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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 computationWed, 21 Dec 2016 14:22:01 +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/21/t1482326707q5iglny2nyosxy4.htm/, Retrieved Mon, 06 May 2024 23:30:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302269, Retrieved Mon, 06 May 2024 23:30:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsN1910
Estimated Impact84

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ML Fitting and QQ Plot- Normal Distribution] [Normal distribution] [2016-12-15 09:27:42] [061bcad4f8cbfaa4a6cadfe6faec1e5a]
- RMPD  [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Chisquared simula...] [2016-12-15 10:38:18] [061bcad4f8cbfaa4a6cadfe6faec1e5a]
- RMPD      [Standard Deviation-Mean Plot] [sd mean plot] [2016-12-21 13:22:01] [9a9519454d094169f95f881e5b6f16f7] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4738.4
4687.2
5930.8
5532
5429.8
6107.4
5960.8
5541.8
5362.2
5237
4827
4781.6
4983.2
4718.4
5523.8
5286.6
5389
5810.4
5057.4
5604.4
5285
5215.2
4625.4
4270.4
4685.4
4233.8
5278.4
4978.8
5333.4
5451
5224
5790.2
5079.4
4705.8
4139.6
3720.8
4594
4638.8
4969.4
4764.4
5010.8
5267.8
5312.2
5723.2
4579.6
5015.2
4282.4
3834.2
4523.4
3884.2
3897.8
4845.6
4929
4955.4
5198.4
5122.2
4643.2
4789.8
3950.8
3824.4
4511.8
4262.4
4616.6
5139.6
4972.8
5222
5242
4979.8
4691.8
4821.6
4123.6
4027.4
4365.2
4333.6
4930
5053
5031.4
5342
5191.4
4852.2
4675.6
4689.2
3809.4
4054.2
4409.6
4210.2
4566.4
4907
5021.8
5215.2
4933.6
5197.8
4734.6
4681.8
4172
4037.8
4462.6
4282.6
4962.4
4969.2
5214.6
5416.8
4764.2
5326.2
4545.4
4797.2
4259
4117
4469.2
4203.2
5033.8
4883
5361.6
5044.6
5005.6
5382
4565.4
4825
4290.2
3933.6
4177.6
3949.4
4492.6
4894.2
5224.4
5071

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=302269&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=302269&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302269&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
15344.66666666667502.9803707236831420.2
25147.43333333333442.3170794666181540
34885.05607.8334827296642069.4
44832.66666666667500.8235932093771889
54547.01666666667519.1064382594621374
64717.61666666667420.1547287138471214.6
74693.93333333333469.1359665933911532.6
84673.98333333333400.793879996221177.4
94759.76666666667433.9691805842551299.8
104749.76666666667459.1787042364251448.4

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 5344.66666666667 & 502.980370723683 & 1420.2 \tabularnewline
2 & 5147.43333333333 & 442.317079466618 & 1540 \tabularnewline
3 & 4885.05 & 607.833482729664 & 2069.4 \tabularnewline
4 & 4832.66666666667 & 500.823593209377 & 1889 \tabularnewline
5 & 4547.01666666667 & 519.106438259462 & 1374 \tabularnewline
6 & 4717.61666666667 & 420.154728713847 & 1214.6 \tabularnewline
7 & 4693.93333333333 & 469.135966593391 & 1532.6 \tabularnewline
8 & 4673.98333333333 & 400.79387999622 & 1177.4 \tabularnewline
9 & 4759.76666666667 & 433.969180584255 & 1299.8 \tabularnewline
10 & 4749.76666666667 & 459.178704236425 & 1448.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302269&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]5344.66666666667[/C][C]502.980370723683[/C][C]1420.2[/C][/ROW]
[ROW][C]2[/C][C]5147.43333333333[/C][C]442.317079466618[/C][C]1540[/C][/ROW]
[ROW][C]3[/C][C]4885.05[/C][C]607.833482729664[/C][C]2069.4[/C][/ROW]
[ROW][C]4[/C][C]4832.66666666667[/C][C]500.823593209377[/C][C]1889[/C][/ROW]
[ROW][C]5[/C][C]4547.01666666667[/C][C]519.106438259462[/C][C]1374[/C][/ROW]
[ROW][C]6[/C][C]4717.61666666667[/C][C]420.154728713847[/C][C]1214.6[/C][/ROW]
[ROW][C]7[/C][C]4693.93333333333[/C][C]469.135966593391[/C][C]1532.6[/C][/ROW]
[ROW][C]8[/C][C]4673.98333333333[/C][C]400.79387999622[/C][C]1177.4[/C][/ROW]
[ROW][C]9[/C][C]4759.76666666667[/C][C]433.969180584255[/C][C]1299.8[/C][/ROW]
[ROW][C]10[/C][C]4749.76666666667[/C][C]459.178704236425[/C][C]1448.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302269&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302269&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
15344.66666666667502.9803707236831420.2
25147.43333333333442.3170794666181540
34885.05607.8334827296642069.4
44832.66666666667500.8235932093771889
54547.01666666667519.1064382594621374
64717.61666666667420.1547287138471214.6
74693.93333333333469.1359665933911532.6
84673.98333333333400.793879996221177.4
94759.76666666667433.9691805842551299.8
104749.76666666667459.1787042364251448.4






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha273.126812288124
beta0.0418809871304271
S.D.0.0876631329811978
T-STAT0.477749148429475
p-value0.645609541055103

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 273.126812288124 \tabularnewline
beta & 0.0418809871304271 \tabularnewline
S.D. & 0.0876631329811978 \tabularnewline
T-STAT & 0.477749148429475 \tabularnewline
p-value & 0.645609541055103 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302269&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]273.126812288124[/C][/ROW]
[ROW][C]beta[/C][C]0.0418809871304271[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0876631329811978[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.477749148429475[/C][/ROW]
[ROW][C]p-value[/C][C]0.645609541055103[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302269&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302269&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)
alpha273.126812288124
beta0.0418809871304271
S.D.0.0876631329811978
T-STAT0.477749148429475
p-value0.645609541055103






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha2.35155920451562
beta0.448713720305037
S.D.0.87475980475666
T-STAT0.51295649144494
p-value0.621842338023543
Lambda0.551286279694963

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.35155920451562 \tabularnewline
beta & 0.448713720305037 \tabularnewline
S.D. & 0.87475980475666 \tabularnewline
T-STAT & 0.51295649144494 \tabularnewline
p-value & 0.621842338023543 \tabularnewline
Lambda & 0.551286279694963 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302269&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.35155920451562[/C][/ROW]
[ROW][C]beta[/C][C]0.448713720305037[/C][/ROW]
[ROW][C]S.D.[/C][C]0.87475980475666[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.51295649144494[/C][/ROW]
[ROW][C]p-value[/C][C]0.621842338023543[/C][/ROW]
[ROW][C]Lambda[/C][C]0.551286279694963[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302269&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302269&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)
alpha2.35155920451562
beta0.448713720305037
S.D.0.87475980475666
T-STAT0.51295649144494
p-value0.621842338023543
Lambda0.551286279694963


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')