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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 computationSat, 06 Dec 2008 07:47:15 -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/06/t1228574865atg3ifbgs7wxgem.htm/, Retrieved Fri, 17 May 2024 06:38:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29666, Retrieved Fri, 17 May 2024 06:38:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact164

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Back to Back Histogram] [] [2008-12-06 14:15:54] [4c8dfb519edec2da3492d7e6be9a5685]
-   PD  [Back to Back Histogram] [] [2008-12-06 14:41:51] [4c8dfb519edec2da3492d7e6be9a5685]
- RMP       [Pearson Correlation] [] [2008-12-06 14:47:15] [6d40a467de0f28bd2350f82ac9522c51] [Current]
-    D        [Pearson Correlation] [] [2008-12-06 14:54:12] [4c8dfb519edec2da3492d7e6be9a5685]
-    D          [Pearson Correlation] [] [2008-12-06 14:58:38] [4c8dfb519edec2da3492d7e6be9a5685]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12055
12113
9617
12646
13581
12162
10970
11880
11888
12927
12300
12093
12381
12197
9455
13168
13428
11981
11885
11692
12234
14341
13131
12421
14286
12865
11160
14316
14389
14014
13419
12770
13316
15333
14243
13824
14963
13203
12199
15509
14200
15170
14058
13786
14148
16542
13588
15582
15803
14131
12923
15612
16034
16037
14038
15331
15038
17402
14993
16044
16930
15921
14417
15961
17852
16484
14216
17430
17840
17629
Dataseries Y:
Download CSV
Histogram 
15107
15024
12083
15761
16943
15070
13660
14769
14725
15998
15371
14957
15470
15102
11704
16284
16727
14969
14861
14583
15306
17904
16379
15420
17871
15913
13867
17823
17872
17422
16705
15991
16584
19124
17839
17209
18587
16258
15142
19202
17747
19090
18040
17516
17752
21073
17170
19440
19795
17575
16165
19465
19932
19961
17343
18924
18574
21351
18595
19823
20844
19640
17735
19814
22239
20682
17819
21872
22117
21866

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 & 0 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29666&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]0 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=29666&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29666&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 time0 seconds
R Server'George Udny Yule' @ 72.249.76.132






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean13964.214285714317393.5
Biased Variance3558203.854081635501545.76428571
Biased Standard Deviation1886.320188642862345.53741481259
Covariance4480405.07971014
Correlation0.998183884114919
Determination0.996371066506746
T-Test136.639261355877
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom68
Number of Observations70

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 13964.2142857143 & 17393.5 \tabularnewline
Biased Variance & 3558203.85408163 & 5501545.76428571 \tabularnewline
Biased Standard Deviation & 1886.32018864286 & 2345.53741481259 \tabularnewline
Covariance & 4480405.07971014 \tabularnewline
Correlation & 0.998183884114919 \tabularnewline
Determination & 0.996371066506746 \tabularnewline
T-Test & 136.639261355877 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 68 \tabularnewline
Number of Observations & 70 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29666&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]13964.2142857143[/C][C]17393.5[/C][/ROW]
[ROW][C]Biased Variance[/C][C]3558203.85408163[/C][C]5501545.76428571[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1886.32018864286[/C][C]2345.53741481259[/C][/ROW]
[ROW][C]Covariance[/C][C]4480405.07971014[/C][/ROW]
[ROW][C]Correlation[/C][C]0.998183884114919[/C][/ROW]
[ROW][C]Determination[/C][C]0.996371066506746[/C][/ROW]
[ROW][C]T-Test[/C][C]136.639261355877[/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]68[/C][/ROW]
[ROW][C]Number of Observations[/C][C]70[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29666&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29666&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
Mean13964.214285714317393.5
Biased Variance3558203.854081635501545.76428571
Biased Standard Deviation1886.320188642862345.53741481259
Covariance4480405.07971014
Correlation0.998183884114919
Determination0.996371066506746
T-Test136.639261355877
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom68
Number of Observations70


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')