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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 computationThu, 12 Mar 2015 18:11:29 +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/2015/Mar/12/t1426184053q10q7yn8qohoufs.htm/, Retrieved Sun, 19 May 2024 14:10:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278320, Retrieved Sun, 19 May 2024 14:10:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact98

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] [] [2015-03-12 18:11:29] [57f5dbee1b697c074ab0c7d81efd3c32] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
732
768
902
739
744
848
745
752
833
703
824
759
797
840
988
819
831
904
814
798
828
789
930
744
832
826
907
776
835
715
729
733
736
712
711
667
799
661
692
649
729
622
671
635
648
744
624
476
710
515
461
590
415
554
585
513
591
561
684
668
795
776
1043
964
762
1030
939
779
918
839
874
840
794
820
1003
780
607
1001
743
810
716
775
883
633
755
782
882
694
896
674
702
799
791
797
1021
738
1023
955
912
850
1011
872
1074
811
878
1081
956
812
1125
1051
1090
1028
1178
1041
1146
866
875
1116
903
887

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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278320&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278320&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278320&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'Gertrude Mary Cox' @ cox.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1779.08333333333358.8116536586126199
2840.16666666666768.0051245840854244
3764.91666666666770.3141759059532240
4662.579.598423922268323
5570.58333333333388.3067570083588295
6879.91666666666798.4114353419388281
7797.083333333333122.623190994595396
8794.2598.8038690814006347
9936.2595.5635200462832270
101025.5114.098442344559312

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 779.083333333333 & 58.8116536586126 & 199 \tabularnewline
2 & 840.166666666667 & 68.0051245840854 & 244 \tabularnewline
3 & 764.916666666667 & 70.3141759059532 & 240 \tabularnewline
4 & 662.5 & 79.598423922268 & 323 \tabularnewline
5 & 570.583333333333 & 88.3067570083588 & 295 \tabularnewline
6 & 879.916666666667 & 98.4114353419388 & 281 \tabularnewline
7 & 797.083333333333 & 122.623190994595 & 396 \tabularnewline
8 & 794.25 & 98.8038690814006 & 347 \tabularnewline
9 & 936.25 & 95.5635200462832 & 270 \tabularnewline
10 & 1025.5 & 114.098442344559 & 312 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278320&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]779.083333333333[/C][C]58.8116536586126[/C][C]199[/C][/ROW]
[ROW][C]2[/C][C]840.166666666667[/C][C]68.0051245840854[/C][C]244[/C][/ROW]
[ROW][C]3[/C][C]764.916666666667[/C][C]70.3141759059532[/C][C]240[/C][/ROW]
[ROW][C]4[/C][C]662.5[/C][C]79.598423922268[/C][C]323[/C][/ROW]
[ROW][C]5[/C][C]570.583333333333[/C][C]88.3067570083588[/C][C]295[/C][/ROW]
[ROW][C]6[/C][C]879.916666666667[/C][C]98.4114353419388[/C][C]281[/C][/ROW]
[ROW][C]7[/C][C]797.083333333333[/C][C]122.623190994595[/C][C]396[/C][/ROW]
[ROW][C]8[/C][C]794.25[/C][C]98.8038690814006[/C][C]347[/C][/ROW]
[ROW][C]9[/C][C]936.25[/C][C]95.5635200462832[/C][C]270[/C][/ROW]
[ROW][C]10[/C][C]1025.5[/C][C]114.098442344559[/C][C]312[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278320&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278320&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
1779.08333333333358.8116536586126199
2840.16666666666768.0051245840854244
3764.91666666666770.3141759059532240
4662.579.598423922268323
5570.58333333333388.3067570083588295
6879.91666666666798.4114353419388281
7797.083333333333122.623190994595396
8794.2598.8038690814006347
9936.2595.5635200462832270
101025.5114.098442344559312






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha41.1535702815288
beta0.0599982472684409
S.D.0.0518495592633851
T-STAT1.15716021738318
p-value0.280587570733757

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 41.1535702815288 \tabularnewline
beta & 0.0599982472684409 \tabularnewline
S.D. & 0.0518495592633851 \tabularnewline
T-STAT & 1.15716021738318 \tabularnewline
p-value & 0.280587570733757 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278320&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]41.1535702815288[/C][/ROW]
[ROW][C]beta[/C][C]0.0599982472684409[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0518495592633851[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.15716021738318[/C][/ROW]
[ROW][C]p-value[/C][C]0.280587570733757[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278320&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278320&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)
alpha41.1535702815288
beta0.0599982472684409
S.D.0.0518495592633851
T-STAT1.15716021738318
p-value0.280587570733757






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.49284467168723
beta0.445662309131968
S.D.0.473846916279415
T-STAT0.940519593608947
p-value0.374478232325002
Lambda0.554337690868032

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.49284467168723 \tabularnewline
beta & 0.445662309131968 \tabularnewline
S.D. & 0.473846916279415 \tabularnewline
T-STAT & 0.940519593608947 \tabularnewline
p-value & 0.374478232325002 \tabularnewline
Lambda & 0.554337690868032 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278320&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.49284467168723[/C][/ROW]
[ROW][C]beta[/C][C]0.445662309131968[/C][/ROW]
[ROW][C]S.D.[/C][C]0.473846916279415[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.940519593608947[/C][/ROW]
[ROW][C]p-value[/C][C]0.374478232325002[/C][/ROW]
[ROW][C]Lambda[/C][C]0.554337690868032[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278320&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278320&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)
alpha1.49284467168723
beta0.445662309131968
S.D.0.473846916279415
T-STAT0.940519593608947
p-value0.374478232325002
Lambda0.554337690868032


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')