FreeStatistics.org

Free Statistics

of Irreproducible Research!

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, 11 Dec 2014 12:39:16 +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/2014/Dec/11/t1418301644bjmaz9n1re64e9z.htm/, Retrieved Sun, 19 May 2024 20:59:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=265913, Retrieved Sun, 19 May 2024 20:59:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65

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] [standard deviatio...] [2014-12-11 12:39:16] [80d519c92fcb7b7b3d91f00690b8e112] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9.769
9.321
9.939
9.336
10.195
9.464
10.010
10.213
9.563
9.890
9.305
9.391
9.928
8.686
9.843
9.627
10.074
9.503
10.119
10.000
9.313
9.866
9.172
9.241
9.659
8.904
9.755
9.080
9.435
8.971
10.063
9.793
9.454
9.759
8.820
9.403
9.676
8.642
9.402
9.610
9.294
9.448
10.319
9.548
9.801
9.596
8.923
9.746
9.829
9.125
9.782
9.441
9.162
9.915
10.444
10.209
9.985
9.842
9.429
10.132
9.849
9.172
10.313
9.819
9.955
10.048
10.082
10.541
10.208
10.233
9.439
9.963
10.158
9.225
10.474
9.757
10.490
10.281
10.444
10.640
10.695
10.786
9.832
9.747
10.411
9.511
10.402
9.701
10.540
10.112
10.915
11.183
10.384
10.834
9.886
10.216
10.943
9.867
10.203
10.837
10.573
10.647
11.502
10.656
10.866
10.835
9.945
10.331
10.718
9.462
10.579
10.633
10.346
10.757
11.207
11.013
11.015
10.765
10.042
10.661

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'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265913&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265913&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265913&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'Herman Ole Andreas Wold' @ wold.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
19.699666666666670.3443548205328950.907999999999999
29.614333333333330.4399306419163931.433
39.424666666666670.4024595594214371.243
49.500416666666670.4264343620670311.677
59.774583333333330.4116550759011131.319
69.96850.3747223214352441.369
710.210750.4762713369116771.561
810.341250.4959059890745421.672
910.60041666666670.4588284405731491.635
1010.59983333333330.472249516739411.745

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 9.69966666666667 & 0.344354820532895 & 0.907999999999999 \tabularnewline
2 & 9.61433333333333 & 0.439930641916393 & 1.433 \tabularnewline
3 & 9.42466666666667 & 0.402459559421437 & 1.243 \tabularnewline
4 & 9.50041666666667 & 0.426434362067031 & 1.677 \tabularnewline
5 & 9.77458333333333 & 0.411655075901113 & 1.319 \tabularnewline
6 & 9.9685 & 0.374722321435244 & 1.369 \tabularnewline
7 & 10.21075 & 0.476271336911677 & 1.561 \tabularnewline
8 & 10.34125 & 0.495905989074542 & 1.672 \tabularnewline
9 & 10.6004166666667 & 0.458828440573149 & 1.635 \tabularnewline
10 & 10.5998333333333 & 0.47224951673941 & 1.745 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265913&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]9.69966666666667[/C][C]0.344354820532895[/C][C]0.907999999999999[/C][/ROW]
[ROW][C]2[/C][C]9.61433333333333[/C][C]0.439930641916393[/C][C]1.433[/C][/ROW]
[ROW][C]3[/C][C]9.42466666666667[/C][C]0.402459559421437[/C][C]1.243[/C][/ROW]
[ROW][C]4[/C][C]9.50041666666667[/C][C]0.426434362067031[/C][C]1.677[/C][/ROW]
[ROW][C]5[/C][C]9.77458333333333[/C][C]0.411655075901113[/C][C]1.319[/C][/ROW]
[ROW][C]6[/C][C]9.9685[/C][C]0.374722321435244[/C][C]1.369[/C][/ROW]
[ROW][C]7[/C][C]10.21075[/C][C]0.476271336911677[/C][C]1.561[/C][/ROW]
[ROW][C]8[/C][C]10.34125[/C][C]0.495905989074542[/C][C]1.672[/C][/ROW]
[ROW][C]9[/C][C]10.6004166666667[/C][C]0.458828440573149[/C][C]1.635[/C][/ROW]
[ROW][C]10[/C][C]10.5998333333333[/C][C]0.47224951673941[/C][C]1.745[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265913&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265913&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
19.699666666666670.3443548205328950.907999999999999
29.614333333333330.4399306419163931.433
39.424666666666670.4024595594214371.243
49.500416666666670.4264343620670311.677
59.774583333333330.4116550759011131.319
69.96850.3747223214352441.369
710.210750.4762713369116771.561
810.341250.4959059890745421.672
910.60041666666670.4588284405731491.635
1010.59983333333330.472249516739411.745






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.257471755896636
beta0.0689584383545892
S.D.0.0297960314177619
T-STAT2.3143497665089
p-value0.0493528268369602

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.257471755896636 \tabularnewline
beta & 0.0689584383545892 \tabularnewline
S.D. & 0.0297960314177619 \tabularnewline
T-STAT & 2.3143497665089 \tabularnewline
p-value & 0.0493528268369602 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265913&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.257471755896636[/C][/ROW]
[ROW][C]beta[/C][C]0.0689584383545892[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0297960314177619[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.3143497665089[/C][/ROW]
[ROW][C]p-value[/C][C]0.0493528268369602[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265913&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265913&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-0.257471755896636
beta0.0689584383545892
S.D.0.0297960314177619
T-STAT2.3143497665089
p-value0.0493528268369602






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.50537815587457
beta1.59032793402499
S.D.0.733155186285711
T-STAT2.16915594920887
p-value0.0618998955659381
Lambda-0.590327934024988

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.50537815587457 \tabularnewline
beta & 1.59032793402499 \tabularnewline
S.D. & 0.733155186285711 \tabularnewline
T-STAT & 2.16915594920887 \tabularnewline
p-value & 0.0618998955659381 \tabularnewline
Lambda & -0.590327934024988 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265913&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.50537815587457[/C][/ROW]
[ROW][C]beta[/C][C]1.59032793402499[/C][/ROW]
[ROW][C]S.D.[/C][C]0.733155186285711[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.16915594920887[/C][/ROW]
[ROW][C]p-value[/C][C]0.0618998955659381[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.590327934024988[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265913&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265913&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-4.50537815587457
beta1.59032793402499
S.D.0.733155186285711
T-STAT2.16915594920887
p-value0.0618998955659381
Lambda-0.590327934024988


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')