FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_correlation.wasp
Title produced by softwarePearson Correlation
Date of computationThu, 02 Jul 2009 15:17:00 -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/2009/Jul/02/t1246569530w8iqni254y3s9h3.htm/, Retrieved Sat, 18 May 2024 17:18:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42320, Retrieved Sat, 18 May 2024 17:18:10 +0000
QR Codes:

Original text written by user:Pearson Correlation for Student Posts / Instructor Posts: SNHU Online / UG Social Sciences courses.
IsPrivate?No (this computation is public)
User-defined keywordse-learning participation
Estimated Impact204

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [SNHU Online BbWor...] [2009-07-02 21:17:00] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.68
4.37
6.50
6.47
8.92
5.85
9.14
7.69
7.50
1.90
3.83
4.50
2.64
4.18
4.91
4.00
3.60
5.28
5.35
3.56
5.81
5.25
3.69
3.38
5.20
5.88
3.71
6.25
5.38
7.44
5.00
3.00
4.33
3.75
3.50
4.50
3.88
3.88
2.55
1.63
1.75
2.42
2.36
2.20
1.40
2.22
1.91
2.30
3.00
1.64
1.63
4.00
3.09
2.92
2.67
2.45
3.00
4.00
4.25
4.00
2.17
2.63
3.75
5.91
3.18
4.44
4.42
3.91
4.77
3.38
6.90
5.10
5.00
2.55
4.30
3.80
5.87
4.19
4.31
4.53
4.81
4.63
4.40
4.81
4.80
3.93
3.33
4.71
3.29
5.20
6.73
5.10
3.30
4.60
3.60
3.57
4.63
8.45
7.73
8.17
9.22
5.64
5.73
6.67
3.89
4.78
4.44
3.88
3.00
4.88
4.89
5.00
6.13
6.50
6.06
5.14
6.42
5.36
3.22
3.78
4.56
3.44
4.63
3.88
3.67
3.44
3.22
4.33
3.44
1.67
3.33
3.50
6.11
5.43
3.57
4.75
4.11
3.53
4.50
4.38
4.47
3.87
3.25
5.60
4.80
6.56
4.67
4.63
6.70
6.00
4.33
9.60
4.70
5.00
5.50
5.70
7.80
5.20
8.90
5.60
6.30
5.22
6.50
5.80
5.67
4.75
4.56
3.80
4.88
3.50
4.73
3.80
4.87
4.14
4.07
4.53
5.00
3.87
8.45
7.89
12.00
6.44
8.00
5.25
6.50
24.00
11.17
21.50
Dataseries Y:
Download CSV
Histogram 
15.00
10.00
20.00
24.00
19.00
8.00
23.00
28.00
15.00
18.00
5.00
6.00
2.00
8.00
1.00
3.00
1.00
10.00
14.00
2.00
7.00
1.00
7.00
5.00
20.00
14.00
15.00
12.00
12.00
15.00
15.00
12.00
9.00
6.00
8.00
9.00
7.00
6.00
5.00
3.00
5.00
11.00
9.00
5.00
2.00
4.00
4.00
8.00
8.00
5.00
5.00
8.00
7.00
8.00
11.00
7.00
7.00
7.00
6.00
3.00
2.00
3.00
3.00
8.00
2.00
2.00
3.00
5.00
7.00
2.00
7.00
8.00
6.00
3.00
1.00
2.00
7.00
5.00
6.00
4.00
3.00
5.00
1.00
6.00
3.00
1.00
2.00
3.00
1.00
16.00
27.00
12.00
5.00
5.00
6.00
4.00
5.00
29.00
25.00
31.00
27.00
20.00
19.00
18.00
8.00
9.00
8.00
5.00
2.00
10.00
10.00
6.00
7.00
12.00
10.00
4.00
5.00
2.00
4.00
6.00
5.00
6.00
4.00
2.00
6.00
4.00
6.00
6.00
3.00
6.00
5.00
4.00
7.00
6.00
5.00
8.00
8.00
6.00
8.00
7.00
6.00
8.00
6.00
12.00
9.00
10.00
8.00
5.00
15.00
13.00
12.00
10.00
6.00
6.00
8.00
6.00
13.00
10.00
11.00
6.00
9.00
6.00
7.00
8.00
8.00
9.00
15.00
3.00
3.00
3.00
3.00
4.00
5.00
3.00
3.00
3.00
3.00
3.00
27.00
21.00
28.00
18.00
11.00
12.00
8.00
39.00
18.00
30.00

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42320&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42320&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42320&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'George Udny Yule' @ 72.249.76.132






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean4.937127659574478.61702127659574
Biased Variance6.569823664554146.2575826165686
Biased Standard Deviation2.563166725859656.80129271657738
Covariance12.4377710774832
Correlation0.709672527392386
Determination0.503635096135497
T-Test13.7376969627121
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom186
Number of Observations188

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 4.93712765957447 & 8.61702127659574 \tabularnewline
Biased Variance & 6.5698236645541 & 46.2575826165686 \tabularnewline
Biased Standard Deviation & 2.56316672585965 & 6.80129271657738 \tabularnewline
Covariance & 12.4377710774832 \tabularnewline
Correlation & 0.709672527392386 \tabularnewline
Determination & 0.503635096135497 \tabularnewline
T-Test & 13.7376969627121 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 186 \tabularnewline
Number of Observations & 188 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42320&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]4.93712765957447[/C][C]8.61702127659574[/C][/ROW]
[ROW][C]Biased Variance[/C][C]6.5698236645541[/C][C]46.2575826165686[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2.56316672585965[/C][C]6.80129271657738[/C][/ROW]
[ROW][C]Covariance[/C][C]12.4377710774832[/C][/ROW]
[ROW][C]Correlation[/C][C]0.709672527392386[/C][/ROW]
[ROW][C]Determination[/C][C]0.503635096135497[/C][/ROW]
[ROW][C]T-Test[/C][C]13.7376969627121[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]186[/C][/ROW]
[ROW][C]Number of Observations[/C][C]188[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42320&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42320&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
Mean4.937127659574478.61702127659574
Biased Variance6.569823664554146.2575826165686
Biased Standard Deviation2.563166725859656.80129271657738
Covariance12.4377710774832
Correlation0.709672527392386
Determination0.503635096135497
T-Test13.7376969627121
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom186
Number of Observations188


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')