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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 computationMon, 20 Oct 2008 14:09:14 -0600
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/Oct/20/t1224533380k9dbilzch2xjtki.htm/, Retrieved Sun, 19 May 2024 13:36:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18053, Retrieved Sun, 19 May 2024 13:36:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact160

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 3] [2008-10-20 20:09:14] [8758b22b4a10c08c31202f233362e983] [Current]
F    D    [Pearson Correlation] [Correlation uitvo...] [2008-10-26 08:30:05] [7d3039e6253bb5fb3b26df1537d500b4]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
102,304
92,21
94,286
109,345
109,86
117,246
111,809
111,632
112,409
121,071
107,623
113,404
112,668
95,427
92,277
105,719
107,744
103,928
99,202
98,849
101,745
113,954
107,602
105,701
105,36
99,026
88,89
108,373
116,241
105,09
109,849
106,491
108,557
116,774
107,602
100,462
107,728
99,877
86,387
110,637
118,557
106,845
113,374
104,78
111,239
129,093
113,399
104,622
127,335
105,192
104,149
124,768
123,846
122,667
129,199
114,973
121,42
139,194
126,568
120,341
131,997
108,813
113,012
136,439
125,17
139,811
142,757
134,35
135,657
162,163
129,7
140,799
142,35
122,134
125,81
141,304
142,108
143,785
131,428
137,147
136,219
153,798
133,063
143,912
149,099
140,254
129,512
143,443
162,133
155,445
147,506
172,927
175,685
179,308
186,447
166,948
172,428
Dataseries Y:
Download CSV
Histogram 
34,679
32,566
37,111
35,977
41,811
43,465
36,466
39,188
35,318
39,76
35,102
38,829
36,304
35,199
33,761
30,579
36,467
35,855
30,077
35,45
32,956
33,903
35,319
37,387
34,77
33,383
32,644
34,524
40,451
36,605
35,849
38,199
34,092
36,435
36,733
36,452
34,213
35,314
32,192
35,523
37,877
33,927
35,5
36,819
35,191
42,832
40,462
38,249
47,931
39,777
39,834
41,529
42,861
43,481
39,493
41,667
42,179
45,282
42,322
44,709
51,212
41,708
43,986
44,914
42,518
49,019
47,452
46,669
42,104
52,736
40,953
46,101
47,181
41,855
43,147
44,226
50,592
50,436
44,366
49,226
44,548
50,587
47,689
51,718
49,893
52,021
48,384
48,765
58,453
56,863
47,538
66,204
55,972
56,435
63,573
59,091
61,658

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'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18053&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18053&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18053&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'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean122.90495876288742.0888969072165
Biased Variance466.7513348436659.895269288341
Biased Standard Deviation21.60442859331537.73920340140644
Covariance157.881501495704
Correlation0.934526673279209
Determination0.873340103070305
T-Test25.5937509191467
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom95
Number of Observations97

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 122.904958762887 & 42.0888969072165 \tabularnewline
Biased Variance & 466.75133484366 & 59.895269288341 \tabularnewline
Biased Standard Deviation & 21.6044285933153 & 7.73920340140644 \tabularnewline
Covariance & 157.881501495704 \tabularnewline
Correlation & 0.934526673279209 \tabularnewline
Determination & 0.873340103070305 \tabularnewline
T-Test & 25.5937509191467 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 95 \tabularnewline
Number of Observations & 97 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18053&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]122.904958762887[/C][C]42.0888969072165[/C][/ROW]
[ROW][C]Biased Variance[/C][C]466.75133484366[/C][C]59.895269288341[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]21.6044285933153[/C][C]7.73920340140644[/C][/ROW]
[ROW][C]Covariance[/C][C]157.881501495704[/C][/ROW]
[ROW][C]Correlation[/C][C]0.934526673279209[/C][/ROW]
[ROW][C]Determination[/C][C]0.873340103070305[/C][/ROW]
[ROW][C]T-Test[/C][C]25.5937509191467[/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]95[/C][/ROW]
[ROW][C]Number of Observations[/C][C]97[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18053&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18053&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
Mean122.90495876288742.0888969072165
Biased Variance466.7513348436659.895269288341
Biased Standard Deviation21.60442859331537.73920340140644
Covariance157.881501495704
Correlation0.934526673279209
Determination0.873340103070305
T-Test25.5937509191467
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom95
Number of Observations97


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')