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Author's title

Author

*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Thu, 18 Aug 2011 17:18:30 -0400

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Aug/18/t131370244907vzufb24v2aek1.htm/, Retrieved Thu, 16 May 2024 00:17:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124164, Retrieved Thu, 16 May 2024 00:17:30 +0000

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Original text written by user:

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No (this computation is public)

User-defined keywords

Van Tongelen Caroline

Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Standard Deviation-Mean Plot] [TIJDREEKS A - STA...] [2011-08-18 21:18:30] [7d6606cca1b3596736d7d387043cb02b] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	0 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124164&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124164&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124164&T=0

As an alternative you can also use a 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 Output	view raw output of R engine
Computing time	0 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	14153.25	555.320553074228	1297
2	16440.75	4090.62565508016	8484
3	12102.25	462.960311473889	982
4	12602.25	1148.73854727697	2280
5	19053	3602.26715648169	8169
6	16852.25	1649.92876108839	3577
7	15949.75	2965.37905109392	7222
8	22164.25	4797.27522488895	10796
9	22495.25	3708.40490193111	8515
10	23467.5	3908.84659032133	9182
11	28218.75	3347.44692514559	8169
12	29199.5	4127.90523954544	9502
13	29199.75	2995.93206142373	6871
14	33047.5	3364.01719179119	8168
15	36316.25	4542.99492809167	10796
16	32960.75	5453.54370264571	13075
17	30917.5	4054.25245883874	9813
18	35089.75	4505.40663166674	10795
19	32145.25	4945.89603442423	12094
20	31328.75	3629.34497074426	8836
21	35003	4685.22322484924	11116
22	34764	4835.05856565702	11782
23	34433	3437.65569344381	7853
24	39997.5	5113.76994007357	11116
25	37710.5	6207.59762978669	15071
26	34526.25	2338.11767240231	4911
27	42854	5794.0292830925	12760
28	41058.75	6652.01435030523	16022
29	37044.25	2407.98856240362	5227
30	43598.25	4718.44510935541	10133

