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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationMon, 16 May 2011 15:59:01 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/May/16/t13055612935x04lbegj4jn42w.htm/, Retrieved Mon, 13 May 2024 10:42:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121639, Retrieved Mon, 13 May 2024 10:42:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [4th grade wkce an...] [2011-05-16 15:59:01] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
523
468
468
457
559
456
508
475
508
491
466
472
526
495
428
531
508
591
461
521
485
487
Dataseries Y:
Download CSV
Histogram 
36
23
27
23
47
30
24
41
35
32
35
41
39
19
19
28
35
51
25
35
33
35

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'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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121639&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121639&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121639&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean494.72727272727332.4090909090909
Biased Variance1343.2892561983568.7871900826446
Biased Standard Deviation36.65091071444678.29380431904712
Covariance210.593073593074
Correlation0.661305510930812
Determination0.437324978787463
T-Test3.94265087568109
p-value (2 sided)0.000804458821964005
p-value (1 sided)0.000402229410982002
Degrees of Freedom20
Number of Observations22

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 494.727272727273 & 32.4090909090909 \tabularnewline
Biased Variance & 1343.28925619835 & 68.7871900826446 \tabularnewline
Biased Standard Deviation & 36.6509107144467 & 8.29380431904712 \tabularnewline
Covariance & 210.593073593074 \tabularnewline
Correlation & 0.661305510930812 \tabularnewline
Determination & 0.437324978787463 \tabularnewline
T-Test & 3.94265087568109 \tabularnewline
p-value (2 sided) & 0.000804458821964005 \tabularnewline
p-value (1 sided) & 0.000402229410982002 \tabularnewline
Degrees of Freedom & 20 \tabularnewline
Number of Observations & 22 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121639&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]494.727272727273[/C][C]32.4090909090909[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1343.28925619835[/C][C]68.7871900826446[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]36.6509107144467[/C][C]8.29380431904712[/C][/ROW]
[ROW][C]Covariance[/C][C]210.593073593074[/C][/ROW]
[ROW][C]Correlation[/C][C]0.661305510930812[/C][/ROW]
[ROW][C]Determination[/C][C]0.437324978787463[/C][/ROW]
[ROW][C]T-Test[/C][C]3.94265087568109[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.000804458821964005[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.000402229410982002[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]20[/C][/ROW]
[ROW][C]Number of Observations[/C][C]22[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121639&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121639&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
Mean494.72727272727332.4090909090909
Biased Variance1343.2892561983568.7871900826446
Biased Standard Deviation36.65091071444678.29380431904712
Covariance210.593073593074
Correlation0.661305510930812
Determination0.437324978787463
T-Test3.94265087568109
p-value (2 sided)0.000804458821964005
p-value (1 sided)0.000402229410982002
Degrees of Freedom20
Number of Observations22


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')