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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 computationSat, 13 Dec 2008 08:08:38 -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/13/t1229181090erbcr4yzxi13kbf.htm/, Retrieved Fri, 17 May 2024 06:18:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33144, Retrieved Fri, 17 May 2024 06:18:04 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact202

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Partial Correlation] [Various EDA topics] [2007-11-04 16:20:59] [dc28704e2f48edede7e5c93fa6811a5e]
- RM D    [Pearson Correlation] [Correlatie] [2008-12-13 15:08:38] [de3f0516a1536f7c4a656924d8bc8d07] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2560
2491
2380
2291
2079
1929
1851
1607
1661
2259
1668
2011
1944
1958
1844
1868
1701
2338
2018
1302
2168
2139
1560
2093
1973
2090
2811
1984
1849
2433
2071
1855
1756
1898
1770
1969
1769
2139
3013
2061
2132
2973
2081
2257
2075
2084
1747
2092
1919
2551
2643
2153
2496
2645
2035
2294
2205
2044
1762
1897
1821
1905
2111
1643
1956
1977
1685
1393
1574
1793
1562
1510
1675
1965
2173
2395
2197
2257
2885
1594
1950
1772
1280
1724
1473
1461
1576
1900
1618
2303
1994
1575
1893
1788
1817
3233
727
1121
1665
1401
1415
2058
1544
1379
1402
1313
1296
1398
1288
1563
1972
1496
1481
1819
1479
1635
1511
1547
1388
1958
1390
1597
1842
1396
1671
1385
1632
1313
1300
1431
1398
1198
1292
1434
1660
1837
1455
1315
1642
1069
1209
1586
1122
1063
1125
1414
1347
1403
1299
1547
1515
1247
1639
1296
1063
1282
1365
1268
1532
1455
1393
1515
1510
1225
1577
1417
1224
1693
1633
1639
1914
1586
1552
2081
1500
1437
1470
1849
1387
1592
1589
1798
1935
1887
2027
2080
1556
1682
1785
1869
1781
2082
2570
1862
1936
1504
1765
1607
1577
1493
1615
1700
1335
1523
1623
1540
1637
1524
1419
1821
1593
1357
1263
1750
1405
1393
1639
1679
1551
1744
1429
1784
Dataseries Y:
Download CSV
Histogram 
727
817
918
786
803
756
725
523
538
587
505
521
498
550
637
622
668
669
670
499
539
593
429
622
533
655
835
686
706
869
777
739
637
597
629
940
444
496
801
659
767
876
601
697
745
655
572
628
650
677
900
780
896
1092
823
735
770
915
645
566
707
785
762
712
714
823
609
620
619
638
483
535
617
698
804
824
878
1019
974
773
734
827
804
721
659
732
839
994
828
1039
1072
803
1035
922
834
1739
359
513
699
741
793
877
750
752
675
682
583
632
606
645
980
847
941
1066
936
880
808
741
780
675
782
795
873
727
998
768
714
782
578
664
560
516
752
597
716
691
752
718
737
621
472
719
497
536
653
605
637
743
719
653
675
590
527
534
463
542
568
501
678
774
665
742
715
638
656
606
498
587
677
547
871
731
752
862
619
700
667
667
650
547
637
655
703
886
896
831
741
833
750
779
655
739
845
795
1021
726
1045
915
852
772
729
755
691
729
702
702
894
765
753
876
781
776
606
775
663
649
821
771
635
1070
693
779

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=33144&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=33144&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33144&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
Mean1740.84234234234724.536036036036
Biased Variance150981.36703595523432.9964491519
Biased Standard Deviation388.563208546505153.078399681836
Covariance28484.5011821777
Correlation0.476729830280085
Determination0.227271331078879
T-Test8.04396469013576
p-value (2 sided)5.35127497869325e-14
p-value (1 sided)2.67563748934663e-14
Degrees of Freedom220
Number of Observations222

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1740.84234234234 & 724.536036036036 \tabularnewline
Biased Variance & 150981.367035955 & 23432.9964491519 \tabularnewline
Biased Standard Deviation & 388.563208546505 & 153.078399681836 \tabularnewline
Covariance & 28484.5011821777 \tabularnewline
Correlation & 0.476729830280085 \tabularnewline
Determination & 0.227271331078879 \tabularnewline
T-Test & 8.04396469013576 \tabularnewline
p-value (2 sided) & 5.35127497869325e-14 \tabularnewline
p-value (1 sided) & 2.67563748934663e-14 \tabularnewline
Degrees of Freedom & 220 \tabularnewline
Number of Observations & 222 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33144&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]1740.84234234234[/C][C]724.536036036036[/C][/ROW]
[ROW][C]Biased Variance[/C][C]150981.367035955[/C][C]23432.9964491519[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]388.563208546505[/C][C]153.078399681836[/C][/ROW]
[ROW][C]Covariance[/C][C]28484.5011821777[/C][/ROW]
[ROW][C]Correlation[/C][C]0.476729830280085[/C][/ROW]
[ROW][C]Determination[/C][C]0.227271331078879[/C][/ROW]
[ROW][C]T-Test[/C][C]8.04396469013576[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]5.35127497869325e-14[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.67563748934663e-14[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]220[/C][/ROW]
[ROW][C]Number of Observations[/C][C]222[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33144&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33144&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
Mean1740.84234234234724.536036036036
Biased Variance150981.36703595523432.9964491519
Biased Standard Deviation388.563208546505153.078399681836
Covariance28484.5011821777
Correlation0.476729830280085
Determination0.227271331078879
T-Test8.04396469013576
p-value (2 sided)5.35127497869325e-14
p-value (1 sided)2.67563748934663e-14
Degrees of Freedom220
Number of Observations222


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')