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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 computationTue, 27 Oct 2009 14:06:32 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/27/t1256674142i2xuv1g7bhu2ap2.htm/, Retrieved Tue, 07 May 2024 14:42:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51208, Retrieved Tue, 07 May 2024 14:42:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsws4p2.2b
Estimated Impact114

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2009-10-27 20:06:32] [9ea4b07b6662a0f40f92decdf1e3b5d5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4.1209
8.1796
6.5025
5.1529
5.1076
6.6049
9.4249
7.6176
6.3001
8.2369
9.8596
9.6721
9.9856
6.1009
6.6049
8.3521
6.9169
5.6644
2.8561
3.8416
4.7961
3.4969
2.56
2.6569
1.4884
1.4641
2.2201
2.6896
2.7556
3.1329
3.3124
3.1684
1.6384
1.6641
1.8769
1.2544
2.2801
5.0176
8.6436
9.5481
11.9716
13.2496
19.2721
17.2225
27.1441
33.64
34.9281
29.0521
29.8116
22.2784
9.8596
6.9169
5.3824
3.7249
0.3844
0.36
0.1369
1.21
2.8224
Dataseries Y:
Download CSV
Histogram 
2849.27
2921.44
2981.85
3080.58
3106.22
3119.31
3061.26
3097.31
3161.69
3257.16
3277.01
3295.32
3363.99
3494.17
3667.03
3813.06
3917.96
3895.51
3801.06
3570.12
3701.61
3862.27
3970.1
4138.52
4199.75
4290.89
4443.91
4502.64
4356.98
4591.27
4696.96
4621.4
4562.84
4202.52
4296.49
4435.23
4105.18
4116.68
3844.49
3720.98
3674.4
3857.62
3801.06
3504.37
3032.6
3047.03
2962.34
2197.82
2014.45
1862.83
1905.41
1810.99
1670.07
1864.44
2052.02
2029.6
2070.83
2293.41
2443.27

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=51208&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=51208&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51208&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
Mean8.002276271186443381.1286440678
Biased Variance68.7325662597759714762.177181212
Biased Standard Deviation8.29051061514162845.436086987782
Covariance-2230.57998206721
Correlation-0.312846802875636
Determination0.0978731220695072
T-Test-2.48676838680743
p-value (2 sided)0.0158433620951807
p-value (1 sided)0.00792168104759033
Degrees of Freedom57
Number of Observations59

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 8.00227627118644 & 3381.1286440678 \tabularnewline
Biased Variance & 68.7325662597759 & 714762.177181212 \tabularnewline
Biased Standard Deviation & 8.29051061514162 & 845.436086987782 \tabularnewline
Covariance & -2230.57998206721 \tabularnewline
Correlation & -0.312846802875636 \tabularnewline
Determination & 0.0978731220695072 \tabularnewline
T-Test & -2.48676838680743 \tabularnewline
p-value (2 sided) & 0.0158433620951807 \tabularnewline
p-value (1 sided) & 0.00792168104759033 \tabularnewline
Degrees of Freedom & 57 \tabularnewline
Number of Observations & 59 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51208&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]8.00227627118644[/C][C]3381.1286440678[/C][/ROW]
[ROW][C]Biased Variance[/C][C]68.7325662597759[/C][C]714762.177181212[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]8.29051061514162[/C][C]845.436086987782[/C][/ROW]
[ROW][C]Covariance[/C][C]-2230.57998206721[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.312846802875636[/C][/ROW]
[ROW][C]Determination[/C][C]0.0978731220695072[/C][/ROW]
[ROW][C]T-Test[/C][C]-2.48676838680743[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0158433620951807[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00792168104759033[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]57[/C][/ROW]
[ROW][C]Number of Observations[/C][C]59[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51208&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51208&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
Mean8.002276271186443381.1286440678
Biased Variance68.7325662597759714762.177181212
Biased Standard Deviation8.29051061514162845.436086987782
Covariance-2230.57998206721
Correlation-0.312846802875636
Determination0.0978731220695072
T-Test-2.48676838680743
p-value (2 sided)0.0158433620951807
p-value (1 sided)0.00792168104759033
Degrees of Freedom57
Number of Observations59


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')