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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 computationWed, 22 Dec 2010 14:44:43 +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/22/t1293029412k17wkobghzmcqo8.htm/, Retrieved Mon, 06 May 2024 01:01:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114286, Retrieved Mon, 06 May 2024 01:01:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119

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] [] [2010-12-07 17:03:16] [0175b38674e1402e67841c9c82e4a5a3]
-   PD        [Standard Deviation-Mean Plot] [] [2010-12-22 14:44:43] [c2e23af56713b360851e64c7775b3f2b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13.193
15.234
14.718
16.961
13.945
15.876
16.226
18.316
16.748
17.904
17.209
18.950
17.225
18.710
17.236
18.687
17.580
19.568
17.381
19.580
17.260
18.661
15.658
18.674
15.908
17.475
17.725
19.562
16.368
19.555
17.743
19.867
15.703
19.324
18.162
19.074
15.323
19.704
18.375
18.352
13.927
17.795
16.761
18.902
16.239
19.158
18.279
15.698
16.239
18.431
18.414
19.801
14.995
18.706
18.232
19.409
16.263
19.017
20.298
19.891
15.203
17.845
17.502
18.532
15.737
17.770
17.224
17.601
14.940
18.507
17.635
19.392
15.699
17.661
18.243
19.643
15.770
17.344
17.229
17.322
16.152
17.919
16.918
18.114
16.308
17.759
16.021
17.952
15.954
17.762
16.610
17.751
15.458
18.106
15.990
15.349
13.185
15.409
16.007
16.633
14.800
15.974
15.693

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114286&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114286&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114286&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
115.02651.553731100716383.768
216.090751.790753170223824.371
317.702750.9576830982463172.202
417.96450.8476141024467841.485
518.527251.211419931320272.199
617.563251.43303393190813.016
717.66751.497256713682283.654
818.383251.637647168959183.499
918.065751.652433836295223.621
1017.93851.854664839443154.381
1116.846252.133504374653754.975
1217.34351.642676778919093.46
1318.221251.472647587397163.562
1417.83551.954424467714224.414
1518.867251.816558353040164.035
1617.27051.44332729021063.329
1717.0830.9259031626831532.033
1817.61851.924350020136674.452
1917.81151.635633516408863.944
2016.916250.7657903868988351.574
2117.275750.9141904889026141.962
2217.010.9864566217866181.931
2317.019250.8924458433615641.808
2416.225751.284399827416162.757
2515.30851.501283339901793.448

