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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 computationThu, 06 Dec 2007 07:19:31 -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/2007/Dec/06/t1196950329s38neun0a0o7rxo.htm/, Retrieved Fri, 03 May 2024 06:41:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2621, Retrieved Fri, 03 May 2024 06:41:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact180

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Pearson correlation] [2007-12-06 14:19:31] [6d644d07a16de69cd360f404f1ea3fa3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
18.33
22.6
24.9
24.8
23.8
25.1
26
27.4
27.3
24.3
28.4
24.4
30.3
31.5
29.8
25.3
25.6
26.7
27.4
28.6
26.3
28.5
28.4
29.4
30.3
29.6
32.1
32.4
36.3
34.6
36.3
40.3
40.4
45.4
39
35.7
40.2
41.7
49.1
49.6
47
52
53.1
57.8
57.9
54.6
51.3
52.7
58.5
56.6
57.9
64.4
65.1
64.6
68.9
68.8
59.3
55
55.4
58
50.8
54.6
58.6
63.6
64.5
66.9
71.9
68.7
74.2
75.8
Dataseries Y:
Download CSV
Histogram 
0.8833
0.8700
0.8758
0.8858
0.9170
0.9554
0.9922
0.9778
0.9808
0.9811
1.0014
1.0183
1.0622
1.0773
1.0807
1.0848
1.1582
1.1663
1.1372
1.1139
1.1222
1.1692
1.1702
1.2286
1.2613
1.2646
1.2262
1.1985
1.2007
1.2138
1.2266
1.2176
1.2218
1.2490
1.2991
1.3408
1.3119
1.3014
1.3201
1.2938
1.2694
1.2165
1.2037
1.2292
1.2256
1.2015
1.1786
1.1856
1.2103
1.1938
1.2020
1.2271
1.2770
1.2650
1.2684
1.2811
1.2727
1.2611
1.2881
1.3213
1.2999
1.3074
1.3242
1.3516
1.3511
1.3419
1.3716
1.3622
1.3896
1.4227

Tables (Output of Computation)





Summary of compuational 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 compuational 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=2621&T=0

[TABLE]
[ROW][C]Summary of compuational 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=2621&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2621&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 compuational 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
Mean43.66614285714291.19081571428571
Biased Variance259.8962379795920.0183734253244898
Biased Standard Deviation16.12129765185150.135548608714696
Covariance1.68211887308489
Correlation0.758774406057424
Determination0.575738599287796
T-Test9.60617223384508
p-value (2 sided)2.75335310107039e-14
p-value (1 sided)1.37667655053519e-14
Degrees of Freedom68
Number of Observations70

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 43.6661428571429 & 1.19081571428571 \tabularnewline
Biased Variance & 259.896237979592 & 0.0183734253244898 \tabularnewline
Biased Standard Deviation & 16.1212976518515 & 0.135548608714696 \tabularnewline
Covariance & 1.68211887308489 \tabularnewline
Correlation & 0.758774406057424 \tabularnewline
Determination & 0.575738599287796 \tabularnewline
T-Test & 9.60617223384508 \tabularnewline
p-value (2 sided) & 2.75335310107039e-14 \tabularnewline
p-value (1 sided) & 1.37667655053519e-14 \tabularnewline
Degrees of Freedom & 68 \tabularnewline
Number of Observations & 70 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2621&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]43.6661428571429[/C][C]1.19081571428571[/C][/ROW]
[ROW][C]Biased Variance[/C][C]259.896237979592[/C][C]0.0183734253244898[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]16.1212976518515[/C][C]0.135548608714696[/C][/ROW]
[ROW][C]Covariance[/C][C]1.68211887308489[/C][/ROW]
[ROW][C]Correlation[/C][C]0.758774406057424[/C][/ROW]
[ROW][C]Determination[/C][C]0.575738599287796[/C][/ROW]
[ROW][C]T-Test[/C][C]9.60617223384508[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.75335310107039e-14[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.37667655053519e-14[/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=2621&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2621&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
Mean43.66614285714291.19081571428571
Biased Variance259.8962379795920.0183734253244898
Biased Standard Deviation16.12129765185150.135548608714696
Covariance1.68211887308489
Correlation0.758774406057424
Determination0.575738599287796
T-Test9.60617223384508
p-value (2 sided)2.75335310107039e-14
p-value (1 sided)1.37667655053519e-14
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')