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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 computationMon, 22 Dec 2008 03:08:54 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/22/t1229940614jrot6i4m1vzxhrk.htm/, Retrieved Mon, 13 May 2024 14:44:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35975, Retrieved Mon, 13 May 2024 14:44:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact165

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] [SDMP] [2008-12-22 10:08:54] [a413cf7744efd6bb212437a3916e2f23] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1025,5
691,2
971,6
926
997,1
964,9
860
948
951,4
827,3
994
944,5
976,2
668,8
939,9
1096,1
977,7
1096,9
1060,8
1121,4
1190,9
1177,9
1108,1
1045,6
1263,9
911
1175,9
1091,3
1027,7
1081,7
879,7
955,5
1037,9
959,9
931,8
1062,2
1077,2
668,4
954,3
797,2
829,2
957,3
844,2
893,6
1132
898,8
1064
1279,7
1382,5
824,1
1304,1
1253,5
1136,3
1414,7
1293,2
1325,7
1463,8
1244,2
1573,6
1327,3
1418,5
1042,2
1384,8
1474,8
1556,5
1466,2
1221,7
1279,7
1348,4
1189,8
1296,6
1417,6
1513,9
1006,1
1202,8
1258,8
1211,5
1283,3
1332,3
1374,3
1406,1
1419,1
1554,4
1499,8
1609,6
1033,9
1550,5
1491,4
1368,9
1537,1
1492,3
1504,1
1301,2
1344,2
1319,1
1420,3
1582,9
1002,6
1559,1
1462,7
1414,8
1537,5
1455,9
1619,9
1667,2
1488,9
1442,5
1779,6
1801,9
1233,4
1581,1
1515
1439,2
1585,8
1488,8
1601,3
1646,8
1630,2
1720,7
2013,5
2051,2
1404,7
2015,9
1544,1
1816,6
1773,4
1577,4
1709,8
1810,2
1520,5
1798,6
1666,8
1730,4
1147,8
1777
1700
1907,4
1745,8
1771,6
1790,2
1958,7
1560,4
1752,1
2011,6
2082,8
1616,4
1846,1
1824,9
1711,3
1805
1737,6
1939,6
1711,4
1964,8
1864,4
1980,7
2226,7
1433,3
1960,7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35975&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35975&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35975&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1925.12592.3742302219126334.3
21038.35833333333140.009236437739522.1
31031.54166666667112.960656532451384.2
4949.658333333333166.598971176204611.3
51295.25186.206681356546749.5
61341.4143.326467770738514.3
71338.53333333333156.73203149634548.3
81414.38333333333155.339720573583575.7
91501.13333333333189.183755468944777
101604.80833333333192.953684778749780.1
111724.1194.695529201133646.5
121737.75221.415912625169863.8
131840.41666666667134.810101006317466.4