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 15.0265 & 1.55373110071638 & 3.768 \tabularnewline
2 & 16.09075 & 1.79075317022382 & 4.371 \tabularnewline
3 & 17.70275 & 0.957683098246317 & 2.202 \tabularnewline
4 & 17.9645 & 0.847614102446784 & 1.485 \tabularnewline
5 & 18.52725 & 1.21141993132027 & 2.199 \tabularnewline
6 & 17.56325 & 1.4330339319081 & 3.016 \tabularnewline
7 & 17.6675 & 1.49725671368228 & 3.654 \tabularnewline
8 & 18.38325 & 1.63764716895918 & 3.499 \tabularnewline
9 & 18.06575 & 1.65243383629522 & 3.621 \tabularnewline
10 & 17.9385 & 1.85466483944315 & 4.381 \tabularnewline
11 & 16.84625 & 2.13350437465375 & 4.975 \tabularnewline
12 & 17.3435 & 1.64267677891909 & 3.46 \tabularnewline
13 & 18.22125 & 1.47264758739716 & 3.562 \tabularnewline
14 & 17.8355 & 1.95442446771422 & 4.414 \tabularnewline
15 & 18.86725 & 1.81655835304016 & 4.035 \tabularnewline
16 & 17.2705 & 1.4433272902106 & 3.329 \tabularnewline
17 & 17.083 & 0.925903162683153 & 2.033 \tabularnewline
18 & 17.6185 & 1.92435002013667 & 4.452 \tabularnewline
19 & 17.8115 & 1.63563351640886 & 3.944 \tabularnewline
20 & 16.91625 & 0.765790386898835 & 1.574 \tabularnewline
21 & 17.27575 & 0.914190488902614 & 1.962 \tabularnewline
22 & 17.01 & 0.986456621786618 & 1.931 \tabularnewline
23 & 17.01925 & 0.892445843361564 & 1.808 \tabularnewline
24 & 16.22575 & 1.28439982741616 & 2.757 \tabularnewline
25 & 15.3085 & 1.50128333990179 & 3.448 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114286&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]15.0265[/C][C]1.55373110071638[/C][C]3.768[/C][/ROW]
[ROW][C]2[/C][C]16.09075[/C][C]1.79075317022382[/C][C]4.371[/C][/ROW]
[ROW][C]3[/C][C]17.70275[/C][C]0.957683098246317[/C][C]2.202[/C][/ROW]
[ROW][C]4[/C][C]17.9645[/C][C]0.847614102446784[/C][C]1.485[/C][/ROW]
[ROW][C]5[/C][C]18.52725[/C][C]1.21141993132027[/C][C]2.199[/C][/ROW]
[ROW][C]6[/C][C]17.56325[/C][C]1.4330339319081[/C][C]3.016[/C][/ROW]
[ROW][C]7[/C][C]17.6675[/C][C]1.49725671368228[/C][C]3.654[/C][/ROW]
[ROW][C]8[/C][C]18.38325[/C][C]1.63764716895918[/C][C]3.499[/C][/ROW]
[ROW][C]9[/C][C]18.06575[/C][C]1.65243383629522[/C][C]3.621[/C][/ROW]
[ROW][C]10[/C][C]17.9385[/C][C]1.85466483944315[/C][C]4.381[/C][/ROW]
[ROW][C]11[/C][C]16.84625[/C][C]2.13350437465375[/C][C]4.975[/C][/ROW]
[ROW][C]12[/C][C]17.3435[/C][C]1.64267677891909[/C][C]3.46[/C][/ROW]
[ROW][C]13[/C][C]18.22125[/C][C]1.47264758739716[/C][C]3.562[/C][/ROW]
[ROW][C]14[/C][C]17.8355[/C][C]1.95442446771422[/C][C]4.414[/C][/ROW]
[ROW][C]15[/C][C]18.86725[/C][C]1.81655835304016[/C][C]4.035[/C][/ROW]
[ROW][C]16[/C][C]17.2705[/C][C]1.4433272902106[/C][C]3.329[/C][/ROW]
[ROW][C]17[/C][C]17.083[/C][C]0.925903162683153[/C][C]2.033[/C][/ROW]
[ROW][C]18[/C][C]17.6185[/C][C]1.92435002013667[/C][C]4.452[/C][/ROW]
[ROW][C]19[/C][C]17.8115[/C][C]1.63563351640886[/C][C]3.944[/C][/ROW]
[ROW][C]20[/C][C]16.91625[/C][C]0.765790386898835[/C][C]1.574[/C][/ROW]
[ROW][C]21[/C][C]17.27575[/C][C]0.914190488902614[/C][C]1.962[/C][/ROW]
[ROW][C]22[/C][C]17.01[/C][C]0.986456621786618[/C][C]1.931[/C][/ROW]
[ROW][C]23[/C][C]17.01925[/C][C]0.892445843361564[/C][C]1.808[/C][/ROW]
[ROW][C]24[/C][C]16.22575[/C][C]1.28439982741616[/C][C]2.757[/C][/ROW]
[ROW][C]25[/C][C]15.3085[/C][C]1.50128333990179[/C][C]3.448[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114286&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114286&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
115.02651.553731100716383.768
216.090751.790753170223824.371
317.702750.9576830982463172.202
417.96450.8476141024467841.485
518.527251.211419931320272.199
617.563251.43303393190813.016
717.66751.497256713682283.654
818.383251.637647168959183.499
918.065751.652433836295223.621
1017.93851.854664839443154.381
1116.846252.133504374653754.975
1217.34351.642676778919093.46
1318.221251.472647587397163.562
1417.83551.954424467714224.414
1518.867251.816558353040164.035
1617.27051.44332729021063.329
1717.0830.9259031626831532.033
1817.61851.924350020136674.452
1917.81151.635633516408863.944
2016.916250.7657903868988351.574
2117.275750.9141904889026141.962
2217.010.9864566217866181.931
2317.019250.8924458433615641.808
2416.225751.284399827416162.757
2515.30851.501283339901793.448






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha0.86067341027658
beta0.0327803509151557
S.D.0.0885831380629638
T-STAT0.370051813832288
p-value0.71472966445752

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 0.86067341027658 \tabularnewline
beta & 0.0327803509151557 \tabularnewline
S.D. & 0.0885831380629638 \tabularnewline
T-STAT & 0.370051813832288 \tabularnewline
p-value & 0.71472966445752 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114286&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.86067341027658[/C][/ROW]
[ROW][C]beta[/C][C]0.0327803509151557[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0885831380629638[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.370051813832288[/C][/ROW]
[ROW][C]p-value[/C][C]0.71472966445752[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114286&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114286&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)
alpha0.86067341027658
beta0.0327803509151557
S.D.0.0885831380629638
T-STAT0.370051813832288
p-value0.71472966445752






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-0.611659925548495
beta0.325299344262244
S.D.1.14050130784507
T-STAT0.285224876135289
p-value0.778024587607916
Lambda0.674700655737756

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.611659925548495 \tabularnewline
beta & 0.325299344262244 \tabularnewline
S.D. & 1.14050130784507 \tabularnewline
T-STAT & 0.285224876135289 \tabularnewline
p-value & 0.778024587607916 \tabularnewline
Lambda & 0.674700655737756 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114286&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.611659925548495[/C][/ROW]
[ROW][C]beta[/C][C]0.325299344262244[/C][/ROW]
[ROW][C]S.D.[/C][C]1.14050130784507[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.285224876135289[/C][/ROW]
[ROW][C]p-value[/C][C]0.778024587607916[/C][/ROW]
[ROW][C]Lambda[/C][C]0.674700655737756[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114286&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114286&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-0.611659925548495
beta0.325299344262244
S.D.1.14050130784507
T-STAT0.285224876135289
p-value0.778024587607916
Lambda0.674700655737756


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')