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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 Oct 2008 10:33:21 -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/2008/Oct/20/t1224520512lt3phrfq3jd3gqd.htm/, Retrieved Sun, 19 May 2024 15:39:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17613, Retrieved Sun, 19 May 2024 15:39:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsPearson Correlation; reeks 2; reeks 4
Estimated Impact147

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Industriele produ...] [2008-10-13 18:27:09] [6743688719638b0cb1c0a6e0bf433315]
-   PD  [Univariate Data Series] [Reeks 2 Productie...] [2008-10-20 05:44:53] [6743688719638b0cb1c0a6e0bf433315]
- RMPD      [Pearson Correlation] [Pearson Correlati...] [2008-10-20 16:33:21] [9b05d7ef5dbcfba4217d280d9092f628] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
117.8
113.5
121.2
130.4
115.2
117.9
110.7
107.6
124.3
115.1
112.5
127.9
117.4
119.3
130.4
126
125.4
130.5
115.9
108.7
124
119.4
118.6
131.3
111.1
124.8
132.3
126.7
131.7
130.9
122.1
113.2
133.6
119.2
129.4
131.4
117.1
130.5
132.3
140.8
137.5
128.6
126.7
120.8
139.3
128.6
131.3
136.3
128.8
133.2
136.3
151.1
145
134.4
135.7
128.7
129.2
138.6
132.7
132.5
135.2
Dataseries Y:
Download CSV
Histogram 
85,7
61,9
104,9
107,9
95,6
79,8
94,8
93,7
108,1
96,9
88,8
106,7
86,8
69,8
110,9
105,4
99,2
84,4
87,2
91,9
97,9
94,5
85
100,3
78,7
65,8
104,8
96
103,3
82,9
91,4
94,5
109,3
92,1
99,3
109,6
87,5
73,1
110,7
111,6
110,7
84
101,6
102,1
113,9
99
100,4
109,5
93,1
77
108
119,9
105,9
78,2
100,3
102,2
97
101,3
89,2
93,3
86,4

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17613&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17613&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17613&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean126.53442622950895.4377049180328
Biased Variance84.5478312281645150.674807847353
Biased Standard Deviation9.1949894631894212.2749667147147
Covariance55.7175136612022
Correlation0.485558526195615
Determination0.235767082361257
T-Test4.26633270469831
p-value (2 sided)7.29320044545734e-05
p-value (1 sided)3.64660022272867e-05
Degrees of Freedom59
Number of Observations61

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 126.534426229508 & 95.4377049180328 \tabularnewline
Biased Variance & 84.5478312281645 & 150.674807847353 \tabularnewline
Biased Standard Deviation & 9.19498946318942 & 12.2749667147147 \tabularnewline
Covariance & 55.7175136612022 \tabularnewline
Correlation & 0.485558526195615 \tabularnewline
Determination & 0.235767082361257 \tabularnewline
T-Test & 4.26633270469831 \tabularnewline
p-value (2 sided) & 7.29320044545734e-05 \tabularnewline
p-value (1 sided) & 3.64660022272867e-05 \tabularnewline
Degrees of Freedom & 59 \tabularnewline
Number of Observations & 61 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17613&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]126.534426229508[/C][C]95.4377049180328[/C][/ROW]
[ROW][C]Biased Variance[/C][C]84.5478312281645[/C][C]150.674807847353[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]9.19498946318942[/C][C]12.2749667147147[/C][/ROW]
[ROW][C]Covariance[/C][C]55.7175136612022[/C][/ROW]
[ROW][C]Correlation[/C][C]0.485558526195615[/C][/ROW]
[ROW][C]Determination[/C][C]0.235767082361257[/C][/ROW]
[ROW][C]T-Test[/C][C]4.26633270469831[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]7.29320044545734e-05[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]3.64660022272867e-05[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]59[/C][/ROW]
[ROW][C]Number of Observations[/C][C]61[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17613&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17613&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
Mean126.53442622950895.4377049180328
Biased Variance84.5478312281645150.674807847353
Biased Standard Deviation9.1949894631894212.2749667147147
Covariance55.7175136612022
Correlation0.485558526195615
Determination0.235767082361257
T-Test4.26633270469831
p-value (2 sided)7.29320044545734e-05
p-value (1 sided)3.64660022272867e-05
Degrees of Freedom59
Number of Observations61


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')