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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, 02 Dec 2008 10:34:04 -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/02/t1228239634kel833tw4w9zp6n.htm/, Retrieved Wed, 15 May 2024 05:37:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28130, Retrieved Wed, 15 May 2024 05:37:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact187

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:35:57] [b731da8b544846036771bbf9bf2f34ce]
- RMPD  [Pearson Correlation] [correlation] [2008-10-17 11:28:19] [1df53680523b3d683eb04eb09d7bca8b]
F   P     [Pearson Correlation] [] [2008-10-20 14:18:47] [4c8dfb519edec2da3492d7e6be9a5685]
-    D        [Pearson Correlation] [] [2008-12-02 17:34:04] [c60a842d48931bd392d024d8e9ef4583] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1160,9
1470,1
1653
1390
1550,7
1852,1
1797,9
1256,4
1835,5
1793,2
1874,8
1948,6
1819,9
1823,6
2042,7
1705,9
1876,8
1919,5
1803,4
1380,4
1812,1
1856,4
1934,3
1977,5
1813,7
1937,1
2178,7
1699,9
1943,8
2151
1927,7
1418,2
1899,8
1974,9
1918,7
1818,3
1751
1888
1947,7
1818,1
2110,8
2009
2124,2
1542,5
2044,1
2324,3
2055,6
2137,9
2140,7
2301,5
2412,6
2477
2311,8
2326,6
2745,3
1937,2
2668,7
2636,1
2327,6
2584,6
2282,8
2337
2499,3
2389,6
2327,1
2556,6
2580
1831,4
2382,1
2237,9
2117,7
2240,9
1946,1
2149,6
2690
2171,1
2358,6
2841,4
3064,6
2037,3
2799,9
2852,3
2541,2
2910
2694,6
3081,7
3648,2
2823,3
3670,1
3027,6
3578,5
2655,1
3835,3
3766
3716
3531,7
3194
3442,2
3610
3105,5
3428,4
3489,7
3679
2596,1
3110,7
3401,7
3431,8
3383,1
3797,5
3860,5
4054,1
4044,9
4402,4
4046,4
4329,7
3204,2
4037,2
4678,4
4174,6
4151,4
3874,7
3568
3431
3733,2
3278,3
3583,7
4060,3
2979
4078,4
4002,1
3542,4
3928,2
3626
3998,4
4413,5
3853,1
3920,5
4616,2
4332,7
3362,7
3855,4
4087,1
3860,2
4018,1
3627,7
3996
4420,7
4386,5
4631,8
4875,3
4549,3
3933
4963,3
4419,7
4646,7
5000,2
4302,2
4432,1
5125,5
4299,9
5145,6
4537,8
4880,9
4136,9
4668,8
4818,5
4933,9
4524,4
4676,1
4911
5745
4483,7
4772,7
5021,4
5535,6
4736
5001,7
5486,3
4958,5
4756,4
4763,3
4951,2
4692,8
5301,2
4929,7
5223,3
5708,3
4018
Dataseries Y:
Download CSV
Histogram 
283,9
340,5
383
335,4
356
431
441,9
262,3
481,1
442,8
458,4
472,7
498,8
463,3
538,3
494,2
446,2
497,5
433,2
359,4
455,9
483
469,7
423,8
371
435,7
438,1
364,5
392,7
405,1
391,4
282,8
408
480,9
416,9
350,7
399,9
438,1
454,9
407,7
485
494
521,2
333
520,3
570,5
501,8
408,4
512,7
596,9
581,5
605,7
581,1
538,3
731,4
457,7
706,3
708,5
683,5
722,1
727,7
674,4
675,3
628,7
658,3
786
736,9
567,3
736,3
719,6
676,8
589,5
596,5
661
840,9
683,1
677,4
780,2
928,8
557,5
760,6
847
719
699,8
745,4
871,5
1199,8
795,4
1054,4
753,7
1093,8
768,4
1405,7
1149,2
1086,8
994,4
958,8
1096,3
1107,4
862,4
983
1021,1
1036,3
684,5
874,1
1031,6
1126,3
1041,9
1419,4
1402,2
1503,6
1503,6
1571,2
1351,2
1448,3
1292,9
1293,7
1824,7
1641,4
1529,1
1417
1060
1117
1226,2
1124
1246
1398,1
1095,2
1507,1
1467
1262,1
1262,9
1184,9
1412,9
1581,8
1348,8
1443,7
1628,7
1393,2
1108,1
1074,8
1323,5
1367
1190,7
1149,2
1281,9
1406,8
1392,4
1674,5
1529,8
1180,9
1282,8
1524,2
1524,6
1520,1
1881,9
1375,2
1336,5
1653,9
1404,3
1731,4
1330,8
1616,3
1503,7
1476,7
1565,6
1581,8
1407,7
1393,7
1662,4
1929
1352,8
1339,8
1251,2
1491,7
1540,7
1383,7
1827,5
1591,3
1289,2
1291,9
1368,3
1264,6
1448,8
1239,2
1280,9
1269,4
1068,5

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28130&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28130&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28130&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean3215.95964.154255319149
Biased Variance1375198.79654255194784.048332956
Biased Standard Deviation1172.68870402275441.343458468522
Covariance496697.478235294
Correlation0.954588672589654
Determination0.911239533836477
T-Test43.698140981666
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom186
Number of Observations188

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 3215.95 & 964.154255319149 \tabularnewline
Biased Variance & 1375198.79654255 & 194784.048332956 \tabularnewline
Biased Standard Deviation & 1172.68870402275 & 441.343458468522 \tabularnewline
Covariance & 496697.478235294 \tabularnewline
Correlation & 0.954588672589654 \tabularnewline
Determination & 0.911239533836477 \tabularnewline
T-Test & 43.698140981666 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 186 \tabularnewline
Number of Observations & 188 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28130&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]3215.95[/C][C]964.154255319149[/C][/ROW]
[ROW][C]Biased Variance[/C][C]1375198.79654255[/C][C]194784.048332956[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1172.68870402275[/C][C]441.343458468522[/C][/ROW]
[ROW][C]Covariance[/C][C]496697.478235294[/C][/ROW]
[ROW][C]Correlation[/C][C]0.954588672589654[/C][/ROW]
[ROW][C]Determination[/C][C]0.911239533836477[/C][/ROW]
[ROW][C]T-Test[/C][C]43.698140981666[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]186[/C][/ROW]
[ROW][C]Number of Observations[/C][C]188[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28130&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28130&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
Mean3215.95964.154255319149
Biased Variance1375198.79654255194784.048332956
Biased Standard Deviation1172.68870402275441.343458468522
Covariance496697.478235294
Correlation0.954588672589654
Determination0.911239533836477
T-Test43.698140981666
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom186
Number of Observations188


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')