FreeStatistics.org

Free Statistics

of Irreproducible Research!

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, 12 Mar 2015 11:31:03 +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/2015/Mar/12/t1426160091piujqmm34dc7j9a.htm/, Retrieved Sun, 19 May 2024 15:41:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278261, Retrieved Sun, 19 May 2024 15:41:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120

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] [] [2015-03-12 11:31:03] [7281bb56277fa48a38e7263e2ca5f521] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1,2999
1,3074
1,3242
1,3516
1,3511
1,3419
1,3716
1,3622
1,3896
1,4227
1,4684
1,457
1,4718
1,4748
1,5527
1,5751
1,5557
1,5553
1,577
1,4975
1,4369
1,3322
1,2732
1,3449
1,3239
1,2785
1,305
1,319
1,365
1,4016
1,4088
1,4268
1,4562
1,4816
1,4914
1,4614
1,4272
1,3686
1,3569
1,3406
1,2565
1,2209
1,277
1,2894
1,3067
1,3898
1,3661
1,322
1,336
1,3649
1,3999
1,4442
1,4349
1,4388
1,4264
1,4343
1,377
1,3706
1,3556
1,3179
1,2905
1,3224
1,3201
1,3162
1,2789
1,2526
1,2288
1,24
1,2856
1,2974
1,2828
1,3119
1,3288
1,3359
1,2964
1,3026
1,2982
1,3189
1,308
1,331
1,3348
1,3635
1,3493
1,3704

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278261&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278261&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278261&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
11.370633333333330.05467872003112750.1685
21.470591666666670.1040969430896320.3038
31.393266666666670.07358332732763630.2129
41.326808333333330.05946740066981440.2063
51.391708333333330.04385789984470160.1263
61.28560.0313094815728980.0936000000000001
71.328150.02457694780961140.0740000000000001

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1.37063333333333 & 0.0546787200311275 & 0.1685 \tabularnewline
2 & 1.47059166666667 & 0.104096943089632 & 0.3038 \tabularnewline
3 & 1.39326666666667 & 0.0735833273276363 & 0.2129 \tabularnewline
4 & 1.32680833333333 & 0.0594674006698144 & 0.2063 \tabularnewline
5 & 1.39170833333333 & 0.0438578998447016 & 0.1263 \tabularnewline
6 & 1.2856 & 0.031309481572898 & 0.0936000000000001 \tabularnewline
7 & 1.32815 & 0.0245769478096114 & 0.0740000000000001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278261&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]1.37063333333333[/C][C]0.0546787200311275[/C][C]0.1685[/C][/ROW]
[ROW][C]2[/C][C]1.47059166666667[/C][C]0.104096943089632[/C][C]0.3038[/C][/ROW]
[ROW][C]3[/C][C]1.39326666666667[/C][C]0.0735833273276363[/C][C]0.2129[/C][/ROW]
[ROW][C]4[/C][C]1.32680833333333[/C][C]0.0594674006698144[/C][C]0.2063[/C][/ROW]
[ROW][C]5[/C][C]1.39170833333333[/C][C]0.0438578998447016[/C][C]0.1263[/C][/ROW]
[ROW][C]6[/C][C]1.2856[/C][C]0.031309481572898[/C][C]0.0936000000000001[/C][/ROW]
[ROW][C]7[/C][C]1.32815[/C][C]0.0245769478096114[/C][C]0.0740000000000001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278261&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278261&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
11.370633333333330.05467872003112750.1685
21.470591666666670.1040969430896320.3038
31.393266666666670.07358332732763630.2129
41.326808333333330.05946740066981440.2063
51.391708333333330.04385789984470160.1263
61.28560.0313094815728980.0936000000000001
71.328150.02457694780961140.0740000000000001






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.460173663358252
beta0.377639555424453
S.D.0.108060549401079
T-STAT3.49470327068949
p-value0.0173826779495446

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.460173663358252 \tabularnewline
beta & 0.377639555424453 \tabularnewline
S.D. & 0.108060549401079 \tabularnewline
T-STAT & 3.49470327068949 \tabularnewline
p-value & 0.0173826779495446 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278261&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.460173663358252[/C][/ROW]
[ROW][C]beta[/C][C]0.377639555424453[/C][/ROW]
[ROW][C]S.D.[/C][C]0.108060549401079[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.49470327068949[/C][/ROW]
[ROW][C]p-value[/C][C]0.0173826779495446[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278261&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278261&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-0.460173663358252
beta0.377639555424453
S.D.0.108060549401079
T-STAT3.49470327068949
p-value0.0173826779495446






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-5.77157742106862
beta8.94309551760631
S.D.3.07623800712597
T-STAT2.90715331417466
p-value0.0335104957631233
Lambda-7.94309551760631

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.77157742106862 \tabularnewline
beta & 8.94309551760631 \tabularnewline
S.D. & 3.07623800712597 \tabularnewline
T-STAT & 2.90715331417466 \tabularnewline
p-value & 0.0335104957631233 \tabularnewline
Lambda & -7.94309551760631 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278261&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.77157742106862[/C][/ROW]
[ROW][C]beta[/C][C]8.94309551760631[/C][/ROW]
[ROW][C]S.D.[/C][C]3.07623800712597[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.90715331417466[/C][/ROW]
[ROW][C]p-value[/C][C]0.0335104957631233[/C][/ROW]
[ROW][C]Lambda[/C][C]-7.94309551760631[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278261&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278261&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-5.77157742106862
beta8.94309551760631
S.D.3.07623800712597
T-STAT2.90715331417466
p-value0.0335104957631233
Lambda-7.94309551760631


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')