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 925.125 & 92.3742302219126 & 334.3 \tabularnewline
2 & 1038.35833333333 & 140.009236437739 & 522.1 \tabularnewline
3 & 1031.54166666667 & 112.960656532451 & 384.2 \tabularnewline
4 & 949.658333333333 & 166.598971176204 & 611.3 \tabularnewline
5 & 1295.25 & 186.206681356546 & 749.5 \tabularnewline
6 & 1341.4 & 143.326467770738 & 514.3 \tabularnewline
7 & 1338.53333333333 & 156.73203149634 & 548.3 \tabularnewline
8 & 1414.38333333333 & 155.339720573583 & 575.7 \tabularnewline
9 & 1501.13333333333 & 189.183755468944 & 777 \tabularnewline
10 & 1604.80833333333 & 192.953684778749 & 780.1 \tabularnewline
11 & 1724.1 & 194.695529201133 & 646.5 \tabularnewline
12 & 1737.75 & 221.415912625169 & 863.8 \tabularnewline
13 & 1840.41666666667 & 134.810101006317 & 466.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35975&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]925.125[/C][C]92.3742302219126[/C][C]334.3[/C][/ROW]
[ROW][C]2[/C][C]1038.35833333333[/C][C]140.009236437739[/C][C]522.1[/C][/ROW]
[ROW][C]3[/C][C]1031.54166666667[/C][C]112.960656532451[/C][C]384.2[/C][/ROW]
[ROW][C]4[/C][C]949.658333333333[/C][C]166.598971176204[/C][C]611.3[/C][/ROW]
[ROW][C]5[/C][C]1295.25[/C][C]186.206681356546[/C][C]749.5[/C][/ROW]
[ROW][C]6[/C][C]1341.4[/C][C]143.326467770738[/C][C]514.3[/C][/ROW]
[ROW][C]7[/C][C]1338.53333333333[/C][C]156.73203149634[/C][C]548.3[/C][/ROW]
[ROW][C]8[/C][C]1414.38333333333[/C][C]155.339720573583[/C][C]575.7[/C][/ROW]
[ROW][C]9[/C][C]1501.13333333333[/C][C]189.183755468944[/C][C]777[/C][/ROW]
[ROW][C]10[/C][C]1604.80833333333[/C][C]192.953684778749[/C][C]780.1[/C][/ROW]
[ROW][C]11[/C][C]1724.1[/C][C]194.695529201133[/C][C]646.5[/C][/ROW]
[ROW][C]12[/C][C]1737.75[/C][C]221.415912625169[/C][C]863.8[/C][/ROW]
[ROW][C]13[/C][C]1840.41666666667[/C][C]134.810101006317[/C][C]466.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35975&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35975&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
1925.12592.3742302219126334.3
21038.35833333333140.009236437739522.1
31031.54166666667112.960656532451384.2
4949.658333333333166.598971176204611.3
51295.25186.206681356546749.5
61341.4143.326467770738514.3
71338.53333333333156.73203149634548.3
81414.38333333333155.339720573583575.7
91501.13333333333189.183755468944777
101604.80833333333192.953684778749780.1
111724.1194.695529201133646.5
121737.75221.415912625169863.8
131840.41666666667134.810101006317466.4






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha63.1777640957108
beta0.0713145845761651
S.D.0.027767920461357
T-STAT2.56823641782644
p-value0.0261323707514615

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 63.1777640957108 \tabularnewline
beta & 0.0713145845761651 \tabularnewline
S.D. & 0.027767920461357 \tabularnewline
T-STAT & 2.56823641782644 \tabularnewline
p-value & 0.0261323707514615 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35975&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]63.1777640957108[/C][/ROW]
[ROW][C]beta[/C][C]0.0713145845761651[/C][/ROW]
[ROW][C]S.D.[/C][C]0.027767920461357[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.56823641782644[/C][/ROW]
[ROW][C]p-value[/C][C]0.0261323707514615[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35975&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35975&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)
alpha63.1777640957108
beta0.0713145845761651
S.D.0.027767920461357
T-STAT2.56823641782644
p-value0.0261323707514615






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha0.347212576484115
beta0.654094118568401
S.D.0.239311444782471
T-STAT2.7332337538765
p-value0.0194654896200249
Lambda0.345905881431599

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 0.347212576484115 \tabularnewline
beta & 0.654094118568401 \tabularnewline
S.D. & 0.239311444782471 \tabularnewline
T-STAT & 2.7332337538765 \tabularnewline
p-value & 0.0194654896200249 \tabularnewline
Lambda & 0.345905881431599 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35975&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]0.347212576484115[/C][/ROW]
[ROW][C]beta[/C][C]0.654094118568401[/C][/ROW]
[ROW][C]S.D.[/C][C]0.239311444782471[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.7332337538765[/C][/ROW]
[ROW][C]p-value[/C][C]0.0194654896200249[/C][/ROW]
[ROW][C]Lambda[/C][C]0.345905881431599[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35975&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35975&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)
alpha0.347212576484115
beta0.654094118568401
S.D.0.239311444782471
T-STAT2.7332337538765
p-value0.0194654896200249
Lambda0.345905881431599


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')