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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 computationThu, 18 Dec 2008 14:25:46 -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/18/t1229635596wabnpe1sunx0i16.htm/, Retrieved Sat, 11 May 2024 09:50:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34957, Retrieved Sat, 11 May 2024 09:50:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordscorr 1
Estimated Impact158

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Pearson Correlation] [Q3 Clothing produ...] [2007-10-20 14:22:11] [b731da8b544846036771bbf9bf2f34ce]
F    D  [Pearson Correlation] [Clothing producti...] [2008-10-20 16:24:29] [fe7291e888d31b8c4db0b24d6c0f75c6]
-    D      [Pearson Correlation] [corr 1] [2008-12-18 21:25:46] [783db4b4a0f63b73ca8b14666b7f4329] [Current]
-    D        [Pearson Correlation] [cor 2] [2008-12-18 21:49:17] [fe7291e888d31b8c4db0b24d6c0f75c6]
-    D        [Pearson Correlation] [COR 3] [2008-12-18 21:52:20] [fe7291e888d31b8c4db0b24d6c0f75c6]
-    D        [Pearson Correlation] [cor 3] [2008-12-18 22:32:14] [fe7291e888d31b8c4db0b24d6c0f75c6]
-    D        [Pearson Correlation] [1] [2008-12-22 18:34:11] [fe7291e888d31b8c4db0b24d6c0f75c6]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
519164
517009
509933
509127
500857
506971
569323
579714
577992
565464
547344
554788
562325
560854
555332
543599
536662
542722
593530
610763
612613
611324
594167
595454
590865
589379
584428
573100
567456
569028
620735
628884
628232
612117
595404
597141
593408
590072
579799
574205
572775
572942
619567
625809
619916
587625
565742
557274
560576
548854
531673
525919
511038
498662
555362
564591
541657
527070
509846
514258
516922
507561
492622
490243
469357
477580
528379
533590
517945
506174
501866
Dataseries Y:
Download CSV
Histogram 
15
12
3
20
27
22
19
21
29
18
31
31
35
38
36
33
29
37
28
32
31
24
25
27
27
29
33
26
16
15
13
18
8
21
21
25
28
27
24
24
24
28
31
26
28
34
33
24
30
31
28
35
33
34
31
21
21
22
9
15
13
17
19
14
8
3
0
10
12
9
9

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34957&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34957&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34957&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'George Udny Yule' @ 72.249.76.132






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean556685.6197183122.9577464788732
Biased Variance1651897888.7990581.8432850624876
Biased Standard Deviation40643.54670546179.04672786495137
Covariance135980.297987928
Correlation0.364613340245117
Determination0.132942887884702
T-Test3.25261939417221
p-value (2 sided)0.00177125778509124
p-value (1 sided)0.00088562889254562
Degrees of Freedom69
Number of Observations71

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 556685.61971831 & 22.9577464788732 \tabularnewline
Biased Variance & 1651897888.79905 & 81.8432850624876 \tabularnewline
Biased Standard Deviation & 40643.5467054617 & 9.04672786495137 \tabularnewline
Covariance & 135980.297987928 \tabularnewline
Correlation & 0.364613340245117 \tabularnewline
Determination & 0.132942887884702 \tabularnewline
T-Test & 3.25261939417221 \tabularnewline
p-value (2 sided) & 0.00177125778509124 \tabularnewline
p-value (1 sided) & 0.00088562889254562 \tabularnewline
Degrees of Freedom & 69 \tabularnewline
Number of Observations & 71 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34957&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]556685.61971831[/C][C]22.9577464788732[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1651897888.79905[/C][C]81.8432850624876[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]40643.5467054617[/C][C]9.04672786495137[/C][/ROW]
[ROW][C]Covariance[/C][C]135980.297987928[/C][/ROW]
[ROW][C]Correlation[/C][C]0.364613340245117[/C][/ROW]
[ROW][C]Determination[/C][C]0.132942887884702[/C][/ROW]
[ROW][C]T-Test[/C][C]3.25261939417221[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00177125778509124[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00088562889254562[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]69[/C][/ROW]
[ROW][C]Number of Observations[/C][C]71[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34957&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34957&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
Mean556685.6197183122.9577464788732
Biased Variance1651897888.7990581.8432850624876
Biased Standard Deviation40643.54670546179.04672786495137
Covariance135980.297987928
Correlation0.364613340245117
Determination0.132942887884702
T-Test3.25261939417221
p-value (2 sided)0.00177125778509124
p-value (1 sided)0.00088562889254562
Degrees of Freedom69
Number of Observations71


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')