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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, 14 Dec 2016 13:27:55 +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/14/t1481718497ctw6mcymop8h9dr.htm/, Retrieved Fri, 03 May 2024 22:23:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299355, Retrieved Fri, 03 May 2024 22:23:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88

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...] [2016-12-14 12:27:55] [f916b4255bf1e1993d1067800ff1f972] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5033
4509.5
3970
3378
2866
2315.5
1895
8401.5
8040
7534
7135.5
6466.5
5661.5
4896
4064.5
3296
2593.5
2007
1513.5
6645
6221.5
5474
5135.5
4630.5
4164
3600.5
2969
2503.5
2054.5
1608.5
1297.5
8485
8163.5
7814
7453.5
6888.5
6283.5
5712
5030
4488
4058.5
3585
3199.5
8181
8219.5
7865.5
7516.5
7116
6615.5
6216.5
5699.5
5179
4727.5
4224.5
3780.5
7023.5
6558
6257.5
5862.5
5343
4756
4173.5
3451.5
2849
2351
1887.5
1416.5
7399
7013
6644.5
6238.5
5721
5137.5
4357
3750.5
3324
2861
2455.5
2027.5
8388.5
7910
7686
7163
6841.5
6448.5
6060.5
5739
5362.5
5081
4764
4522.5
9056.5
8352
7683
7319.5
6708
6204.5
5576.5
4776.5
4279.5
3918
3288.5
2393.5
8131.5
8121
7790.5
7411.5
6861
6197
5622.5
4855.5
4303.5
3853.5
3283.5
2861.5
9486.5
9061
8877.5
8557.5
8031
7404.5
6852.5
6174.5
5341.5
4975.5
4290

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=299355&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=299355&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299355&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
15128.708333333332317.524840097666506.5
24344.8751666.775236047145131.5
34750.166666666672793.016708387787187.5
45937.916666666671846.293964003345020
55623.958333333331003.030871869983243
64491.752105.820456604635982.5
75158.52328.108703725766361
86424.751446.581605340364534
95729.3751988.024729188155738
106249.208333333332448.232084385626625

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5128.70833333333 & 2317.52484009766 & 6506.5 \tabularnewline
2 & 4344.875 & 1666.77523604714 & 5131.5 \tabularnewline
3 & 4750.16666666667 & 2793.01670838778 & 7187.5 \tabularnewline
4 & 5937.91666666667 & 1846.29396400334 & 5020 \tabularnewline
5 & 5623.95833333333 & 1003.03087186998 & 3243 \tabularnewline
6 & 4491.75 & 2105.82045660463 & 5982.5 \tabularnewline
7 & 5158.5 & 2328.10870372576 & 6361 \tabularnewline
8 & 6424.75 & 1446.58160534036 & 4534 \tabularnewline
9 & 5729.375 & 1988.02472918815 & 5738 \tabularnewline
10 & 6249.20833333333 & 2448.23208438562 & 6625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299355&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]5128.70833333333[/C][C]2317.52484009766[/C][C]6506.5[/C][/ROW]
[ROW][C]2[/C][C]4344.875[/C][C]1666.77523604714[/C][C]5131.5[/C][/ROW]
[ROW][C]3[/C][C]4750.16666666667[/C][C]2793.01670838778[/C][C]7187.5[/C][/ROW]
[ROW][C]4[/C][C]5937.91666666667[/C][C]1846.29396400334[/C][C]5020[/C][/ROW]
[ROW][C]5[/C][C]5623.95833333333[/C][C]1003.03087186998[/C][C]3243[/C][/ROW]
[ROW][C]6[/C][C]4491.75[/C][C]2105.82045660463[/C][C]5982.5[/C][/ROW]
[ROW][C]7[/C][C]5158.5[/C][C]2328.10870372576[/C][C]6361[/C][/ROW]
[ROW][C]8[/C][C]6424.75[/C][C]1446.58160534036[/C][C]4534[/C][/ROW]
[ROW][C]9[/C][C]5729.375[/C][C]1988.02472918815[/C][C]5738[/C][/ROW]
[ROW][C]10[/C][C]6249.20833333333[/C][C]2448.23208438562[/C][C]6625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299355&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299355&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
15128.708333333332317.524840097666506.5
24344.8751666.775236047145131.5
34750.166666666672793.016708387787187.5
45937.916666666671846.293964003345020
55623.958333333331003.030871869983243
64491.752105.820456604635982.5
75158.52328.108703725766361
86424.751446.581605340364534
95729.3751988.024729188155738
106249.208333333332448.232084385626625






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha3049.05448800523
beta-0.195900645772903
S.D.0.247272384067784
T-STAT-0.792246358247595
p-value0.451068356521356

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 3049.05448800523 \tabularnewline
beta & -0.195900645772903 \tabularnewline
S.D. & 0.247272384067784 \tabularnewline
T-STAT & -0.792246358247595 \tabularnewline
p-value & 0.451068356521356 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299355&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3049.05448800523[/C][/ROW]
[ROW][C]beta[/C][C]-0.195900645772903[/C][/ROW]
[ROW][C]S.D.[/C][C]0.247272384067784[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.792246358247595[/C][/ROW]
[ROW][C]p-value[/C][C]0.451068356521356[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299355&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299355&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)
alpha3049.05448800523
beta-0.195900645772903
S.D.0.247272384067784
T-STAT-0.792246358247595
p-value0.451068356521356






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha12.4203983172175
beta-0.566127890520448
S.D.0.75052045586055
T-STAT-0.754313738019736
p-value0.472278059840247
Lambda1.56612789052045

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 12.4203983172175 \tabularnewline
beta & -0.566127890520448 \tabularnewline
S.D. & 0.75052045586055 \tabularnewline
T-STAT & -0.754313738019736 \tabularnewline
p-value & 0.472278059840247 \tabularnewline
Lambda & 1.56612789052045 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299355&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]12.4203983172175[/C][/ROW]
[ROW][C]beta[/C][C]-0.566127890520448[/C][/ROW]
[ROW][C]S.D.[/C][C]0.75052045586055[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.754313738019736[/C][/ROW]
[ROW][C]p-value[/C][C]0.472278059840247[/C][/ROW]
[ROW][C]Lambda[/C][C]1.56612789052045[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299355&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299355&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)
alpha12.4203983172175
beta-0.566127890520448
S.D.0.75052045586055
T-STAT-0.754313738019736
p-value0.472278059840247
Lambda1.56612789052045


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; par8 = 1 ; par9 = 0 ;
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')