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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 computationSun, 26 Oct 2008 02:42:59 -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/26/t1225010640dzqd1ul8qccq6du.htm/, Retrieved Sun, 19 May 2024 13:18:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18817, Retrieved Sun, 19 May 2024 13:18:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact166

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Pearson Correlation] [Correlation 4] [2008-10-20 20:11:08] [1ce0d16c8f4225c977b42c8fa93bc163]
-    D    [Pearson Correlation] [Correlation uitvo...] [2008-10-26 08:42:59] [35348cd8592af0baf5f138bd59921307] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
110,089
99,966
94,195
119,588
125,946
118,906
108,717
118,357
115,422
130,937
111,802
120,357
121,12
108,752
98,973
116,721
123,857
114,056
98,309
110,251
108,538
122,526
118,394
116,691
116,014
111,784
95,164
121,028
129,89
116,102
102,055
113,562
113,071
126,486
119,472
117,141
121,925
112,688
90,974
126,398
130,401
116,873
111,917
113,919
117,931
139,332
127,781
118,103
136,984
119,566
107,238
139,389
139,798
138,074
129,739
125,098
129,341
149,083
137,721
130,126
140,499
118,165
115,932
144,662
136,159
147,339
138,807
135,275
135,84
161,702
132,606
147,419
154,865
131,545
126,212
150,316
154,524
154,28
131,059
147,168
141,8
162,022
143,924
151,406
159,601
143,513
132,302
152,021
171,573
161,591
134,057
172,247
173,384
173,706
188,178
165,932
179,795
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 time2 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 & 2 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=18817&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18817&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18817&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean130.26870103092842.0888969072165
Biased Variance413.56743672505059.895269288341
Biased Standard Deviation20.33635750878347.73920340140644
Covariance145.778627323024
Correlation0.916693023780592
Determination0.840326099848005
T-Test22.3598436398696
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 & 130.268701030928 & 42.0888969072165 \tabularnewline
Biased Variance & 413.567436725050 & 59.895269288341 \tabularnewline
Biased Standard Deviation & 20.3363575087834 & 7.73920340140644 \tabularnewline
Covariance & 145.778627323024 \tabularnewline
Correlation & 0.916693023780592 \tabularnewline
Determination & 0.840326099848005 \tabularnewline
T-Test & 22.3598436398696 \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=18817&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]130.268701030928[/C][C]42.0888969072165[/C][/ROW]
[ROW][C]Biased Variance[/C][C]413.567436725050[/C][C]59.895269288341[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]20.3363575087834[/C][C]7.73920340140644[/C][/ROW]
[ROW][C]Covariance[/C][C]145.778627323024[/C][/ROW]
[ROW][C]Correlation[/C][C]0.916693023780592[/C][/ROW]
[ROW][C]Determination[/C][C]0.840326099848005[/C][/ROW]
[ROW][C]T-Test[/C][C]22.3598436398696[/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=18817&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18817&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
Mean130.26870103092842.0888969072165
Biased Variance413.56743672505059.895269288341
Biased Standard Deviation20.33635750878347.73920340140644
Covariance145.778627323024
Correlation0.916693023780592
Determination0.840326099848005
T-Test22.3598436398696
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')