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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 computationFri, 10 Dec 2010 11:40:00 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/10/t129198108280uyabk5193zvs7.htm/, Retrieved Mon, 29 Apr 2024 09:53:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=107566, Retrieved Mon, 29 Apr 2024 09:53:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
-   PD    [Standard Deviation-Mean Plot] [WS9 - Standard De...] [2010-12-04 11:23:29] [8ef49741e164ec6343c90c7935194465]
-   P       [Standard Deviation-Mean Plot] [WS 9 ] [2010-12-07 17:30:24] [8214fe6d084e5ad7598b249a26cc9f06]
-    D          [Standard Deviation-Mean Plot] [paper standard de...] [2010-12-10 11:40:00] [b47314d83d48c7bf812ec2bcd743b159] [Current]
-    D            [Standard Deviation-Mean Plot] [standard deviatio...] [2010-12-20 20:53:15] [8214fe6d084e5ad7598b249a26cc9f06]
-    D              [Standard Deviation-Mean Plot] [standard deviatio...] [2010-12-22 13:50:12] [8214fe6d084e5ad7598b249a26cc9f06]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.579
2.146
2.462
3.695
4.831
5.134
6.250
5.760
6.249
2.917
1.741
2.359
1.511
2.059
2.635
2.867
4.403
5.720
4.502
5.749
5.627
2.846
1.762
2.429
1.169
2.154
2.249
2.687
4.359
5.382
4.459
6.398
4.596
3.024
1.887
2.070
1.351
2.218
2.461
3.028
4.784
4.975
4.607
6.249
4.809
3.157
1.910
2.228
1.594
2.467
2.222
3.607
4.685
4.962
5.770
5.480
5.000
3.228
1.993
2.288
1.580
2.111
2.192
3.601
4.665
4.876
5.813
5.589
5.331
3.075
2.002
2.306
1.507
1.992
2.487
3.490
4.647
5.594
5.611
5.788
6.204
3.013
1.931
2.549
1.504
2.090
2.702
2.939
4.500
6.208
6.415
5.657
5.964
3.163
1.997
2.422
1.376
2.202
2.683
3.303
5.202
5.231
4.880
7.998
4.977
3.531
2.025
2.205
1.442
2.238
2.179
3.218
5.139
4.990
4.914
6.084
5.672
3.548
1.793
2.086

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107566&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]5 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=107566&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107566&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 time5 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
13.760251.789635164699024.671
23.509166666666671.598460954869534.238
33.36951.621986296321445.229
43.481416666666671.541658814885824.898
53.6081.504044124110974.176
63.595083333333331.578135059223874.233
73.734416666666671.729940222736734.697
83.796751.832931339536364.911
93.801083333333331.904047672165486.622
103.608583333333331.671338465168424.642

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 3.76025 & 1.78963516469902 & 4.671 \tabularnewline
2 & 3.50916666666667 & 1.59846095486953 & 4.238 \tabularnewline
3 & 3.3695 & 1.62198629632144 & 5.229 \tabularnewline
4 & 3.48141666666667 & 1.54165881488582 & 4.898 \tabularnewline
5 & 3.608 & 1.50404412411097 & 4.176 \tabularnewline
6 & 3.59508333333333 & 1.57813505922387 & 4.233 \tabularnewline
7 & 3.73441666666667 & 1.72994022273673 & 4.697 \tabularnewline
8 & 3.79675 & 1.83293133953636 & 4.911 \tabularnewline
9 & 3.80108333333333 & 1.90404767216548 & 6.622 \tabularnewline
10 & 3.60858333333333 & 1.67133846516842 & 4.642 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107566&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]3.76025[/C][C]1.78963516469902[/C][C]4.671[/C][/ROW]
[ROW][C]2[/C][C]3.50916666666667[/C][C]1.59846095486953[/C][C]4.238[/C][/ROW]
[ROW][C]3[/C][C]3.3695[/C][C]1.62198629632144[/C][C]5.229[/C][/ROW]
[ROW][C]4[/C][C]3.48141666666667[/C][C]1.54165881488582[/C][C]4.898[/C][/ROW]
[ROW][C]5[/C][C]3.608[/C][C]1.50404412411097[/C][C]4.176[/C][/ROW]
[ROW][C]6[/C][C]3.59508333333333[/C][C]1.57813505922387[/C][C]4.233[/C][/ROW]
[ROW][C]7[/C][C]3.73441666666667[/C][C]1.72994022273673[/C][C]4.697[/C][/ROW]
[ROW][C]8[/C][C]3.79675[/C][C]1.83293133953636[/C][C]4.911[/C][/ROW]
[ROW][C]9[/C][C]3.80108333333333[/C][C]1.90404767216548[/C][C]6.622[/C][/ROW]
[ROW][C]10[/C][C]3.60858333333333[/C][C]1.67133846516842[/C][C]4.642[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107566&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107566&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
13.760251.789635164699024.671
23.509166666666671.598460954869534.238
33.36951.621986296321445.229
43.481416666666671.541658814885824.898
53.6081.504044124110974.176
63.595083333333331.578135059223874.233
73.734416666666671.729940222736734.697
83.796751.832931339536364.911
93.801083333333331.904047672165486.622
103.608583333333331.671338465168424.642






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.904840164459908
beta0.71201196104474
S.D.0.200343800297590
T-STAT3.5539505589248
p-value0.00746628813643318

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.904840164459908 \tabularnewline
beta & 0.71201196104474 \tabularnewline
S.D. & 0.200343800297590 \tabularnewline
T-STAT & 3.5539505589248 \tabularnewline
p-value & 0.00746628813643318 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107566&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.904840164459908[/C][/ROW]
[ROW][C]beta[/C][C]0.71201196104474[/C][/ROW]
[ROW][C]S.D.[/C][C]0.200343800297590[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.5539505589248[/C][/ROW]
[ROW][C]p-value[/C][C]0.00746628813643318[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107566&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107566&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-0.904840164459908
beta0.71201196104474
S.D.0.200343800297590
T-STAT3.5539505589248
p-value0.00746628813643318






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.39275295939141
beta1.48123624288438
S.D.0.439550668617432
T-STAT3.36988736143544
p-value0.0097872171680265
Lambda-0.481236242884381

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.39275295939141 \tabularnewline
beta & 1.48123624288438 \tabularnewline
S.D. & 0.439550668617432 \tabularnewline
T-STAT & 3.36988736143544 \tabularnewline
p-value & 0.0097872171680265 \tabularnewline
Lambda & -0.481236242884381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107566&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.39275295939141[/C][/ROW]
[ROW][C]beta[/C][C]1.48123624288438[/C][/ROW]
[ROW][C]S.D.[/C][C]0.439550668617432[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.36988736143544[/C][/ROW]
[ROW][C]p-value[/C][C]0.0097872171680265[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.481236242884381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107566&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107566&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-1.39275295939141
beta1.48123624288438
S.D.0.439550668617432
T-STAT3.36988736143544
p-value0.0097872171680265
Lambda-0.481236242884381


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')