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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 computationSat, 20 Oct 2007 09:07:07 -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/Oct/20/6tq6gqjlrym046r1192896320.htm/, Retrieved Thu, 02 May 2024 16:50:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1106, Retrieved Thu, 02 May 2024 16:50:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWS2PCME
Estimated Impact233

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [WS2 - Pearson cor...] [2007-10-20 16:07:07] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
93,5
94,7
112,9
99,2
105,6
113,0
83,1
81,1
96,9
104,3
97,7
102,6
89,9
96,0
112,7
107,1
106,2
121,0
101,2
83,2
105,1
113,3
99,1
100,3
93,5
98,8
106,2
98,3
102,1
117,1
101,5
80,5
105,9
109,5
97,2
114,5
93,5
100,9
121,1
116,5
109,3
118,1
108,3
105,4
116,2
111,2
105,8
122,7
99,5
107,9
124,6
115,0
110,3
132,7
99,7
96,5
118,7
112,9
130,5
137,9
115,0
116,8
140,9
120,7
134,2
147,3
112,4
107,1
128,4
137,7
135,0
151,0
137,4
132,4
161,3
139,8
146,0
154,6
142,1
120,5
Dataseries Y:
Download CSV
Histogram 
105,5
106,4
117,9
89,7
88,5
106,4
61,4
92,3
95,5
92,5
89,6
84,3
76,3
80,7
96,3
81,0
82,9
90,3
74,8
70,1
86,7
86,4
89,9
88,1
78,8
81,1
85,4
82,6
80,3
81,2
68,0
67,4
91,3
94,9
82,8
88,6
73,1
76,7
93,2
84,9
83,8
93,5
91,9
69,6
87,0
90,2
82,7
91,4
74,6
76,1
87,1
78,4
81,3
99,3
71,0
73,2
95,6
84,0
90,8
93,6
80,9
84,4
97,3
83,5
88,8
100,7
69,4
74,6
96,6
96,6
93,1
91,8
85,7
79,1
91,3
84,2
85,8
90,0
76,6
81,3

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=1106&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=1106&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1106&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
Mean113.007585.8825
Biased Variance306.4446937596.83919375
Biased Standard Deviation17.50556179475549.84069071508703
Covariance62.9082341772152
Correlation0.360614315981379
Determination0.130042684890718
T-Test3.41461145515309
p-value (2 sided)0.00101629258176139
p-value (1 sided)0.000508146290880696
Degrees of Freedom78
Number of Observations80

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 113.0075 & 85.8825 \tabularnewline
Biased Variance & 306.44469375 & 96.83919375 \tabularnewline
Biased Standard Deviation & 17.5055617947554 & 9.84069071508703 \tabularnewline
Covariance & 62.9082341772152 \tabularnewline
Correlation & 0.360614315981379 \tabularnewline
Determination & 0.130042684890718 \tabularnewline
T-Test & 3.41461145515309 \tabularnewline
p-value (2 sided) & 0.00101629258176139 \tabularnewline
p-value (1 sided) & 0.000508146290880696 \tabularnewline
Degrees of Freedom & 78 \tabularnewline
Number of Observations & 80 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1106&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]113.0075[/C][C]85.8825[/C][/ROW]
[ROW][C]Biased Variance[/C][C]306.44469375[/C][C]96.83919375[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]17.5055617947554[/C][C]9.84069071508703[/C][/ROW]
[ROW][C]Covariance[/C][C]62.9082341772152[/C][/ROW]
[ROW][C]Correlation[/C][C]0.360614315981379[/C][/ROW]
[ROW][C]Determination[/C][C]0.130042684890718[/C][/ROW]
[ROW][C]T-Test[/C][C]3.41461145515309[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00101629258176139[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.000508146290880696[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]78[/C][/ROW]
[ROW][C]Number of Observations[/C][C]80[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1106&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1106&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
Mean113.007585.8825
Biased Variance306.4446937596.83919375
Biased Standard Deviation17.50556179475549.84069071508703
Covariance62.9082341772152
Correlation0.360614315981379
Determination0.130042684890718
T-Test3.41461145515309
p-value (2 sided)0.00101629258176139
p-value (1 sided)0.000508146290880696
Degrees of Freedom78
Number of Observations80


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')