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14153.25 & 555.320553074228 & 1297 \tabularnewline
2 & 16440.75 & 4090.62565508016 & 8484 \tabularnewline
3 & 12102.25 & 462.960311473889 & 982 \tabularnewline
4 & 12602.25 & 1148.73854727697 & 2280 \tabularnewline
5 & 19053 & 3602.26715648169 & 8169 \tabularnewline
6 & 16852.25 & 1649.92876108839 & 3577 \tabularnewline
7 & 15949.75 & 2965.37905109392 & 7222 \tabularnewline
8 & 22164.25 & 4797.27522488895 & 10796 \tabularnewline
9 & 22495.25 & 3708.40490193111 & 8515 \tabularnewline
10 & 23467.5 & 3908.84659032133 & 9182 \tabularnewline
11 & 28218.75 & 3347.44692514559 & 8169 \tabularnewline
12 & 29199.5 & 4127.90523954544 & 9502 \tabularnewline
13 & 29199.75 & 2995.93206142373 & 6871 \tabularnewline
14 & 33047.5 & 3364.01719179119 & 8168 \tabularnewline
15 & 36316.25 & 4542.99492809167 & 10796 \tabularnewline
16 & 32960.75 & 5453.54370264571 & 13075 \tabularnewline
17 & 30917.5 & 4054.25245883874 & 9813 \tabularnewline
18 & 35089.75 & 4505.40663166674 & 10795 \tabularnewline
19 & 32145.25 & 4945.89603442423 & 12094 \tabularnewline
20 & 31328.75 & 3629.34497074426 & 8836 \tabularnewline
21 & 35003 & 4685.22322484924 & 11116 \tabularnewline
22 & 34764 & 4835.05856565702 & 11782 \tabularnewline
23 & 34433 & 3437.65569344381 & 7853 \tabularnewline
24 & 39997.5 & 5113.76994007357 & 11116 \tabularnewline
25 & 37710.5 & 6207.59762978669 & 15071 \tabularnewline
26 & 34526.25 & 2338.11767240231 & 4911 \tabularnewline
27 & 42854 & 5794.0292830925 & 12760 \tabularnewline
28 & 41058.75 & 6652.01435030523 & 16022 \tabularnewline
29 & 37044.25 & 2407.98856240362 & 5227 \tabularnewline
30 & 43598.25 & 4718.44510935541 & 10133 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124164&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]14153.25[/C][C]555.320553074228[/C][C]1297[/C][/ROW]
[ROW][C]2[/C][C]16440.75[/C][C]4090.62565508016[/C][C]8484[/C][/ROW]
[ROW][C]3[/C][C]12102.25[/C][C]462.960311473889[/C][C]982[/C][/ROW]
[ROW][C]4[/C][C]12602.25[/C][C]1148.73854727697[/C][C]2280[/C][/ROW]
[ROW][C]5[/C][C]19053[/C][C]3602.26715648169[/C][C]8169[/C][/ROW]
[ROW][C]6[/C][C]16852.25[/C][C]1649.92876108839[/C][C]3577[/C][/ROW]
[ROW][C]7[/C][C]15949.75[/C][C]2965.37905109392[/C][C]7222[/C][/ROW]
[ROW][C]8[/C][C]22164.25[/C][C]4797.27522488895[/C][C]10796[/C][/ROW]
[ROW][C]9[/C][C]22495.25[/C][C]3708.40490193111[/C][C]8515[/C][/ROW]
[ROW][C]10[/C][C]23467.5[/C][C]3908.84659032133[/C][C]9182[/C][/ROW]
[ROW][C]11[/C][C]28218.75[/C][C]3347.44692514559[/C][C]8169[/C][/ROW]
[ROW][C]12[/C][C]29199.5[/C][C]4127.90523954544[/C][C]9502[/C][/ROW]
[ROW][C]13[/C][C]29199.75[/C][C]2995.93206142373[/C][C]6871[/C][/ROW]
[ROW][C]14[/C][C]33047.5[/C][C]3364.01719179119[/C][C]8168[/C][/ROW]
[ROW][C]15[/C][C]36316.25[/C][C]4542.99492809167[/C][C]10796[/C][/ROW]
[ROW][C]16[/C][C]32960.75[/C][C]5453.54370264571[/C][C]13075[/C][/ROW]
[ROW][C]17[/C][C]30917.5[/C][C]4054.25245883874[/C][C]9813[/C][/ROW]
[ROW][C]18[/C][C]35089.75[/C][C]4505.40663166674[/C][C]10795[/C][/ROW]
[ROW][C]19[/C][C]32145.25[/C][C]4945.89603442423[/C][C]12094[/C][/ROW]
[ROW][C]20[/C][C]31328.75[/C][C]3629.34497074426[/C][C]8836[/C][/ROW]
[ROW][C]21[/C][C]35003[/C][C]4685.22322484924[/C][C]11116[/C][/ROW]
[ROW][C]22[/C][C]34764[/C][C]4835.05856565702[/C][C]11782[/C][/ROW]
[ROW][C]23[/C][C]34433[/C][C]3437.65569344381[/C][C]7853[/C][/ROW]
[ROW][C]24[/C][C]39997.5[/C][C]5113.76994007357[/C][C]11116[/C][/ROW]
[ROW][C]25[/C][C]37710.5[/C][C]6207.59762978669[/C][C]15071[/C][/ROW]
[ROW][C]26[/C][C]34526.25[/C][C]2338.11767240231[/C][C]4911[/C][/ROW]
[ROW][C]27[/C][C]42854[/C][C]5794.0292830925[/C][C]12760[/C][/ROW]
[ROW][C]28[/C][C]41058.75[/C][C]6652.01435030523[/C][C]16022[/C][/ROW]
[ROW][C]29[/C][C]37044.25[/C][C]2407.98856240362[/C][C]5227[/C][/ROW]
[ROW][C]30[/C][C]43598.25[/C][C]4718.44510935541[/C][C]10133[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124164&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124164&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	14153.25	555.320553074228	1297
2	16440.75	4090.62565508016	8484
3	12102.25	462.960311473889	982
4	12602.25	1148.73854727697	2280
5	19053	3602.26715648169	8169
6	16852.25	1649.92876108839	3577
7	15949.75	2965.37905109392	7222
8	22164.25	4797.27522488895	10796
9	22495.25	3708.40490193111	8515
10	23467.5	3908.84659032133	9182
11	28218.75	3347.44692514559	8169
12	29199.5	4127.90523954544	9502
13	29199.75	2995.93206142373	6871
14	33047.5	3364.01719179119	8168
15	36316.25	4542.99492809167	10796
16	32960.75	5453.54370264571	13075
17	30917.5	4054.25245883874	9813
18	35089.75	4505.40663166674	10795
19	32145.25	4945.89603442423	12094
20	31328.75	3629.34497074426	8836
21	35003	4685.22322484924	11116
22	34764	4835.05856565702	11782
23	34433	3437.65569344381	7853
24	39997.5	5113.76994007357	11116
25	37710.5	6207.59762978669	15071
26	34526.25	2338.11767240231	4911
27	42854	5794.0292830925	12760
28	41058.75	6652.01435030523	16022
29	37044.25	2407.98856240362	5227
30	43598.25	4718.44510935541	10133

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	421.095090871136
beta	0.11594176156199
S.D.	0.0217241488388439
T-STAT	5.33699904295815
p-value	1.10451492729493e-05

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 421.095090871136 \tabularnewline
beta & 0.11594176156199 \tabularnewline
S.D. & 0.0217241488388439 \tabularnewline
T-STAT & 5.33699904295815 \tabularnewline
p-value & 1.10451492729493e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124164&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]421.095090871136[/C][/ROW]
[ROW][C]beta[/C][C]0.11594176156199[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0217241488388439[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.33699904295815[/C][/ROW]
[ROW][C]p-value[/C][C]1.10451492729493e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124164&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124164&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	421.095090871136
beta	0.11594176156199
S.D.	0.0217241488388439
T-STAT	5.33699904295815
p-value	1.10451492729493e-05

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-4.64468099715125
beta	1.24790253350852
S.D.	0.210505018812311
T-STAT	5.92813672827993
p-value	2.22080456527266e-06
Lambda	-0.247902533508522

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.64468099715125 \tabularnewline
beta & 1.24790253350852 \tabularnewline
S.D. & 0.210505018812311 \tabularnewline
T-STAT & 5.92813672827993 \tabularnewline
p-value & 2.22080456527266e-06 \tabularnewline
Lambda & -0.247902533508522 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124164&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.64468099715125[/C][/ROW]
[ROW][C]beta[/C][C]1.24790253350852[/C][/ROW]
[ROW][C]S.D.[/C][C]0.210505018812311[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.92813672827993[/C][/ROW]
[ROW][C]p-value[/C][C]2.22080456527266e-06[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.247902533508522[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124164&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124164&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-4.64468099715125
beta	1.24790253350852
S.D.	0.210505018812311
T-STAT	5.92813672827993
p-value	2.22080456527266e-06
Lambda	-0.247902533508522

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 4 ;

Parameters (R input):

par1 = 4 ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code