[/C][C]0.740039132606585[/C][/ROW]
[ROW][C]S.D.[/C][C]1.58328833278472[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.467406420727542[/C][/ROW]
[ROW][C]p-value[/C][C]0.646511624868787[/C][/ROW]
[ROW][C]Lambda[/C][C]0.259960867393415[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=12595&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=12595&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-3.9105141588852
beta0.740039132606585
S.D.1.58328833278472
T-STAT0.467406420727542
p-value0.646511624868787
Lambda0.259960867393415


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ;
Parameters (R input):
par1 = 4 ;
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')