FreeStatistics.org

Free Statistics

of Irreproducible Research!

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, 16 Dec 2016 13:35:37 +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/16/t1481891806lij2grdls4ottq9.htm/, Retrieved Fri, 03 May 2024 00:27:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300218, Retrieved Fri, 03 May 2024 00:27:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63

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] [] [2016-12-16 12:35:37] [85f5800284aab30c091766186b093bb4] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1819,6
1312,4
2584
1479,6
1742
2639,2
1706
1408
1951,6
1690,4
2288,4
2912
1460,8
1009,6
2410
1603,2
2115,2
2330
1690
1358
1806,8
1973,6
1402
1857,6
1974,4
1438
1923,2
1996,8
2238,8
2540,4
1704,4
1856
2214,8
1948
1802
1431,6
2857,6
1784
2770,8
2313,6
3707,6
4322,4
3297,6
2223,6
2136,4
2459,2
1650,4
2921,2
1979,6
1403,2
2374
2876,4
2500
3888
1508,8
1011,2
1590,8
2076,4
3736
2125,6
982,8
2034,8
2260
1726
2270,4
1951,6
2104,4
2972,8
2834,4
4227,6
3392,4
3069,2
3138,8
3570
4800,4
4769,2
5124,8
3476,8
2866,8
2549,2
2728
2448,8
3286,8
2830
3251,2
4188,8
2747,6
2269,2
2493,2
2147,6
2689,2
3557,2
2840
3979,6
2683,2
2852
3012,8
2950,8
3065,2
3942,4
4272
4564
5222,8
5164,4
3883,6
4103,2
5244
8071,6
5441,6
7496
10100,4
9616
5645,6
10490
5582
7579,2
4023,6
8146,4
8534,4
10113,6
8504,4
9782,4
13110
8192,8
8708,8
9528,8

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=300218&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=300218&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300218&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
11961.1524.3355518263961599.6
21751.4415.8119679942761400.4
31922.36666666667318.8592146824031108.8
42703.7784.8444269697372672
52255.83333333333890.1190352810672876.8
62485.53333333333859.321133044553244.8
73465.8932.4490919567192676
82974.9644.1727633879822041.2
94458.066666666671408.657045385845120.8
107730.733333333332159.665009938236466.4

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1961.1 & 524.335551826396 & 1599.6 \tabularnewline
2 & 1751.4 & 415.811967994276 & 1400.4 \tabularnewline
3 & 1922.36666666667 & 318.859214682403 & 1108.8 \tabularnewline
4 & 2703.7 & 784.844426969737 & 2672 \tabularnewline
5 & 2255.83333333333 & 890.119035281067 & 2876.8 \tabularnewline
6 & 2485.53333333333 & 859.32113304455 & 3244.8 \tabularnewline
7 & 3465.8 & 932.449091956719 & 2676 \tabularnewline
8 & 2974.9 & 644.172763387982 & 2041.2 \tabularnewline
9 & 4458.06666666667 & 1408.65704538584 & 5120.8 \tabularnewline
10 & 7730.73333333333 & 2159.66500993823 & 6466.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300218&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]1961.1[/C][C]524.335551826396[/C][C]1599.6[/C][/ROW]
[ROW][C]2[/C][C]1751.4[/C][C]415.811967994276[/C][C]1400.4[/C][/ROW]
[ROW][C]3[/C][C]1922.36666666667[/C][C]318.859214682403[/C][C]1108.8[/C][/ROW]
[ROW][C]4[/C][C]2703.7[/C][C]784.844426969737[/C][C]2672[/C][/ROW]
[ROW][C]5[/C][C]2255.83333333333[/C][C]890.119035281067[/C][C]2876.8[/C][/ROW]
[ROW][C]6[/C][C]2485.53333333333[/C][C]859.32113304455[/C][C]3244.8[/C][/ROW]
[ROW][C]7[/C][C]3465.8[/C][C]932.449091956719[/C][C]2676[/C][/ROW]
[ROW][C]8[/C][C]2974.9[/C][C]644.172763387982[/C][C]2041.2[/C][/ROW]
[ROW][C]9[/C][C]4458.06666666667[/C][C]1408.65704538584[/C][C]5120.8[/C][/ROW]
[ROW][C]10[/C][C]7730.73333333333[/C][C]2159.66500993823[/C][C]6466.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300218&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300218&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
11961.1524.3355518263961599.6
21751.4415.8119679942761400.4
31922.36666666667318.8592146824031108.8
42703.7784.8444269697372672
52255.83333333333890.1190352810672876.8
62485.53333333333859.321133044553244.8
73465.8932.4490919567192676
82974.9644.1727633879822041.2
94458.066666666671408.657045385845120.8
107730.733333333332159.665009938236466.4






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-22.1195746305852
beta0.288855082665402
S.D.0.0299287702560748
T-STAT9.6514183574506
p-value1.10555550644281e-05

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -22.1195746305852 \tabularnewline
beta & 0.288855082665402 \tabularnewline
S.D. & 0.0299287702560748 \tabularnewline
T-STAT & 9.6514183574506 \tabularnewline
p-value & 1.10555550644281e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300218&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-22.1195746305852[/C][/ROW]
[ROW][C]beta[/C][C]0.288855082665402[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0299287702560748[/C][/ROW]
[ROW][C]T-STAT[/C][C]9.6514183574506[/C][/ROW]
[ROW][C]p-value[/C][C]1.10555550644281e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300218&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300218&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-22.1195746305852
beta0.288855082665402
S.D.0.0299287702560748
T-STAT9.6514183574506
p-value1.10555550644281e-05






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-2.28011541996943
beta1.12253397642581
S.D.0.186131253732148
T-STAT6.03087312806258
p-value0.000312474826649478
Lambda-0.122533976425808

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -2.28011541996943 \tabularnewline
beta & 1.12253397642581 \tabularnewline
S.D. & 0.186131253732148 \tabularnewline
T-STAT & 6.03087312806258 \tabularnewline
p-value & 0.000312474826649478 \tabularnewline
Lambda & -0.122533976425808 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300218&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-2.28011541996943[/C][/ROW]
[ROW][C]beta[/C][C]1.12253397642581[/C][/ROW]
[ROW][C]S.D.[/C][C]0.186131253732148[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.03087312806258[/C][/ROW]
[ROW][C]p-value[/C][C]0.000312474826649478[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.122533976425808[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300218&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300218&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-2.28011541996943
beta1.12253397642581
S.D.0.186131253732148
T-STAT6.03087312806258
p-value0.000312474826649478
Lambda-0.122533976425808


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')