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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 14:52:42 +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/t148250123818tw0gxwbohg50n.htm/, Retrieved Tue, 07 May 2024 12:08:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302952, Retrieved Tue, 07 May 2024 12:08:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57

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] [STDMP N2671] [2016-12-23 13:52:42] [11b61e09f442d73f657668491c17a736] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6258.5
6191
5939.5
5517.5
5382.5
5785
5353.5
5205.5
4915
4691.5
4564.5
4496
4877.5
4703.5
4528.5
4262.5
4077
4291
4357
4191
4025.5
3994.5
3934.5
3989
4565.5
4451
4312.5
4075
4005.5
4376.5
4341
4025.5
3992
3958.5
3907.5
3858.5
4236
4520.5
4333.5
4057.5
4079
4387.5
4235.5
3977.5
4007.5
3921
3936
3730.5
4310
4251.5
4062
3653
3659
3827.5
3726.5
3544
3428.5
3422.5
3401
3263
3801.5
3741
3545
3179.5
3276.5
3409.5
3411.5
3329.5
3184
3091
3162.5
3071
3654.5
3441.5
3189
3114.5
3078
3425
3368
3176
3165
3111
3247.5
3150
3628
3567
3348.5
3228.5
3181.5
3351
3472.5
3418.5
3409
3361
3605.5
3671.5
4297.5
4459.5
4402
4024.5
4116.5
4387
4288
4118.5
4035
4006.5
4143
4279.5
4974.5
5080.5
4845.5
4472.5
4584.5
5047.5
4922.5
4695
4545

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=302952&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=302952&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302952&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
15358.33333333333609.5999930406431762.5
24269.29166666667301.895937695375943
34155.75238.26155414128707
44118.5227.241361471974790
53712.375341.351799667681047
63350.20833333333242.075726162227730.5
73260175.119439759891576.5
83436.875156.352330127708490
94213.125158.672780073848453

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5358.33333333333 & 609.599993040643 & 1762.5 \tabularnewline
2 & 4269.29166666667 & 301.895937695375 & 943 \tabularnewline
3 & 4155.75 & 238.26155414128 & 707 \tabularnewline
4 & 4118.5 & 227.241361471974 & 790 \tabularnewline
5 & 3712.375 & 341.35179966768 & 1047 \tabularnewline
6 & 3350.20833333333 & 242.075726162227 & 730.5 \tabularnewline
7 & 3260 & 175.119439759891 & 576.5 \tabularnewline
8 & 3436.875 & 156.352330127708 & 490 \tabularnewline
9 & 4213.125 & 158.672780073848 & 453 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302952&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]5358.33333333333[/C][C]609.599993040643[/C][C]1762.5[/C][/ROW]
[ROW][C]2[/C][C]4269.29166666667[/C][C]301.895937695375[/C][C]943[/C][/ROW]
[ROW][C]3[/C][C]4155.75[/C][C]238.26155414128[/C][C]707[/C][/ROW]
[ROW][C]4[/C][C]4118.5[/C][C]227.241361471974[/C][C]790[/C][/ROW]
[ROW][C]5[/C][C]3712.375[/C][C]341.35179966768[/C][C]1047[/C][/ROW]
[ROW][C]6[/C][C]3350.20833333333[/C][C]242.075726162227[/C][C]730.5[/C][/ROW]
[ROW][C]7[/C][C]3260[/C][C]175.119439759891[/C][C]576.5[/C][/ROW]
[ROW][C]8[/C][C]3436.875[/C][C]156.352330127708[/C][C]490[/C][/ROW]
[ROW][C]9[/C][C]4213.125[/C][C]158.672780073848[/C][C]453[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302952&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302952&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
15358.33333333333609.5999930406431762.5
24269.29166666667301.895937695375943
34155.75238.26155414128707
44118.5227.241361471974790
53712.375341.351799667681047
63350.20833333333242.075726162227730.5
73260175.119439759891576.5
83436.875156.352330127708490
94213.125158.672780073848453






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-400.010776740793
beta0.16866227934613
S.D.0.0518774917999916
T-STAT3.25116487891107
p-value0.0140346677534339

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -400.010776740793 \tabularnewline
beta & 0.16866227934613 \tabularnewline
S.D. & 0.0518774917999916 \tabularnewline
T-STAT & 3.25116487891107 \tabularnewline
p-value & 0.0140346677534339 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302952&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-400.010776740793[/C][/ROW]
[ROW][C]beta[/C][C]0.16866227934613[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0518774917999916[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.25116487891107[/C][/ROW]
[ROW][C]p-value[/C][C]0.0140346677534339[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302952&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302952&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-400.010776740793
beta0.16866227934613
S.D.0.0518774917999916
T-STAT3.25116487891107
p-value0.0140346677534339






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-10.231645312381
beta1.901812143654
S.D.0.760758358696206
T-STAT2.4998899084242
p-value0.0409988224768289
Lambda-0.901812143654

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -10.231645312381 \tabularnewline
beta & 1.901812143654 \tabularnewline
S.D. & 0.760758358696206 \tabularnewline
T-STAT & 2.4998899084242 \tabularnewline
p-value & 0.0409988224768289 \tabularnewline
Lambda & -0.901812143654 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302952&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-10.231645312381[/C][/ROW]
[ROW][C]beta[/C][C]1.901812143654[/C][/ROW]
[ROW][C]S.D.[/C][C]0.760758358696206[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.4998899084242[/C][/ROW]
[ROW][C]p-value[/C][C]0.0409988224768289[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.901812143654[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302952&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302952&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-10.231645312381
beta1.901812143654
S.D.0.760758358696206
T-STAT2.4998899084242
p-value0.0409988224768289
Lambda-0.901812143654


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 <- '12'
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')