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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 computationFri, 17 Oct 2008 11:40:27 -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/2008/Oct/17/t1224265387hkb833qq3d19ev3.htm/, Retrieved Fri, 17 May 2024 11:45:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16518, Retrieved Fri, 17 May 2024 11:45:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact162

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]
-    D    [Pearson Correlation] [Relatie aantal ge...] [2008-10-17 17:40:27] [3dc594a6c62226e1e98766c4d385bfaa] [Current]
-    D      [Pearson Correlation] [relatie aantal ge...] [2008-10-17 17:44:05] [c45c87b96bbf32ffc2144fc37d767b2e]
-    D      [Pearson Correlation] [relatie aantal ge...] [2008-10-17 17:46:26] [c45c87b96bbf32ffc2144fc37d767b2e]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2293
2045
1532
1333
1583
1712
2641
2267
2126
2231
1517
2010
2628
2115
1829
1636
1787
2122
2620
2555
2337
2524
1801
2417
2389
2266
2135
1755
1907
2178
2345
2674
2765
2786
2004
2589
2739
2700
2459
1965
2152
2379
2930
2691
2852
2752
1787
2580
2604
2532
2265
1745
1914
2148
2466
2498
2512
2458
1825
2267
2364
2328
2034
1587
1633
Dataseries Y:
Download CSV
Histogram 
4348
3603
2700
2640
2916
3180
4151
4023
3431
3874
2617
3580
5267
3832
3441
3228
3397
3971
4625
4486
4131
4686
3174
4282
4209
4158
3936
3149
3623
4230
4443
4810
4853
5050
3553
4674
5412
5131
4856
3980
4431
4606
5352
4640
5170
4824
3280
4706
4909
5092
4911
3824
4214
4449
4486
4777
5132
4522
3295
4281
4590
4623
4075
3398
3029

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=16518&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=16518&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16518&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
Mean2224.923076923084157.93846153846
Biased Variance149550.994082840517122.457751479
Biased Standard Deviation386.718236036058719.112270616681
Covariance261885.370192308
Correlation0.927227927370033
Determination0.859751629294928
T-Test19.6520502591699
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom63
Number of Observations65

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 2224.92307692308 & 4157.93846153846 \tabularnewline
Biased Variance & 149550.994082840 & 517122.457751479 \tabularnewline
Biased Standard Deviation & 386.718236036058 & 719.112270616681 \tabularnewline
Covariance & 261885.370192308 \tabularnewline
Correlation & 0.927227927370033 \tabularnewline
Determination & 0.859751629294928 \tabularnewline
T-Test & 19.6520502591699 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 63 \tabularnewline
Number of Observations & 65 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16518&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]2224.92307692308[/C][C]4157.93846153846[/C][/ROW]
[ROW][C]Biased Variance[/C][C]149550.994082840[/C][C]517122.457751479[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]386.718236036058[/C][C]719.112270616681[/C][/ROW]
[ROW][C]Covariance[/C][C]261885.370192308[/C][/ROW]
[ROW][C]Correlation[/C][C]0.927227927370033[/C][/ROW]
[ROW][C]Determination[/C][C]0.859751629294928[/C][/ROW]
[ROW][C]T-Test[/C][C]19.6520502591699[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]63[/C][/ROW]
[ROW][C]Number of Observations[/C][C]65[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16518&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16518&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
Mean2224.923076923084157.93846153846
Biased Variance149550.994082840517122.457751479
Biased Standard Deviation386.718236036058719.112270616681
Covariance261885.370192308
Correlation0.927227927370033
Determination0.859751629294928
T-Test19.6520502591699
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom63
Number of Observations65


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')