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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationSun, 23 Nov 2014 15:12:34 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/23/t1416755576kb1nxzew1kezmqh.htm/, Retrieved Sun, 19 May 2024 13:33:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=258023, Retrieved Sun, 19 May 2024 13:33:20 +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] [] [2014-11-23 15:12:34] [11722998b98bb8551244d4a68b29baca] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15.579
16.348
15.928
16.171
15.937
15.713
15.594
15.683
16.438
17.032
17.696
17.745
19.394
20.148
20.108
18.584
18.441
18.391
19.178
18.079
18.483
19.644
19.195
19.650
20.830
23.595
22.937
21.814
21.928
21.777
21.383
21.467
22.052
22.680
24.320
24.977
25.204
25.739
26.434
27.525
30.695
32.436
30.160
30.236
31.293
31.077
32.226
33.865
32.810
32.242
32.700
32.819
33.947
34.148
35.261
39.506
41.591
39.148
41.216
40.225
41.126
42.362
40.740
40.256
39.804
41.002
41.702
42.254
43.605
43.271
43.221
41.373
40.435
39.217
39.457
36.710
34.977
32.729
31.584
32.510
32.565
30.988
30.383
28.673

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258023&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258023&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258023&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 time1 seconds
R Server'George Udny Yule' @ yule.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
116.3220.7756835109056462.166
219.10791666666670.7032356980200142.069
322.481.260966944992474.147
429.74083333333332.835123945770068.661
536.30108333333333.704161626611439.349
641.72633333333331.231130694881253.80099999999999
734.18566666666673.9144686237164611.762

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 16.322 & 0.775683510905646 & 2.166 \tabularnewline
2 & 19.1079166666667 & 0.703235698020014 & 2.069 \tabularnewline
3 & 22.48 & 1.26096694499247 & 4.147 \tabularnewline
4 & 29.7408333333333 & 2.83512394577006 & 8.661 \tabularnewline
5 & 36.3010833333333 & 3.70416162661143 & 9.349 \tabularnewline
6 & 41.7263333333333 & 1.23113069488125 & 3.80099999999999 \tabularnewline
7 & 34.1856666666667 & 3.91446862371646 & 11.762 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258023&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]16.322[/C][C]0.775683510905646[/C][C]2.166[/C][/ROW]
[ROW][C]2[/C][C]19.1079166666667[/C][C]0.703235698020014[/C][C]2.069[/C][/ROW]
[ROW][C]3[/C][C]22.48[/C][C]1.26096694499247[/C][C]4.147[/C][/ROW]
[ROW][C]4[/C][C]29.7408333333333[/C][C]2.83512394577006[/C][C]8.661[/C][/ROW]
[ROW][C]5[/C][C]36.3010833333333[/C][C]3.70416162661143[/C][C]9.349[/C][/ROW]
[ROW][C]6[/C][C]41.7263333333333[/C][C]1.23113069488125[/C][C]3.80099999999999[/C][/ROW]
[ROW][C]7[/C][C]34.1856666666667[/C][C]3.91446862371646[/C][C]11.762[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258023&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258023&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
116.3220.7756835109056462.166
219.10791666666670.7032356980200142.069
322.481.260966944992474.147
429.74083333333332.835123945770068.661
536.30108333333333.704161626611439.349
641.72633333333331.231130694881253.80099999999999
734.18566666666673.9144686237164611.762






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-0.390376215989958
beta0.0858454692411101
S.D.0.05280410275482
T-STAT1.62573483427429
p-value0.164934384380712

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -0.390376215989958 \tabularnewline
beta & 0.0858454692411101 \tabularnewline
S.D. & 0.05280410275482 \tabularnewline
T-STAT & 1.62573483427429 \tabularnewline
p-value & 0.164934384380712 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258023&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.390376215989958[/C][/ROW]
[ROW][C]beta[/C][C]0.0858454692411101[/C][/ROW]
[ROW][C]S.D.[/C][C]0.05280410275482[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.62573483427429[/C][/ROW]
[ROW][C]p-value[/C][C]0.164934384380712[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258023&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258023&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-0.390376215989958
beta0.0858454692411101
S.D.0.05280410275482
T-STAT1.62573483427429
p-value0.164934384380712






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.30795054787896
beta1.4589564322684
S.D.0.644638618685693
T-STAT2.2632159941689
p-value0.0730567809978876
Lambda-0.458956432268405

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.30795054787896 \tabularnewline
beta & 1.4589564322684 \tabularnewline
S.D. & 0.644638618685693 \tabularnewline
T-STAT & 2.2632159941689 \tabularnewline
p-value & 0.0730567809978876 \tabularnewline
Lambda & -0.458956432268405 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=258023&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.30795054787896[/C][/ROW]
[ROW][C]beta[/C][C]1.4589564322684[/C][/ROW]
[ROW][C]S.D.[/C][C]0.644638618685693[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.2632159941689[/C][/ROW]
[ROW][C]p-value[/C][C]0.0730567809978876[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.458956432268405[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=258023&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=258023&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-4.30795054787896
beta1.4589564322684
S.D.0.644638618685693
T-STAT2.2632159941689
p-value0.0730567809978876
Lambda-0.458956432268405


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')