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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationMon, 13 Dec 2010 10:28:34 +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/2010/Dec/13/t129223605452aoohlazvw4pdn.htm/, Retrieved Mon, 06 May 2024 17:09:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108785, Retrieved Mon, 06 May 2024 17:09:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [Pearson Correlation] [2010-12-13 10:24:10] [f4dc4aa51d65be851b8508203d9f6001]
-    D    [Pearson Correlation] [- Pearson Correla...] [2010-12-13 10:28:34] [7a87ed98a7b21a29d6a45388a9b7b229] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
989236
1008380
1207763
1368839
1469798
1498721
1761769
1653214
1599104
1421179
1163995
1037735
1015407
1039210
1258049
1469445
1552346
1549144
1785895
1662335
1629440
1467430
1202209
1076982
1039367
1063449
1335135
1491602
1591972
1641248
1898849
1798580
1762444
1622044
1368955
1262973
1195650
1269530
1479279
1607819
1712466
1721766
1949843
1821326
1757802
1590367
1260647
1149235
1016367
1027885
1262159
1520854
1544144
1564709
1821776
1741365
1623386
1498658
1241822
1136029
Dataseries Y:
Download CSV
Histogram 
10489.94
10766.23
10503.76
10192.51
10467.48
10274.97
10640.91
10481.60
10568.70
10440.07
10805.87
10717.50
10864.86
10993.41
11109.32
11367.14
11168.31
11150.22
11185.68
11381.15
11679.07
12080.73
12221.93
12463.15
12621.69
12268.63
12354.35
13062.91
13627.64
13408.62
13211.99
13357.74
13895.63
13930.01
13371.72
13264.82
12650.36
12266.39
12262.89
12820.13
12638.32
11350.01
11378.02
11543.55
10850.66
9325.01
8829.04
8776.39
8000.86
7062.93
7608.92
8168.12
8500.33
8447.00
9171.61
9496.28
9712.28
9712.73
10344.84
10428.05

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108785&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108785&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108785&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean1437985.4511062.2496666667
Biased Variance71463737156.48082684936.66370656
Biased Standard Deviation267327.0228698941638.57763432391
Covariance90396225.7364237
Correlation0.202927626023469
Determination0.0411796214035208
T-Test1.57828905054509
p-value (2 sided)0.11993821226545
p-value (1 sided)0.059969106132725
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1437985.45 & 11062.2496666667 \tabularnewline
Biased Variance & 71463737156.4808 & 2684936.66370656 \tabularnewline
Biased Standard Deviation & 267327.022869894 & 1638.57763432391 \tabularnewline
Covariance & 90396225.7364237 \tabularnewline
Correlation & 0.202927626023469 \tabularnewline
Determination & 0.0411796214035208 \tabularnewline
T-Test & 1.57828905054509 \tabularnewline
p-value (2 sided) & 0.11993821226545 \tabularnewline
p-value (1 sided) & 0.059969106132725 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108785&T=1

[TABLE]
[ROW][C]Pearson Product Moment Correlation - Ungrouped Data[/C][/ROW]
[ROW][C]Statistic[/C][C]Variable X[/C][C]Variable Y[/C][/ROW]
[ROW][C]Mean[/C][C]1437985.45[/C][C]11062.2496666667[/C][/ROW]
[ROW][C]Biased Variance[/C][C]71463737156.4808[/C][C]2684936.66370656[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]267327.022869894[/C][C]1638.57763432391[/C][/ROW]
[ROW][C]Covariance[/C][C]90396225.7364237[/C][/ROW]
[ROW][C]Correlation[/C][C]0.202927626023469[/C][/ROW]
[ROW][C]Determination[/C][C]0.0411796214035208[/C][/ROW]
[ROW][C]T-Test[/C][C]1.57828905054509[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.11993821226545[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.059969106132725[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]58[/C][/ROW]
[ROW][C]Number of Observations[/C][C]60[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108785&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108785&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:

Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean1437985.4511062.2496666667
Biased Variance71463737156.48082684936.66370656
Biased Standard Deviation267327.0228698941638.57763432391
Covariance90396225.7364237
Correlation0.202927626023469
Determination0.0411796214035208
T-Test1.57828905054509
p-value (2 sided)0.11993821226545
p-value (1 sided)0.059969106132725
Degrees of Freedom58
Number of Observations60


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
bitmap(file='test1.png')
histx <- hist(x, plot=FALSE)
histy <- hist(y, plot=FALSE)
maxcounts <- max(c(histx$counts, histx$counts))
xrange <- c(min(x),max(x))
yrange <- c(min(y),max(y))
nf <- layout(matrix(c(2,0,1,3),2,2,byrow=TRUE), c(3,1), c(1,3), TRUE)
par(mar=c(4,4,1,1))
plot(x, y, xlim=xrange, ylim=yrange, xlab=xlab, ylab=ylab)
par(mar=c(0,4,1,1))
barplot(histx$counts, axes=FALSE, ylim=c(0, maxcounts), space=0)
par(mar=c(4,0,1,1))
barplot(histy$counts, axes=FALSE, xlim=c(0, maxcounts), space=0, horiz=TRUE)
dev.off()
lx = length(x)
makebiased = (lx-1)/lx
varx = var(x)*makebiased
vary = var(y)*makebiased
corxy <- cor.test(x,y,method='pearson')
cxy <- as.matrix(corxy$estimate)[1,1]
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Pearson Product Moment Correlation - Ungrouped Data',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistic',1,TRUE)
a<-table.element(a,'Variable X',1,TRUE)
a<-table.element(a,'Variable Y',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm','Mean',''),header=TRUE)
a<-table.element(a,mean(x))
a<-table.element(a,mean(y))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased.htm','Biased Variance',''),header=TRUE)
a<-table.element(a,varx)
a<-table.element(a,vary)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('biased1.htm','Biased Standard Deviation',''),header=TRUE)
a<-table.element(a,sqrt(varx))
a<-table.element(a,sqrt(vary))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('covariance.htm','Covariance',''),header=TRUE)
a<-table.element(a,cov(x,y),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('pearson_correlation.htm','Correlation',''),header=TRUE)
a<-table.element(a,cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('coeff_of_determination.htm','Determination',''),header=TRUE)
a<-table.element(a,cxy*cxy,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('ttest_statistic.htm','T-Test',''),header=TRUE)
a<-table.element(a,as.matrix(corxy$statistic)[1,1],2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value (2 sided)',header=TRUE)
a<-table.element(a,(p2 <- as.matrix(corxy$p.value)[1,1]),2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value (1 sided)',header=TRUE)
a<-table.element(a,p2/2,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Degrees of Freedom',header=TRUE)
a<-table.element(a,lx-2,2)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of Observations',header=TRUE)
a<-table.element(a,lx,2)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')