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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 13:09:52 -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/t1256670643czm2ok7m7hee9dq.htm/, Retrieved Tue, 07 May 2024 07:10:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51146, Retrieved Tue, 07 May 2024 07:10:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSHWWS4V2 model 2
Estimated Impact125

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Explorative Data Analysis] [Bivariate EDA wer...] [2009-10-27 18:39:55] [4395c69e961f9a13a0559fd2f0a72538]
-    D  [Bivariate Explorative Data Analysis] [Bivariate EDA lnY...] [2009-10-27 19:01:52] [4395c69e961f9a13a0559fd2f0a72538]
- RMP     [Bivariate Kernel Density Estimation] [Bivariate Kernel ...] [2009-10-27 19:07:17] [4395c69e961f9a13a0559fd2f0a72538]
- RMPD        [Pearson Correlation] [Pearson Correlati...] [2009-10-27 19:09:52] [d1081bd6cdf1fed9ed45c42dbd523bf1] [Current]
- RM D          [Kendall tau Rank Correlation] [Kendall Rank Corr...] [2009-10-27 19:13:14] [4395c69e961f9a13a0559fd2f0a72538]
-    D            [Kendall tau Rank Correlation] [Kendall Rank Corr...] [2009-10-28 17:25:16] [4395c69e961f9a13a0559fd2f0a72538]
-    D              [Kendall tau Rank Correlation] [Kendall Rank Corr...] [2009-10-28 17:51:25] [4395c69e961f9a13a0559fd2f0a72538]
-    D          [Pearson Correlation] [Pearson Correlati...] [2009-10-28 17:20:47] [4395c69e961f9a13a0559fd2f0a72538]
-    D            [Pearson Correlation] [Pearson correlati...] [2009-10-28 17:48:03] [4395c69e961f9a13a0559fd2f0a72538]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.987874348
2.028148247
2.014903021
2.028148247
2.066862759
2.066862759
2.091864062
2.104134154
2.079441542
2.014903021
1.916922612
1.871802177
1.887069649
2.028148247
2.079441542
2.091864062
2.041220329
2.014903021
2.028148247
2.054123734
2.054123734
2.054123734
2.014903021
2.014903021
1.960094784
2.014903021
2.014903021
2.028148247
2.041220329
2.041220329
2.066862759
2.091864062
2.104134154
2.104134154
2.104134154
2.066862759
1.987874348
1.931521412
1.887069649
1.902107526
1.931521412
1.945910149
1.960094784
1.974081026
1.960094784
1.931521412
1.945910149
1.916922612
1.85629799
1.902107526
1.887069649
1.85629799
1.840549633
1.824549292
1.871802177
1.916922612
1.916922612
1.85629799
1.808288771
1.757857918
1.808288771
1.974081026
1.987874348
1.931521412
1.808288771
1.757857918
1.824549292
1.960094784
2.041220329
2.066862759
2.041220329
2.00148
2.014903021
Dataseries Y:
Download CSV
Histogram 
2.066862759
2.208274414
2.240709689
2.240709689
2.208274414
2.197224577
2.2300144
2.292534757
2.282382386
2.2300144
2.116255515
2.079441542
2.140066163
2.341805806
2.406945108
2.388762789
2.302585093
2.219203484
2.219203484
2.251291799
2.261763098
2.251291799
2.208274414
2.186051277
2.197224577
2.312535424
2.332143895
2.32238772
2.261763098
2.219203484
2.2300144
2.240709689
2.240709689
2.219203484
2.197224577
2.197224577
2.197224577
2.282382386
2.302585093
2.282382386
2.2300144
2.197224577
2.197224577
2.208274414
2.208274414
2.208274414
2.219203484
2.174751721
2.116255515
2.128231706
2.091864062
2.041220329
2.066862759
2.066862759
2.079441542
2.066862759
2.028148247
1.960094784
1.916922612
1.871802177
1.931521412
2.104134154
2.163323026
2.116255515
2.066862759
2.014903021
2.054123734
2.116255515
2.128231706
2.104134154
2.041220329
1.974081026
1.987874348

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51146&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51146&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51146&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean1.973440510219182.17103553236986
Biased Variance0.008251085166108840.0123115005486041
Biased Standard Deviation0.09083548406932640.110957201427416
Covariance0.0068145808078912
Correlation0.666864736607402
Determination0.44470857693046
T-Test7.54060938777224
p-value (2 sided)1.18602905274656e-10
p-value (1 sided)5.93014526373281e-11
Degrees of Freedom71
Number of Observations73

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1.97344051021918 & 2.17103553236986 \tabularnewline
Biased Variance & 0.00825108516610884 & 0.0123115005486041 \tabularnewline
Biased Standard Deviation & 0.0908354840693264 & 0.110957201427416 \tabularnewline
Covariance & 0.0068145808078912 \tabularnewline
Correlation & 0.666864736607402 \tabularnewline
Determination & 0.44470857693046 \tabularnewline
T-Test & 7.54060938777224 \tabularnewline
p-value (2 sided) & 1.18602905274656e-10 \tabularnewline
p-value (1 sided) & 5.93014526373281e-11 \tabularnewline
Degrees of Freedom & 71 \tabularnewline
Number of Observations & 73 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51146&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]1.97344051021918[/C][C]2.17103553236986[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.00825108516610884[/C][C]0.0123115005486041[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.0908354840693264[/C][C]0.110957201427416[/C][/ROW]
[ROW][C]Covariance[/C][C]0.0068145808078912[/C][/ROW]
[ROW][C]Correlation[/C][C]0.666864736607402[/C][/ROW]
[ROW][C]Determination[/C][C]0.44470857693046[/C][/ROW]
[ROW][C]T-Test[/C][C]7.54060938777224[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]1.18602905274656e-10[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]5.93014526373281e-11[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]71[/C][/ROW]
[ROW][C]Number of Observations[/C][C]73[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51146&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51146&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
Mean1.973440510219182.17103553236986
Biased Variance0.008251085166108840.0123115005486041
Biased Standard Deviation0.09083548406932640.110957201427416
Covariance0.0068145808078912
Correlation0.666864736607402
Determination0.44470857693046
T-Test7.54060938777224
p-value (2 sided)1.18602905274656e-10
p-value (1 sided)5.93014526373281e-11
Degrees of Freedom71
Number of Observations73


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')