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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, 27 Oct 2009 14:22:04 -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/Oct/27/t125667497818kom15bce1t5j8.htm/, Retrieved Sun, 10 Nov 2024 19:41:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51217, Retrieved Sun, 10 Nov 2024 19:41:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsws4p2.3b
Estimated Impact154

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2009-10-27 20:22:04] [9ea4b07b6662a0f40f92decdf1e3b5d5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0.708035793
1.050821625
0.936093359
0.819779831
0.815364813
0.943905899
1.121677562
1.01523068
0.920282753
1.05431203
1.1442228
1.134622726
1.150572028
0.904218151
0.943905899
1.061256502
0.966983846
0.867100488
0.524728529
0.672944473
0.783901544
0.625938431
0.470003629
0.488580015
0.198850859
0.19062036
0.39877612
0.494696242
0.506817602
0.570979547
0.598836501
0.576613364
0.246860078
0.254642218
0.31481074
0.113328685
0.412109651
0.806475866
1.078409581
1.128171091
1.241268589
1.291983682
1.479329227
1.423108334
1.650579856
1.757857918
1.776645831
1.684545385
1.69744879
1.5518088
1.1442228
0.966983846
0.841567186
0.657520003
-0.478035801
-0.510825624
Dataseries Y:
Download CSV
Histogram 
2849.27
2921.44
2981.85
3080.58
3106.22
3119.31
3061.26
3097.31
3161.69
3257.16
3277.01
3295.32
3363.99
3494.17
3667.03
3813.06
3917.96
3895.51
3801.06
3570.12
3701.61
3862.27
3970.1
4138.52
4199.75
4290.89
4443.91
4502.64
4356.98
4591.27
4696.96
4621.4
4562.84
4202.52
4296.49
4435.23
4105.18
4116.68
3844.49
3720.98
3674.4
3857.62
3801.06
3504.37
3032.6
3047.03
2962.34
2197.82
2014.45
1862.83
1905.41
1810.99
1670.07
1864.44
2052.02
2029.6

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=51217&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=51217&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51217&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
Mean0.8427051916607143440.69785714286
Biased Variance0.240501734755341682011.780856122
Biased Standard Deviation0.490409762092213825.840045563378
Covariance-128.489538755871
Correlation-0.311592781210801
Determination0.097090061302682
T-Test-2.40969485735977
p-value (2 sided)0.0194037188165829
p-value (1 sided)0.00970185940829146
Degrees of Freedom54
Number of Observations56

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 0.842705191660714 & 3440.69785714286 \tabularnewline
Biased Variance & 0.240501734755341 & 682011.780856122 \tabularnewline
Biased Standard Deviation & 0.490409762092213 & 825.840045563378 \tabularnewline
Covariance & -128.489538755871 \tabularnewline
Correlation & -0.311592781210801 \tabularnewline
Determination & 0.097090061302682 \tabularnewline
T-Test & -2.40969485735977 \tabularnewline
p-value (2 sided) & 0.0194037188165829 \tabularnewline
p-value (1 sided) & 0.00970185940829146 \tabularnewline
Degrees of Freedom & 54 \tabularnewline
Number of Observations & 56 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51217&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]0.842705191660714[/C][C]3440.69785714286[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.240501734755341[/C][C]682011.780856122[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.490409762092213[/C][C]825.840045563378[/C][/ROW]
[ROW][C]Covariance[/C][C]-128.489538755871[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.311592781210801[/C][/ROW]
[ROW][C]Determination[/C][C]0.097090061302682[/C][/ROW]
[ROW][C]T-Test[/C][C]-2.40969485735977[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0194037188165829[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00970185940829146[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]54[/C][/ROW]
[ROW][C]Number of Observations[/C][C]56[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51217&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51217&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
Mean0.8427051916607143440.69785714286
Biased Variance0.240501734755341682011.780856122
Biased Standard Deviation0.490409762092213825.840045563378
Covariance-128.489538755871
Correlation-0.311592781210801
Determination0.097090061302682
T-Test-2.40969485735977
p-value (2 sided)0.0194037188165829
p-value (1 sided)0.00970185940829146
Degrees of Freedom54
Number of Observations56


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')