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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 computationMon, 20 Oct 2008 14:10:10 -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/t1224533460sqm5p7tqxre2lza.htm/, Retrieved Fri, 17 May 2024 01:42:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18056, Retrieved Fri, 17 May 2024 01:42:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109

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...] [2008-10-20 20:10:10] [14a75ec03b2c0d8ddd8b141a7b1594fd] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1113.4
1100.3
1087.2
1075.4
848.7
1060.1
1200.5
1162.4
1320.6
1229.7
1339.6
1426.4
1166.2
1147.6
1335.1
1039.6
1062.6
1275.1
1238.8
1321.3
1608.1
899
936.6
1060.5
933.1
876.6
1045.9
794.8
906.6
976.6
938.2
961.1
976.3
917.6
881.6
1021.4
824
949.5
986.9
824
857.3
1017.2
983.1
950.3
857.9
883.6
903.2
946.1
800.9
848.1
908.7
872.8
799.6
926.2
1016.2
941.3
976.9
1056.4
1003.1
1054.5
Dataseries Y:
Download CSV
Histogram 
1872,7
1742
1769,7
1730,2
1504,1
1851,6
1983,6
1734,2
1856,1
1730,1
1817,5
2090,2
1833,6
1719,2
2033,8
1727,8
1674
1889
1913,4
1993,5
2002,5
1815,2
1878,3
2042,4
1886,7
1831,9
2001,8
1676,2
1710,6
2016,2
2026,8
2297,4
2360,9
2201,3
2156,8
2683,2
2057,7
2165,8
2318,4
1900,3
2016,7
2168,2
2293
2297,6
2200,8
2324,4
2190,7
2552,6
2228,1
2273,9
2421
2392,9
2088
2492,6
2651
2579,7
2469,4
3039,9
2821,4
2843,8

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=18056&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=18056&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18056&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
Mean1024.542097.37333333333
Biased Variance28572.1850666667107387.168288889
Biased Standard Deviation169.033088673983327.699814294865
Covariance-11257.6026440678
Correlation-0.199847515828023
Determination0.039939029582632
T-Test-1.55332861829341
p-value (2 sided)0.125784751741064
p-value (1 sided)0.0628923758705318
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1024.54 & 2097.37333333333 \tabularnewline
Biased Variance & 28572.1850666667 & 107387.168288889 \tabularnewline
Biased Standard Deviation & 169.033088673983 & 327.699814294865 \tabularnewline
Covariance & -11257.6026440678 \tabularnewline
Correlation & -0.199847515828023 \tabularnewline
Determination & 0.039939029582632 \tabularnewline
T-Test & -1.55332861829341 \tabularnewline
p-value (2 sided) & 0.125784751741064 \tabularnewline
p-value (1 sided) & 0.0628923758705318 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18056&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]1024.54[/C][C]2097.37333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]28572.1850666667[/C][C]107387.168288889[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]169.033088673983[/C][C]327.699814294865[/C][/ROW]
[ROW][C]Covariance[/C][C]-11257.6026440678[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.199847515828023[/C][/ROW]
[ROW][C]Determination[/C][C]0.039939029582632[/C][/ROW]
[ROW][C]T-Test[/C][C]-1.55332861829341[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.125784751741064[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0628923758705318[/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=18056&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18056&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
Mean1024.542097.37333333333
Biased Variance28572.1850666667107387.168288889
Biased Standard Deviation169.033088673983327.699814294865
Covariance-11257.6026440678
Correlation-0.199847515828023
Determination0.039939029582632
T-Test-1.55332861829341
p-value (2 sided)0.125784751741064
p-value (1 sided)0.0628923758705318
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')