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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 computationThu, 11 Dec 2008 05:19:36 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/11/t1228998065c75546fbea7qc4p.htm/, Retrieved Sun, 19 May 2024 07:45:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32188, Retrieved Sun, 19 May 2024 07:45:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact199

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...] [2008-12-11 12:19:36] [a9e6d7cd6e144e8b311d9f96a24c5a25] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2648.9
2669.6
3042.3
2604.2
2732.1
2621.7
2483.7
2479.3
2684.6
2834.7
2566.1
2251.2
2350
2299.8
2542.8
2530.2
2508.1
2616.8
2534.1
2181.8
2578.9
2841.9
2529.9
2103.2
2326.2
2452.6
2782.1
2727.3
2648.2
2760.7
2613
2225.4
2713.9
2923.3
2707
2473.9
2521
2531.8
3068.8
2826.9
2674.2
2966.6
2798.8
2629.6
3124.6
3115.7
3083
2863.9
2728.7
2789.4
3225.7
3148.2
2836.5
3153.5
2656.9
2834.7
3172.5
2998.8
3103.1
2735.6
2818.1
2874.4
3438.5
2949.1
3306.8
3530
3003.8
3206.4
3514.6
3522.6
3525.5
2996.2
3231.1
3030
3541.7
3113.2
3390.8
3424.2
3079.8
3123.4
3317.1
3579.9
3317.9
2668.1

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32188&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32188&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32188&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
12634.86666666667195.253091389022791.1
22468.125202.421410675847738.7
32612.8203.956550631390697.9
42850.40833333333224.434632955114603.6
52948.63333333333205.565346094986568.8
63223.83333333333281.917129452589711.9
73234.76666666667252.531907374938911.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2634.86666666667 & 195.253091389022 & 791.1 \tabularnewline
2 & 2468.125 & 202.421410675847 & 738.7 \tabularnewline
3 & 2612.8 & 203.956550631390 & 697.9 \tabularnewline
4 & 2850.40833333333 & 224.434632955114 & 603.6 \tabularnewline
5 & 2948.63333333333 & 205.565346094986 & 568.8 \tabularnewline
6 & 3223.83333333333 & 281.917129452589 & 711.9 \tabularnewline
7 & 3234.76666666667 & 252.531907374938 & 911.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32188&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]2634.86666666667[/C][C]195.253091389022[/C][C]791.1[/C][/ROW]
[ROW][C]2[/C][C]2468.125[/C][C]202.421410675847[/C][C]738.7[/C][/ROW]
[ROW][C]3[/C][C]2612.8[/C][C]203.956550631390[/C][C]697.9[/C][/ROW]
[ROW][C]4[/C][C]2850.40833333333[/C][C]224.434632955114[/C][C]603.6[/C][/ROW]
[ROW][C]5[/C][C]2948.63333333333[/C][C]205.565346094986[/C][C]568.8[/C][/ROW]
[ROW][C]6[/C][C]3223.83333333333[/C][C]281.917129452589[/C][C]711.9[/C][/ROW]
[ROW][C]7[/C][C]3234.76666666667[/C][C]252.531907374938[/C][C]911.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32188&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32188&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
12634.86666666667195.253091389022791.1
22468.125202.421410675847738.7
32612.8203.956550631390697.9
42850.40833333333224.434632955114603.6
52948.63333333333205.565346094986568.8
63223.83333333333281.917129452589711.9
73234.76666666667252.531907374938911.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-37.6387917753487
beta0.09159925489365
S.D.0.0243793062044199
T-STAT3.75725437490274
p-value0.0131947594470037

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -37.6387917753487 \tabularnewline
beta & 0.09159925489365 \tabularnewline
S.D. & 0.0243793062044199 \tabularnewline
T-STAT & 3.75725437490274 \tabularnewline
p-value & 0.0131947594470037 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32188&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-37.6387917753487[/C][/ROW]
[ROW][C]beta[/C][C]0.09159925489365[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0243793062044199[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.75725437490274[/C][/ROW]
[ROW][C]p-value[/C][C]0.0131947594470037[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32188&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32188&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-37.6387917753487
beta0.09159925489365
S.D.0.0243793062044199
T-STAT3.75725437490274
p-value0.0131947594470037






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.40306811603049
beta1.10736907917068
S.D.0.300545276556094
T-STAT3.68453329847624
p-value0.0142263107189295
Lambda-0.107369079170679

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.40306811603049 \tabularnewline
beta & 1.10736907917068 \tabularnewline
S.D. & 0.300545276556094 \tabularnewline
T-STAT & 3.68453329847624 \tabularnewline
p-value & 0.0142263107189295 \tabularnewline
Lambda & -0.107369079170679 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32188&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.40306811603049[/C][/ROW]
[ROW][C]beta[/C][C]1.10736907917068[/C][/ROW]
[ROW][C]S.D.[/C][C]0.300545276556094[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.68453329847624[/C][/ROW]
[ROW][C]p-value[/C][C]0.0142263107189295[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.107369079170679[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32188&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32188&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-3.40306811603049
beta1.10736907917068
S.D.0.300545276556094
T-STAT3.68453329847624
p-value0.0142263107189295
Lambda-0.107369079170679


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')