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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 computationWed, 09 Dec 2009 11:25:06 -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/2009/Dec/09/t1260383189wc2qjg3xg5eqr0s.htm/, Retrieved Mon, 29 Apr 2024 12:43:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=65121, Retrieved Mon, 29 Apr 2024 12:43:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [cs.shw.paper.univ...] [2009-12-09 17:46:01] [74be16979710d4c4e7c6647856088456]
- RMPD    [Pearson Correlation] [cs.shw.paper.scat...] [2009-12-09 18:25:06] [47f146dd9fb230449e079c6cbc92f5f5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1213.8
1245.6
1306.3
1255.8
1257.6
1287.8
1300.4
1320.9
1370.8
1327.3
1320
1345.3
1346.7
1395.4
1462
1491.6
1461.8
1477.9
1490.3
1521.1
1561.9
1552.6
1523.6
1548.3
1552.4
1587
1621.3
1648.7
1641.8
1650.6
1688.6
1670.7
1682.2
1678.9
1650.6
1662.4
1664.5
1683.2
1736.2
1747.6
1749
1759.7
1793.6
1817.4
1858.4
1839.9
1809.1
1877.7
1880.3
1930.9
2039.3
1992.7
1987.8
1984.4
2016.5
2016.7
2064.1
2031.5
2000.3
2057.8
2041.2
2093.2
2158.3
2128.8
2131.9
2170.3
2190.8
2217.7
2254.4
2223.3
2210.5
2250.8
2249.1
2288.6
2329.2
2313.8
2309.8
2345.9
2361.3
2372
2410.4
2398.5
2362.3
2419.1
2421.6
2465
2480.5
2506.1
2506.6
2525.8
2550
2578.3
2807.8
2815.3
2767.7
2815.4
2838.8
2864
2948.6
2922.8
2917.2
2936.8
2993.4
3007.8
3046.3
3011.5
2958.6
3019.8
2998.5
3040.4
3166
3110
3099.2
3150.3
3163.6
3182.6
3244.4
3223.2
3143.6
3217
3182.3
3217.2
3262.5
3227.9
3171.6
3219
3195.4
3221.6
3262.1
3179.5
3133.6
3219.2
3245
3265.3
3312.5
3383.6
3386.3
3411.1
3467.2
3487.7
3575.5
3571.5
3582.3
3637.1
3685
Dataseries Y:
Download CSV
Histogram 
2430.47
2516.3
2633.63
2799.84
3001.93
3229.29
3173.02
3322.08
3417.88
3486.95
3016.22
2709.61
2914.87
3203.08
3320.25
3446.25
3456.85
3566.53
3763.67
3607.75
3747.38
3623.91
3699.76
3629.61
3911.52
4281.47
4742.42
4522.42
4879.79
5059.11
5093.19
4941.81
4832.67
4876.18
5018.07
4780.34
4953.59
4622.32
4557.13
4560.03
4105.66
4004.89
4277.26
4245.98
4057.64
3931.42
3637.15
3339.91
3465.74
3571.25
3706.93
3584.17
3552.11
3695.24
3510
3357.7
3060.91
2736.98
2709.45
2314.96
2561.29
2663.49
2407.87
2237.74
2165.44
2098.89
2318.54
2315.49
2395.47
2474.07
2479.57
2386.92
2537.84
2567.13
2660.37
2696.28
2748.5
2663.32
2707.69
2669.36
2687.68
2650.24
2620.03
2668.47
2692.06
2737.67
2774.77
2819.19
2892.56
2866.08
2817.41
2934.75
3036.54
3139.5
3114.31
3261.3
3201.79
3264.53
3349.1
3446.17
3469.48
3507.13
3536.2
3359.05
3378.85
3449.15
3522.89
3551.04
3669.15
3602
3697.22
3760.9
3665.08
3708.8
3858.21
3933.16
3946.98
3794.29
3765.56
3820.33
3885.12
3752.67
3683.79
3240.75
3188.82
3017.98
3237.2
3182.53
2906.42
2881.35
2915.64
2635.13
2331.43
2159.04
2065.46
1983.48
1770.41
1815.99
2026.97
2124.81
2098.28
2291.39
2401.57
2453.89
2409.53

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65121&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65121&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65121&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'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean2349.215862068973257.92468965517
Biased Variance500346.903403567580676.29537111
Biased Standard Deviation707.352036403068762.021190893738
Covariance-187507.995047126
Correlation-0.345471020666261
Determination0.119350226120188
T-Test-4.40228371148011
p-value (2 sided)2.08300010995576e-05
p-value (1 sided)1.04150005497788e-05
Degrees of Freedom143
Number of Observations145

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 2349.21586206897 & 3257.92468965517 \tabularnewline
Biased Variance & 500346.903403567 & 580676.29537111 \tabularnewline
Biased Standard Deviation & 707.352036403068 & 762.021190893738 \tabularnewline
Covariance & -187507.995047126 \tabularnewline
Correlation & -0.345471020666261 \tabularnewline
Determination & 0.119350226120188 \tabularnewline
T-Test & -4.40228371148011 \tabularnewline
p-value (2 sided) & 2.08300010995576e-05 \tabularnewline
p-value (1 sided) & 1.04150005497788e-05 \tabularnewline
Degrees of Freedom & 143 \tabularnewline
Number of Observations & 145 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65121&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]2349.21586206897[/C][C]3257.92468965517[/C][/ROW]
[ROW][C]Biased Variance[/C][C]500346.903403567[/C][C]580676.29537111[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]707.352036403068[/C][C]762.021190893738[/C][/ROW]
[ROW][C]Covariance[/C][C]-187507.995047126[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.345471020666261[/C][/ROW]
[ROW][C]Determination[/C][C]0.119350226120188[/C][/ROW]
[ROW][C]T-Test[/C][C]-4.40228371148011[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.08300010995576e-05[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.04150005497788e-05[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]143[/C][/ROW]
[ROW][C]Number of Observations[/C][C]145[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65121&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65121&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
Mean2349.215862068973257.92468965517
Biased Variance500346.903403567580676.29537111
Biased Standard Deviation707.352036403068762.021190893738
Covariance-187507.995047126
Correlation-0.345471020666261
Determination0.119350226120188
T-Test-4.40228371148011
p-value (2 sided)2.08300010995576e-05
p-value (1 sided)1.04150005497788e-05
Degrees of Freedom143
Number of Observations145


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 50 ; par2 = 50 ; par3 = 0 ; par4 = 0 ; par5 = 0 ; par6 = Y ; par7 = Y ;
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')