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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 computationWed, 24 Dec 2008 03:51:23 -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/24/t1230115925t16c2la2ng47jc8.htm/, Retrieved Sun, 19 May 2024 11:38:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36456, Retrieved Sun, 19 May 2024 11:38:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact213

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Correlation] [2008-12-24 10:51:23] [80e37024345c6a903bf645806b7fbe14] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1039,2
1033,2
1118,9
1125,7
1152,4
961,9
1190,8
728,8
995,6
1260,3
994
957,3
975,6
884,9
908,4
1022,8
958,6
825,1
1116,6
724,2
1004,5
1058,9
854,7
943,4
792,4
873,2
1101,4
987,1
1038,8
1060,7
1047,7
840
1044
1097,4
987,5
934
977
881,1
1083,3
1074,7
1182,2
1117,5
1117,4
936,2
1246,3
1175,1
1177,7
1035,8
1091,6
998,7
1247,9
1034,7
1287,7
994
1122,8
1017,3
1106
1191,8
1030,1
989,4
979,6
1088
1389,2
1043,9
1182,1
1109,6
1463,3
1276,2
1082,4
1365,5
1134,1
1041,3
1085,7
1011,6
1181,6
1338,1
1257
1194
1402,7
992,6
1474,1
Dataseries Y:
Download CSV
Histogram 
0,8833
0,87
0,8758
0,8858
0,917
0,9554
0,9922
0,9778
0,9808
0,9811
1,0014
1,0183
1,0622
1,0773
1,0807
1,0848
1,1582
1,1663
1,1372
1,1139
1,1222
1,1692
1,1702
1,2286
1,2613
1,2646
1,2262
1,1985
1,2007
1,2138
1,2266
1,2176
1,2218
1,249
1,2991
1,3408
1,3119
1,3014
1,3201
1,2938
1,2694
1,2165
1,2037
1,2292
1,2256
1,2015
1,1786
1,1856
1,2103
1,1938
1,202
1,2271
1,277
1,265
1,2684
1,2811
1,2727
1,2611
1,2881
1,3213
1,2999
1,3074
1,3242
1,3516
1,3511
1,3419
1,3716
1,3622
1,3896
1,4227
1,4684
1,457
1,4718
1,4748
1,5527
1,575
1,5557
1,5553
1,577
1,4975
1,4369

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=36456&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=36456&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36456&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
Mean1072.208641975311.23431111111111
Biased Variance22757.26770309400.0282556108641975
Biased Standard Deviation150.8551215673300.168094053625337
Covariance9.37282965277778
Correlation0.365059187196796
Determination0.133268210156785
T-Test3.48525424820461
p-value (2 sided)0.00080546486890487
p-value (1 sided)0.000402732434452435
Degrees of Freedom79
Number of Observations81

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1072.20864197531 & 1.23431111111111 \tabularnewline
Biased Variance & 22757.2677030940 & 0.0282556108641975 \tabularnewline
Biased Standard Deviation & 150.855121567330 & 0.168094053625337 \tabularnewline
Covariance & 9.37282965277778 \tabularnewline
Correlation & 0.365059187196796 \tabularnewline
Determination & 0.133268210156785 \tabularnewline
T-Test & 3.48525424820461 \tabularnewline
p-value (2 sided) & 0.00080546486890487 \tabularnewline
p-value (1 sided) & 0.000402732434452435 \tabularnewline
Degrees of Freedom & 79 \tabularnewline
Number of Observations & 81 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36456&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]1072.20864197531[/C][C]1.23431111111111[/C][/ROW]
[ROW][C]Biased Variance[/C][C]22757.2677030940[/C][C]0.0282556108641975[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]150.855121567330[/C][C]0.168094053625337[/C][/ROW]
[ROW][C]Covariance[/C][C]9.37282965277778[/C][/ROW]
[ROW][C]Correlation[/C][C]0.365059187196796[/C][/ROW]
[ROW][C]Determination[/C][C]0.133268210156785[/C][/ROW]
[ROW][C]T-Test[/C][C]3.48525424820461[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00080546486890487[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.000402732434452435[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]79[/C][/ROW]
[ROW][C]Number of Observations[/C][C]81[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36456&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36456&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
Mean1072.208641975311.23431111111111
Biased Variance22757.26770309400.0282556108641975
Biased Standard Deviation150.8551215673300.168094053625337
Covariance9.37282965277778
Correlation0.365059187196796
Determination0.133268210156785
T-Test3.48525424820461
p-value (2 sided)0.00080546486890487
p-value (1 sided)0.000402732434452435
Degrees of Freedom79
Number of Observations81


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')