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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 computationFri, 23 Dec 2016 10:31:14 +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/Dec/23/t14824856293nbkitgfg6hgwsy.htm/, Retrieved Wed, 08 May 2024 02:53:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302816, Retrieved Wed, 08 May 2024 02:53:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69

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] [SDMP N2583] [2016-12-23 09:31:14] [11b61e09f442d73f657668491c17a736] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4782
4540
4588
4740
4646
4736
4794
4730
4752
4804
4818
4948
4906
4666
4696
4872
4742
4858
4868
4782
4824
4820
4882
5062
4996
4800
4828
5002
4926
5090
5140
5116
5210
5224
5292
5538
5414
5160
5258
5492
5448
5618
5704
5684
5722
5754
5894
6280
6114
5744
5736
6020
5880
5888
5886
5812
5784
5914
5884
5972
5918
5586
5600
5842
5662
5826
5862
5782
5750
5778
5802
5978
5810
5516
5520
5664
5470
5534
5636
5542
5526
5608
5630
5830
5656
5426
5432
5600
5380
5504
5546
5534
5562
5564
5612
5798
5556
5364
5406
5558
5438
5602
5622
5580
5570
5674
5818
6058
5998
5928
6052
6276
6166
6226
6354
6396

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=302816&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=302816&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302816&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
14739.83333333333108.846709002184408
24831.5105.012986209932396
35096.83333333333207.298569627716738
45619298.6679518370621120
55886.16666666667111.48080416363378
65782.16666666667119.174305752184392
75607.16666666667115.322341392474360
85551.16666666667112.813469000287418
95603.83333333333187.726025382898694

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4739.83333333333 & 108.846709002184 & 408 \tabularnewline
2 & 4831.5 & 105.012986209932 & 396 \tabularnewline
3 & 5096.83333333333 & 207.298569627716 & 738 \tabularnewline
4 & 5619 & 298.667951837062 & 1120 \tabularnewline
5 & 5886.16666666667 & 111.48080416363 & 378 \tabularnewline
6 & 5782.16666666667 & 119.174305752184 & 392 \tabularnewline
7 & 5607.16666666667 & 115.322341392474 & 360 \tabularnewline
8 & 5551.16666666667 & 112.813469000287 & 418 \tabularnewline
9 & 5603.83333333333 & 187.726025382898 & 694 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302816&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]4739.83333333333[/C][C]108.846709002184[/C][C]408[/C][/ROW]
[ROW][C]2[/C][C]4831.5[/C][C]105.012986209932[/C][C]396[/C][/ROW]
[ROW][C]3[/C][C]5096.83333333333[/C][C]207.298569627716[/C][C]738[/C][/ROW]
[ROW][C]4[/C][C]5619[/C][C]298.667951837062[/C][C]1120[/C][/ROW]
[ROW][C]5[/C][C]5886.16666666667[/C][C]111.48080416363[/C][C]378[/C][/ROW]
[ROW][C]6[/C][C]5782.16666666667[/C][C]119.174305752184[/C][C]392[/C][/ROW]
[ROW][C]7[/C][C]5607.16666666667[/C][C]115.322341392474[/C][C]360[/C][/ROW]
[ROW][C]8[/C][C]5551.16666666667[/C][C]112.813469000287[/C][C]418[/C][/ROW]
[ROW][C]9[/C][C]5603.83333333333[/C][C]187.726025382898[/C][C]694[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302816&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302816&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
14739.83333333333108.846709002184408
24831.5105.012986209932396
35096.83333333333207.298569627716738
45619298.6679518370621120
55886.16666666667111.48080416363378
65782.16666666667119.174305752184392
75607.16666666667115.322341392474360
85551.16666666667112.813469000287418
95603.83333333333187.726025382898694






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha26.5690701426162
beta0.0231378390676515
S.D.0.0598443028309948
T-STAT0.386633947979888
p-value0.710511592826679

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 26.5690701426162 \tabularnewline
beta & 0.0231378390676515 \tabularnewline
S.D. & 0.0598443028309948 \tabularnewline
T-STAT & 0.386633947979888 \tabularnewline
p-value & 0.710511592826679 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302816&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]26.5690701426162[/C][/ROW]
[ROW][C]beta[/C][C]0.0231378390676515[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0598443028309948[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.386633947979888[/C][/ROW]
[ROW][C]p-value[/C][C]0.710511592826679[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302816&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302816&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)
alpha26.5690701426162
beta0.0231378390676515
S.D.0.0598443028309948
T-STAT0.386633947979888
p-value0.710511592826679






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.79747549042118
beta0.785545116457959
S.D.1.76570426304696
T-STAT0.444890536256845
p-value0.669830059778467
Lambda0.214454883542041

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.79747549042118 \tabularnewline
beta & 0.785545116457959 \tabularnewline
S.D. & 1.76570426304696 \tabularnewline
T-STAT & 0.444890536256845 \tabularnewline
p-value & 0.669830059778467 \tabularnewline
Lambda & 0.214454883542041 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302816&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.79747549042118[/C][/ROW]
[ROW][C]beta[/C][C]0.785545116457959[/C][/ROW]
[ROW][C]S.D.[/C][C]1.76570426304696[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.444890536256845[/C][/ROW]
[ROW][C]p-value[/C][C]0.669830059778467[/C][/ROW]
[ROW][C]Lambda[/C][C]0.214454883542041[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302816&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302816&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-1.79747549042118
beta0.785545116457959
S.D.1.76570426304696
T-STAT0.444890536256845
p-value0.669830059778467
Lambda0.214454883542041


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')