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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 10:24:10 +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/t1292235880ki61b3ffk0l00l8.htm/, Retrieved Mon, 06 May 2024 16:00:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108781, Retrieved Mon, 06 May 2024 16:00:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130

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] [7a87ed98a7b21a29d6a45388a9b7b229] [Current]
-    D    [Pearson Correlation] [- Pearson Correla...] [2010-12-13 10:28:34] [f4dc4aa51d65be851b8508203d9f6001]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
989 236
1 008 380
1 207 763
1 368 839
1 469 798
1 498 721
1 761 769
1 653 214
1 599 104
1 421 179
1 163 995
1 037 735
1 015 407
1 039 210
1 258 049
1 469 445
1 552 346
1 549 144
1 785 895
1 662 335
1 629 440
1 467 430
1 202 209
1 076 982
1 039 367
1 063 449
1 335 135
1 491 602
1 591 972
1 641 248
1 898 849
1 798 580
1 762 444
1 622 044
1 368 955
1 262 973
1 195 650
1 269 530
1 479 279
1 607 819
1 712 466
1 721 766
1 949 843
1 821 326
1 757 802
1 590 367
1 260 647
1 149 235
1 016 367
1 027 885
1 262 159
1 520 854
1 544 144
1 564 709
1 821 776
1 741 365
1 623 386
1 498 658
1 241 822
1 136 029
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 time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108781&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]1 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=108781&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108781&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 time1 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=108781&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=108781&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108781&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')