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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, 14 Dec 2010 21:53:29 +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/14/t12923635001v3c12eeju5vqjv.htm/, Retrieved Thu, 02 May 2024 14:55:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=110232, Retrieved Thu, 02 May 2024 14:55:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Competence to learn] [2010-11-17 07:43:53] [b98453cac15ba1066b407e146608df68]
- R PD  [Multiple Regression] [Workshop 7 - Firs...] [2010-11-19 10:36:36] [8b017ffbf7b0eded54d8efebfb3e4cfa]
-   P     [Multiple Regression] [Workshop 7 - Firs...] [2010-11-19 10:41:24] [8b017ffbf7b0eded54d8efebfb3e4cfa]
- R PD      [Multiple Regression] [] [2010-11-23 16:27:22] [1ad9dd03b6c5806e9fe90049663fcef1]
- RMPD          [Pearson Correlation] [correlatie SWS - ...] [2010-12-14 21:53:29] [5f761c4a622da19727fd2adf71158b48] [Current]
- RM D            [Multiple Regression] [multiple regressi...] [2010-12-14 23:18:51] [ca5ab8c53423c489dac59e1a1d654047]
- RM D            [Multiple Regression] [multiple regressi...] [2010-12-14 23:18:51] [ca5ab8c53423c489dac59e1a1d654047]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6.3
2.1
9.1
15.8
5.2
10.9
8.3
11
3.2
6.3
8.6
6.6
9.5
3.3
11
4.7
10.4
7.4
2.1
7.7
17.9
6.1
11.9
10.8
13.8
14.3
15.2
10
11.9
6.5
7.5
10.6
7.4
8.4
5.7
4.9
3.2
11
4.9
13.2
9.7
12.8
Dataseries Y:
Download CSV
Histogram 
42
624
180
35
392
63
230
112
281
42
28
42
120
148
16
310
28
68
336
21,5
50
267
19
30
12
120
140
170
17
115
31
21
52
164
225
225
151
60
200
46
210
14

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110232&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110232&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110232&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'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean8.74285714285714129.940476190476
Biased Variance14.375306122449015953.9071712018
Biased Standard Deviation3.79147809204392126.308777094871
Covariance-297.341289198606
Correlation-0.606104774550641
Determination0.367362997733084
T-Test-4.81948248108329
p-value (2 sided)2.10089705179409e-05
p-value (1 sided)1.05044852589705e-05
Degrees of Freedom40
Number of Observations42

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 8.74285714285714 & 129.940476190476 \tabularnewline
Biased Variance & 14.3753061224490 & 15953.9071712018 \tabularnewline
Biased Standard Deviation & 3.79147809204392 & 126.308777094871 \tabularnewline
Covariance & -297.341289198606 \tabularnewline
Correlation & -0.606104774550641 \tabularnewline
Determination & 0.367362997733084 \tabularnewline
T-Test & -4.81948248108329 \tabularnewline
p-value (2 sided) & 2.10089705179409e-05 \tabularnewline
p-value (1 sided) & 1.05044852589705e-05 \tabularnewline
Degrees of Freedom & 40 \tabularnewline
Number of Observations & 42 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110232&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]8.74285714285714[/C][C]129.940476190476[/C][/ROW]
[ROW][C]Biased Variance[/C][C]14.3753061224490[/C][C]15953.9071712018[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]3.79147809204392[/C][C]126.308777094871[/C][/ROW]
[ROW][C]Covariance[/C][C]-297.341289198606[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.606104774550641[/C][/ROW]
[ROW][C]Determination[/C][C]0.367362997733084[/C][/ROW]
[ROW][C]T-Test[/C][C]-4.81948248108329[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.10089705179409e-05[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.05044852589705e-05[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]40[/C][/ROW]
[ROW][C]Number of Observations[/C][C]42[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110232&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110232&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
Mean8.74285714285714129.940476190476
Biased Variance14.375306122449015953.9071712018
Biased Standard Deviation3.79147809204392126.308777094871
Covariance-297.341289198606
Correlation-0.606104774550641
Determination0.367362997733084
T-Test-4.81948248108329
p-value (2 sided)2.10089705179409e-05
p-value (1 sided)1.05044852589705e-05
Degrees of Freedom40
Number of Observations42


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = pearson ;
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')