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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 computationSun, 21 Dec 2008 09:53:10 -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/21/t122987842330jg7qex20rcwdu.htm/, Retrieved Sat, 18 May 2024 10:37:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35683, Retrieved Sat, 18 May 2024 10:37:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact174

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [Investigating ass...] [2007-10-22 22:08:56] [8cd6641b921d30ebe00b648d1481bba0]
F    D  [Pearson Correlation] [Correlatie tussen...] [2008-10-21 00:01:19] [504b73e6de93b01331326637b3288ad4]
F    D    [Pearson Correlation] [Correlatie tussen...] [2008-10-21 00:32:08] [504b73e6de93b01331326637b3288ad4]
-    D      [Pearson Correlation] [Pearsons - invoer...] [2008-12-21 16:47:00] [504b73e6de93b01331326637b3288ad4]
-    D          [Pearson Correlation] [Pearsons - Uitvoe...] [2008-12-21 16:53:10] [ba85d9d0a82357dd3edf208eef933423] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15916,4
16535,9
15796
14418,6
15044,5
14944,2
16754,8
14254
15454,9
15644,8
14568,3
12520,2
14803
15873,2
14755,3
12875,1
14291,1
14205,3
15859,4
15258,9
15498,6
15106,5
15023,6
12083
15761,3
16943
15070,3
13659,6
14768,9
14725,1
15998,1
15370,6
14956,9
15469,7
15101,8
11703,7
16283,6
16726,5
14968,9
14861
14583,3
15305,8
17903,9
16379,4
15420,3
17870,5
15912,8
13866,5
17823,2
17872
17420,4
16704,4
15991,2
16583,6
19123,5
17838,7
17209,4
18586,5
16258,1
15141,6
19202,1
17746,5
19090,1
18040,3
17515,5
17751,8
21072,4
17170
19439,5
19795,4
17574,9
16165,4
19464,6
19932,1
19961,2
17343,4
18924,2
18574,1
21350,6
18594,6
19823,1
20844,4
19640,2
17735,4
19813,6
22238,5
20682,2
17818,6
21872,1
22117
21865,9
23451,3
20953,7
22497,3
Dataseries Y:
Download CSV
Histogram 
1384.2
1368.9
-275.1
-408.9
-37.5
171.5
671.8
-18.5
231.6
747.5
1505.7
-83.6
1173.2
1452.1
777
-52.8
861.2
735.2
1073.6
966.9
1189.8
1093.5
1782.7
-70.4
1471.6
1273.8
900.8
-910.2
299.8
460.2
677.2
937.1
1265.4
1275.6
1582.6
-154.2
1667.6
1083.1
891.7
-26.5
423.4
662.8
711.4
993.3
1133.2
343.9
1415.8
-531.8
1193.6
1201.3
805.6
-164.8
327.3
223.7
675.8
949.7
704.4
265.6
1206
-558.2
1066.8
977.8
207.1
-980.7
-586.4
-24.3
-417.5
104.7
749.5
842.3
1176
-730.3
911.6
662.1
539.1
-236
286.9
497.4
912
519.4
260.1
945.2
412.7
-54.2
592.8
179.9
-548.6
-1685.8
-2041
-1048.7
-1708.4
-1550.7
-1650.2
-911.3

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=35683&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=35683&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35683&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
Mean17018.2095744681410.494680851064
Biased Variance6262016.65405727683518.980290856
Biased Standard Deviation2502.40217672085826.75206700126
Covariance-670362.958228094
Correlation-0.320577254512074
Determination0.102769776110499
T-Test-3.24619550105393
p-value (2 sided)0.00163212520348077
p-value (1 sided)0.000816062601740384
Degrees of Freedom92
Number of Observations94

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 17018.2095744681 & 410.494680851064 \tabularnewline
Biased Variance & 6262016.65405727 & 683518.980290856 \tabularnewline
Biased Standard Deviation & 2502.40217672085 & 826.75206700126 \tabularnewline
Covariance & -670362.958228094 \tabularnewline
Correlation & -0.320577254512074 \tabularnewline
Determination & 0.102769776110499 \tabularnewline
T-Test & -3.24619550105393 \tabularnewline
p-value (2 sided) & 0.00163212520348077 \tabularnewline
p-value (1 sided) & 0.000816062601740384 \tabularnewline
Degrees of Freedom & 92 \tabularnewline
Number of Observations & 94 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35683&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]17018.2095744681[/C][C]410.494680851064[/C][/ROW]
[ROW][C]Biased Variance[/C][C]6262016.65405727[/C][C]683518.980290856[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2502.40217672085[/C][C]826.75206700126[/C][/ROW]
[ROW][C]Covariance[/C][C]-670362.958228094[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.320577254512074[/C][/ROW]
[ROW][C]Determination[/C][C]0.102769776110499[/C][/ROW]
[ROW][C]T-Test[/C][C]-3.24619550105393[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00163212520348077[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.000816062601740384[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]92[/C][/ROW]
[ROW][C]Number of Observations[/C][C]94[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35683&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35683&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
Mean17018.2095744681410.494680851064
Biased Variance6262016.65405727683518.980290856
Biased Standard Deviation2502.40217672085826.75206700126
Covariance-670362.958228094
Correlation-0.320577254512074
Determination0.102769776110499
T-Test-3.24619550105393
p-value (2 sided)0.00163212520348077
p-value (1 sided)0.000816062601740384
Degrees of Freedom92
Number of Observations94


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')