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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 computationTue, 11 Dec 2012 15:07:04 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/11/t1355256460kshks1mdl2e12ob.htm/, Retrieved Sat, 20 Apr 2024 14:44:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=198678, Retrieved Sat, 20 Apr 2024 14:44:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15.3
19.2
31.3
0.5
24.8
45.7
88.8
22.1
3.9
30.4
8.6
31.6
12
30.8
15
30.3
17.2
32
19.9
6.2
31.2
0.6
11.9
10.4
36.4
1.1
22.6
25.5
7.3
13.5
11.9
22.5
16.3
1.6
8.5
35
8.3
24.8
9.2
5.5
1.3
8.9
0.7
21.7
7.8
10.7
19
10.2
12.5
14
21.7
15
31.8
0.7
7.3
4.9
21
6.2
14.7
23.1
1.3
10.7
9.9
58.2
8
24.1
7.3
12.7
18.8
3.5
5.9
5.1
0.1
3.8
17.3
8.6
6.5
7.6
15.6
1.3
4.9
8.1
13.4
6.6
5.8
12.6
10
3.5
6.4
11.5
17.3
12.5
3.5
1.5
7.3
17
5
13.1
0.5
1.9
0.5
4.7
6.2
34.2
4.2
14.6
7.1
1.5
0.4
7.7
11.6
1.2
1.6
1.5
0.9
2.8
4.3
54.8
1
2.8
5.5
2
0.4
0.5
6.4
2.7
1.4
8.9
1.1
1.4
1.4
1.1
0.8
1.6
0.6
4.6
0.6
1.2
1.8
0.4
1.1
1
5.1
0.8
0.7
0.6
1
0.7
1.2
0.5
1.6
Dataseries Y:
Download CSV
Histogram 
2.465174278
0.931192069
0.711452013
0.377183262
2.236740543
0.713040346
5.398554225
0.836420224
1.066455767
0.539451529
1.148668486
0.887746415
0.982298258
1.833295857
1.213173841
0.875413916
1.886406807
2.501723932
20.68464671
1.273047089
1.351081227
0.510491792
1.02685726
0.9435998
0.83565382
2.323293959
1.215575543
0.682603434
2.298259358
0.495497906
1.449464423
1.230981011
1.946545359
41.09568458
1.166003988
1.039045527
1.727527078
0.57014764
6.258638225
1.456811622
1.20360678
11.6070412
8.86957821
1.606921259
8.450290249
3.500918366
4.358933039
5.803955039
3.271119553
13.79015521
19.1986642
12.66054399
6.604966516
2.283512797
5.588444625
14.48342128
6.047639561
2.265745018
3.73875744
3.655522621
10.73115923
51.9968201
11.32211324
1.422567613
22.78075733
1.753938078
3.028556706
36.79690672
11.70628687
2.146786529
35.86205879
24.76992116
1.141761387
4.227539945
1.74873164
2.923244097
1.625318562
1.498778844
5.821176903
18.54626322
1.115054801
59.47912753
8.348444665
5.885859465
51.86285367
17.2267059
34.4208771
1.012470134
12.87098797
1.819797467
18.99327441
2.695604249
0.998056641
7.267825576
5.985410164
15.11979791
1.360090159
45.9577151
2.8079531
7.947593866
8.071039311
6.454250195
61.25096573
2.038822398
3.437673071
21.02243546
6.492329285
3.099361502
3.723876516
13.05988721
7.201885679
13.03962519
14.71813705
12.22706716
8.012906737
19.7240993
3.353902438
3.862711115
1.763453356
3.389291708
24.21336095
8.712897965
15.67216479
2.81760235
20.10899999
32.99783963
15.10295621
38.04642666
15.82539576
24.50336329
36.28979145
17.95651738
3.17242222
20.22346238
17.07301372
2.386059461
5.0429669
22.51255609
12.1945271
25.47503117
8.001388659
10.85369035
8.825689919
8.124307221
35.97971684
14.91412617
29.25935373
3.820067354
21.7287718
17.76647335
10.14087895

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'George Udny Yule' @ yule.wessa.net

\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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198678&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198678&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198678&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'George Udny Yule' @ yule.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean10.952980132450310.3171345240596
Biased Variance162.097325555897156.472685044617
Biased Standard Deviation12.73174479621312.508904230372
Covariance-37.9024662670805
Correlation-0.236414761189256
Determination0.0558919393081727
T-Test-2.97000288237303
p-value (2 sided)0.00347213542189348
p-value (1 sided)0.00173606771094674
Degrees of Freedom149
Number of Observations151

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 10.9529801324503 & 10.3171345240596 \tabularnewline
Biased Variance & 162.097325555897 & 156.472685044617 \tabularnewline
Biased Standard Deviation & 12.731744796213 & 12.508904230372 \tabularnewline
Covariance & -37.9024662670805 \tabularnewline
Correlation & -0.236414761189256 \tabularnewline
Determination & 0.0558919393081727 \tabularnewline
T-Test & -2.97000288237303 \tabularnewline
p-value (2 sided) & 0.00347213542189348 \tabularnewline
p-value (1 sided) & 0.00173606771094674 \tabularnewline
Degrees of Freedom & 149 \tabularnewline
Number of Observations & 151 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=198678&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]10.9529801324503[/C][C]10.3171345240596[/C][/ROW]
[ROW][C]Biased Variance[/C][C]162.097325555897[/C][C]156.472685044617[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]12.731744796213[/C][C]12.508904230372[/C][/ROW]
[ROW][C]Covariance[/C][C]-37.9024662670805[/C][/ROW]
[ROW][C]Correlation[/C][C]-0.236414761189256[/C][/ROW]
[ROW][C]Determination[/C][C]0.0558919393081727[/C][/ROW]
[ROW][C]T-Test[/C][C]-2.97000288237303[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.00347213542189348[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.00173606771094674[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]149[/C][/ROW]
[ROW][C]Number of Observations[/C][C]151[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=198678&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=198678&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
Mean10.952980132450310.3171345240596
Biased Variance162.097325555897156.472685044617
Biased Standard Deviation12.73174479621312.508904230372
Covariance-37.9024662670805
Correlation-0.236414761189256
Determination0.0558919393081727
T-Test-2.97000288237303
p-value (2 sided)0.00347213542189348
p-value (1 sided)0.00173606771094674
Degrees of Freedom149
Number of Observations151


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
x <- x[!is.na(y)]
y <- y[!is.na(y)]
y <- y[!is.na(x)]
x <- x[!is.na(x)]
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', na.rm = T)
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')