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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 computationMon, 20 Dec 2010 15:44:31 +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/2010/Dec/20/t1292859845aheusjbhfr0uuit.htm/, Retrieved Fri, 03 May 2024 20:18:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113000, Retrieved Fri, 03 May 2024 20:18:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [] [correlation betwe...] [1970-01-01 00:00:00] [1df589bc3feb749f1946d8c1ee38b85f]
- RM D    [Pearson Correlation] [correlation betwe...] [2010-12-20 15:44:31] [36a5183bc8f6439b2481209b0fbe6bda] [Current]
- RMPD      [Variance Reduction Matrix] [Paper: VRM] [2010-12-20 16:52:21] [1df589bc3feb749f1946d8c1ee38b85f]
- RMP         [(Partial) Autocorrelation Function] [paper: autocorrel...] [2010-12-20 17:36:06] [1df589bc3feb749f1946d8c1ee38b85f]
- RMPD          [] [paper] [-0001-11-30 00:00:00] [83d13bd1a1b3e64dad996f4022b3c29f]
- RMP         [(Partial) Autocorrelation Function] [paper: autocorrel...] [2010-12-20 17:48:08] [1df589bc3feb749f1946d8c1ee38b85f]
-               [(Partial) Autocorrelation Function] [paper] [2010-12-28 19:23:11] [83d13bd1a1b3e64dad996f4022b3c29f]
-             [Variance Reduction Matrix] [paper] [2010-12-28 19:17:46] [83d13bd1a1b3e64dad996f4022b3c29f]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10,6
9,6
10,1
10,2
10,1
9,6
10,1
10,3
10,1
9,4
9,9
9,8
9,4
8,6
8,9
8,4
7,9
7
7,4
7,2
6,8
6,1
6,7
6,6
6,4
6
6,6
6,8
6,8
6,5
7,3
7,7
8
8
9,1
9,5
9,7
9,4
10
9,9
9,7
9,2
9,9
10
9,9
9,2
9,6
9,4
9,1
8,7
9,5
9,5
9,4
9
9,6
9,3
9
8,5
8,5
7,9
7,2
6,5
7,1
6,8
6,2
6,2
6,5
7,5
7,4
6,9
7,6
8,1
8,2
7,7
8,3
8,5
8,7
7,4
9,1
8,4
8,6
8,1
8,7
8,5
8,7
8,3
8,1
7,9
8
7,6
7,3
7,1
7,1
6,3
7,7
6,8
7,9
7,5
8,2
8,1
8,6
8,1
8,8
Dataseries Y:
Download CSV
Histogram 
42.645
42.800
43.090
43.313
43.551
43.639
44.177
43.666
43.974
44.463
45.084
45.666
46.118
46.548
47.120
47.582
47.944
48.404
48.584
49.215
49.985
49.808
49.874
50.479
50.261
50.848
51.191
51.450
52.171
51.537
51.696
51.059
50.671
51.183
51.345
51.834
52.199
52.799
52.947
53.837
64.597
64.795
65.246
65.338
65.307
65.630
65.732
66.184
66.995
68.216
68.776
69.144
69.375
69.525
69.705
69.763
70.647
71.539
72.526
73.478
73.957
74.507
74.962
75.705
75.397
75.532
75.223
75.110
75.836
76.212
76.592
76.720
76.621
76.672
76.973
77.488
78.540
79.004
79.779
79.873
80.060
80.602
81.206
81.736
82.268
82.521
83.329
84.190
85.032
85.268
85.557
85.730
86.385
86.851
86.464
84.603
83.178
83.298
84.163
84.531
84.595
85.472
85.822

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113000&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113000&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113000&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean8.3077669902912665.639213592233
Biased Variance1.43256103308512222.881721527194
Biased Standard Deviation1.1968964170240914.9292237416148
Covariance-5.19493010660575
Correlation-0.287904771277789
Determination0.082889157324516
T-Test-3.02133328470282
p-value (2 sided)0.00318843180787373
p-value (1 sided)0.00159421590393687
Degrees of Freedom101
Number of Observations103

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 8.30776699029126 & 65.639213592233 \tabularnewline
Biased Variance & 1.43256103308512 & 222.881721527194 \tabularnewline
Biased Standard Deviation & 1.19689641702409 & 14.9292237416148 \tabularnewline
Covariance & -5.19493010660575 \tabularnewline
Correlation & -0.287904771277789 \tabularnewline
Determination & 0.082889157324516 \tabularnewline
T-Test & -3.02133328470282 \tabularnewline
p-value (2 sided) & 0.00318843180787373 \tabularnewline
p-value (1 sided) & 0.00159421590393687 \tabularnewline
Degrees of Freedom & 101 \tabularnewline
Number of Observations & 103 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113000&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]8.30776699029126[/C][C]65.639213592233[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1.43256103308512[/C][C]222.881721527194[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1.19689641702409[/C][C]14.9292237416148[/C][/ROW]
[ROW][C]Covariance[/C][C]-5.19493010660575[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.287904771277789[/C][/ROW]
[ROW][C]Determination[/C][C]0.082889157324516[/C][/ROW]
[ROW][C]T-Test[/C][C]-3.02133328470282[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00318843180787373[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00159421590393687[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]101[/C][/ROW]
[ROW][C]Number of Observations[/C][C]103[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113000&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113000&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
Mean8.3077669902912665.639213592233
Biased Variance1.43256103308512222.881721527194
Biased Standard Deviation1.1968964170240914.9292237416148
Covariance-5.19493010660575
Correlation-0.287904771277789
Determination0.082889157324516
T-Test-3.02133328470282
p-value (2 sided)0.00318843180787373
p-value (1 sided)0.00159421590393687
Degrees of Freedom101
Number of Observations103


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')