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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 computationThu, 23 Nov 2017 14:09:49 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Nov/23/t1511442638hk4qy0878t075gt.htm/, Retrieved Fri, 17 May 2024 09:53:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308195, Retrieved Fri, 17 May 2024 09:53:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact82

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] [] [2017-11-23 13:09:49] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1028
869
2698
2367
1928
1846
1404
1316
1008
865
586
343
1143
1807
2380
2334
2116
1788
1571
1306
952
806
473
278
993
1038
2259
2283
1746
1515
1230
882
1028
704
390
238
594
692
2125
1849
1468
1531
1203
878
818
605
316
136
528
654
1892
1597
1515
1241
1026
758
733
481
280
117
651
611
1898
1385
1047
1007
842
827
711
443
313
202
473
566
1609
1296
1153
1155
859
798
557
402
223
153
548
647
1757
1326
1308
1175
992
808
758
551
310
146
649
602
1801
1481
1400
1319
1153
950
829
636
310
191
679
842
1975
1677
1418
1540
1173
941
989
614
352
405

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308195&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308195&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308195&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11354.83333333333721.1268748957912355
21412.83333333333702.9488321393392102
31192.16666666667654.9972704083772045
41017.91666666667618.1242091026591989
5901.833333333333555.9772450107081775
6828.083333333333470.2785360987161696
7770.333333333333454.7457498093821456
8860.5467.3633003836041611
9943.416666666667495.0789575839641610
101050.41666666667516.037077303091623

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1354.83333333333 & 721.126874895791 & 2355 \tabularnewline
2 & 1412.83333333333 & 702.948832139339 & 2102 \tabularnewline
3 & 1192.16666666667 & 654.997270408377 & 2045 \tabularnewline
4 & 1017.91666666667 & 618.124209102659 & 1989 \tabularnewline
5 & 901.833333333333 & 555.977245010708 & 1775 \tabularnewline
6 & 828.083333333333 & 470.278536098716 & 1696 \tabularnewline
7 & 770.333333333333 & 454.745749809382 & 1456 \tabularnewline
8 & 860.5 & 467.363300383604 & 1611 \tabularnewline
9 & 943.416666666667 & 495.078957583964 & 1610 \tabularnewline
10 & 1050.41666666667 & 516.03707730309 & 1623 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308195&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]1354.83333333333[/C][C]721.126874895791[/C][C]2355[/C][/ROW]
[ROW][C]2[/C][C]1412.83333333333[/C][C]702.948832139339[/C][C]2102[/C][/ROW]
[ROW][C]3[/C][C]1192.16666666667[/C][C]654.997270408377[/C][C]2045[/C][/ROW]
[ROW][C]4[/C][C]1017.91666666667[/C][C]618.124209102659[/C][C]1989[/C][/ROW]
[ROW][C]5[/C][C]901.833333333333[/C][C]555.977245010708[/C][C]1775[/C][/ROW]
[ROW][C]6[/C][C]828.083333333333[/C][C]470.278536098716[/C][C]1696[/C][/ROW]
[ROW][C]7[/C][C]770.333333333333[/C][C]454.745749809382[/C][C]1456[/C][/ROW]
[ROW][C]8[/C][C]860.5[/C][C]467.363300383604[/C][C]1611[/C][/ROW]
[ROW][C]9[/C][C]943.416666666667[/C][C]495.078957583964[/C][C]1610[/C][/ROW]
[ROW][C]10[/C][C]1050.41666666667[/C][C]516.03707730309[/C][C]1623[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308195&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308195&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
11354.83333333333721.1268748957912355
21412.83333333333702.9488321393392102
31192.16666666667654.9972704083772045
41017.91666666667618.1242091026591989
5901.833333333333555.9772450107081775
6828.083333333333470.2785360987161696
7770.333333333333454.7457498093821456
8860.5467.3633003836041611
9943.416666666667495.0789575839641610
101050.41666666667516.037077303091623






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha123.942572858744
beta0.427517404021182
S.D.0.0583834358152013
T-STAT7.32258042117262
p-value8.20782365729226e-05

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 123.942572858744 \tabularnewline
beta & 0.427517404021182 \tabularnewline
S.D. & 0.0583834358152013 \tabularnewline
T-STAT & 7.32258042117262 \tabularnewline
p-value & 8.20782365729226e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308195&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]123.942572858744[/C][/ROW]
[ROW][C]beta[/C][C]0.427517404021182[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0583834358152013[/C][/ROW]
[ROW][C]T-STAT[/C][C]7.32258042117262[/C][/ROW]
[ROW][C]p-value[/C][C]8.20782365729226e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308195&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308195&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)
alpha123.942572858744
beta0.427517404021182
S.D.0.0583834358152013
T-STAT7.32258042117262
p-value8.20782365729226e-05






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.852132586347541
beta0.790627713677028
S.D.0.111618688534859
T-STAT7.08329155318925
p-value0.000103691277059979
Lambda0.209372286322972

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.852132586347541 \tabularnewline
beta & 0.790627713677028 \tabularnewline
S.D. & 0.111618688534859 \tabularnewline
T-STAT & 7.08329155318925 \tabularnewline
p-value & 0.000103691277059979 \tabularnewline
Lambda & 0.209372286322972 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308195&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.852132586347541[/C][/ROW]
[ROW][C]beta[/C][C]0.790627713677028[/C][/ROW]
[ROW][C]S.D.[/C][C]0.111618688534859[/C][/ROW]
[ROW][C]T-STAT[/C][C]7.08329155318925[/C][/ROW]
[ROW][C]p-value[/C][C]0.000103691277059979[/C][/ROW]
[ROW][C]Lambda[/C][C]0.209372286322972[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308195&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308195&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)
alpha0.852132586347541
beta0.790627713677028
S.D.0.111618688534859
T-STAT7.08329155318925
p-value0.000103691277059979
Lambda0.209372286322972


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')