FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationSun, 21 Dec 2008 16:05:38 -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/2008/Dec/22/t1229900828ws4clutmxuj4jf7.htm/, Retrieved Sun, 12 May 2024 16:31:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35902, Retrieved Sun, 12 May 2024 16:31:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact195

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Pearson Correlation] [Pearson Correlati...] [2007-11-09 11:33:47] [d255a97fd5d03c71781b63d0b6fcea5d]
-    D    [Pearson Correlation] [] [2008-12-21 23:05:38] [0e4dd4b7713a9edf1ca3fab1bbbafcc9] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3999
4864
5134
5410
4669
3546
5040
4850
4808
4441
4227
3620
3153
3936
4159
4209
4282
3174
4686
4131
4486
4625
3971
3397
3228
3441
3832
5267
3580
2617
3874
3431
4023
4151
3180
2916
2640
2700
3603
4348
3322
2312
3472
3592
3481
3451
2725
2574
2429
3160
3371
3448
3229
1986
2955
3000
8255
4191
3520
2497
Dataseries Y:
Download CSV
Histogram 
5732
4491
4755
5208
4962
4163
5592
5754
4929
5219
4429
4142
4308
3996
4634
4138
3759
3922
5560
4004
3937
5250
3908
4814
4407
3243
3740
3949
3711
3796
4145
3499
4164
3902
3186
3353
3475
3032
3341
3811
3655
4058
3682
3348
3848
3289
3851
2766
2837
2734
3764
3215
3287
3507
3060
3734
3849
4404
3497
3389

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35902&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35902&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35902&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean3776.966666666674002.23333333333
Biased Variance957662.865555555541854.478888889
Biased Standard Deviation978.60250641185736.107654415364
Covariance396425.194350282
Correlation0.541145874043134
Determination0.292838856993908
T-Test4.90082453586467
p-value (2 sided)8.03588992992488e-06
p-value (1 sided)4.01794496496244e-06
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 3776.96666666667 & 4002.23333333333 \tabularnewline
Biased Variance & 957662.865555555 & 541854.478888889 \tabularnewline
Biased Standard Deviation & 978.60250641185 & 736.107654415364 \tabularnewline
Covariance & 396425.194350282 \tabularnewline
Correlation & 0.541145874043134 \tabularnewline
Determination & 0.292838856993908 \tabularnewline
T-Test & 4.90082453586467 \tabularnewline
p-value (2 sided) & 8.03588992992488e-06 \tabularnewline
p-value (1 sided) & 4.01794496496244e-06 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35902&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]3776.96666666667[/C][C]4002.23333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]957662.865555555[/C][C]541854.478888889[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]978.60250641185[/C][C]736.107654415364[/C][/ROW]
[ROW][C]Covariance[/C][C]396425.194350282[/C][/ROW]
[ROW][C]Correlation[/C][C]0.541145874043134[/C][/ROW]
[ROW][C]Determination[/C][C]0.292838856993908[/C][/ROW]
[ROW][C]T-Test[/C][C]4.90082453586467[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]8.03588992992488e-06[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]4.01794496496244e-06[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]58[/C][/ROW]
[ROW][C]Number of Observations[/C][C]60[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35902&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35902&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
Mean3776.966666666674002.23333333333
Biased Variance957662.865555555541854.478888889
Biased Standard Deviation978.60250641185736.107654415364
Covariance396425.194350282
Correlation0.541145874043134
Determination0.292838856993908
T-Test4.90082453586467
p-value (2 sided)8.03588992992488e-06
p-value (1 sided)4.01794496496244e-06
Degrees of Freedom58
Number of Observations60


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')