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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, 23 Nov 2016 11:16:49 +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/2016/Nov/23/t14798963787364sk83xyjreuq.htm/, Retrieved Mon, 06 May 2024 19:39:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296968, Retrieved Mon, 06 May 2024 19:39:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81

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] [G1 MEAN PLOT] [2016-11-23 10:16:49] [8b2c6464bd93a4843579a2d15e9e0aeb] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4181.5
4264
4283
4405
4508.5
4514.5
4602.5
4679
4742
4860.5
5034.5
5216.5
5286
5349.5
5437
5393
5516.5
5583.5
5667
5698.5
5764.5
5873
5782.5
5840
5742.5
5808
5814
5862.5
5782
5895
5932.5
6027.5
5970.5
5942
5913.5
5915.5
5845.5
5869.5
5858.5
5856
5871
5736
5716
5651.5
5640
5685.5
5772.5
5721.5
5595
5641.5
5769.5
5723
5769
5779
5779
5685
5895
5874
5911
5958
6029
5992
5977
5972.5
5953.5
6018
5955.5
5969.5
5987
5990.5
6054
6071.5
6239.5
6223.5
6252
6218.5
6287
6204.5
6567
6350.5
6190
6189.5
6092.5
5918
6118.5
5933
5890.5
6019.5
6156.5
6086.5
6352
6160.5
6153
6124
6305.5
6513
6633
6609.5
6462
6432.5
6275
6284.5
6260
6199
6210.5
6217.5
6309
6251
6114.5
6002
6090.5
6048.5
6027
6057.5
5974
6065

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296968&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=296968&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296968&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 time1 seconds
R ServerBig Analytics Cloud Computing Center






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
14607.625316.8984727723611035
25599.25201.062801134372587
35883.7916666666783.8495563855922285
45768.62588.1734151338352231
55781.58333333333111.514539071111363
65997.537.898788658982118
76227.70833333333151.406955876798649
86151.04166666667174.267748324412622.5
96345.29166666667152.502825358825434

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4607.625 & 316.898472772361 & 1035 \tabularnewline
2 & 5599.25 & 201.062801134372 & 587 \tabularnewline
3 & 5883.79166666667 & 83.8495563855922 & 285 \tabularnewline
4 & 5768.625 & 88.1734151338352 & 231 \tabularnewline
5 & 5781.58333333333 & 111.514539071111 & 363 \tabularnewline
6 & 5997.5 & 37.898788658982 & 118 \tabularnewline
7 & 6227.70833333333 & 151.406955876798 & 649 \tabularnewline
8 & 6151.04166666667 & 174.267748324412 & 622.5 \tabularnewline
9 & 6345.29166666667 & 152.502825358825 & 434 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296968&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]4607.625[/C][C]316.898472772361[/C][C]1035[/C][/ROW]
[ROW][C]2[/C][C]5599.25[/C][C]201.062801134372[/C][C]587[/C][/ROW]
[ROW][C]3[/C][C]5883.79166666667[/C][C]83.8495563855922[/C][C]285[/C][/ROW]
[ROW][C]4[/C][C]5768.625[/C][C]88.1734151338352[/C][C]231[/C][/ROW]
[ROW][C]5[/C][C]5781.58333333333[/C][C]111.514539071111[/C][C]363[/C][/ROW]
[ROW][C]6[/C][C]5997.5[/C][C]37.898788658982[/C][C]118[/C][/ROW]
[ROW][C]7[/C][C]6227.70833333333[/C][C]151.406955876798[/C][C]649[/C][/ROW]
[ROW][C]8[/C][C]6151.04166666667[/C][C]174.267748324412[/C][C]622.5[/C][/ROW]
[ROW][C]9[/C][C]6345.29166666667[/C][C]152.502825358825[/C][C]434[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296968&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296968&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
14607.625316.8984727723611035
25599.25201.062801134372587
35883.7916666666783.8495563855922285
45768.62588.1734151338352231
55781.58333333333111.514539071111363
65997.537.898788658982118
76227.70833333333151.406955876798649
86151.04166666667174.267748324412622.5
96345.29166666667152.502825358825434






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha761.900946393876
beta-0.105792164828691
S.D.0.0447473484536723
T-STAT-2.36421080766874
p-value0.0500304173977453

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 761.900946393876 \tabularnewline
beta & -0.105792164828691 \tabularnewline
S.D. & 0.0447473484536723 \tabularnewline
T-STAT & -2.36421080766874 \tabularnewline
p-value & 0.0500304173977453 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296968&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]761.900946393876[/C][/ROW]
[ROW][C]beta[/C][C]-0.105792164828691[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0447473484536723[/C][/ROW]
[ROW][C]T-STAT[/C][C]-2.36421080766874[/C][/ROW]
[ROW][C]p-value[/C][C]0.0500304173977453[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296968&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296968&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)
alpha761.900946393876
beta-0.105792164828691
S.D.0.0447473484536723
T-STAT-2.36421080766874
p-value0.0500304173977453






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha31.6368619320843
beta-3.09299306436876
S.D.2.13645371384132
T-STAT-1.44772294589411
p-value0.190954894892269
Lambda4.09299306436876

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 31.6368619320843 \tabularnewline
beta & -3.09299306436876 \tabularnewline
S.D. & 2.13645371384132 \tabularnewline
T-STAT & -1.44772294589411 \tabularnewline
p-value & 0.190954894892269 \tabularnewline
Lambda & 4.09299306436876 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296968&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]31.6368619320843[/C][/ROW]
[ROW][C]beta[/C][C]-3.09299306436876[/C][/ROW]
[ROW][C]S.D.[/C][C]2.13645371384132[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.44772294589411[/C][/ROW]
[ROW][C]p-value[/C][C]0.190954894892269[/C][/ROW]
[ROW][C]Lambda[/C][C]4.09299306436876[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296968&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296968&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)
alpha31.6368619320843
beta-3.09299306436876
S.D.2.13645371384132
T-STAT-1.44772294589411
p-value0.190954894892269
Lambda4.09299306436876


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')