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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, 19 Dec 2010 10:06:34 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/19/t12927538365009ugnhi6mtzyq.htm/, Retrieved Sat, 04 May 2024 23:28:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112249, Retrieved Sat, 04 May 2024 23:28:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact199

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] [Screen dimensions] [2010-09-25 10:10:17] [b98453cac15ba1066b407e146608df68]
F    D  [Pearson Correlation] [Task 8] [2010-10-01 13:31:00] [39c51da0be01189e8a44eb69e891b7a1]
- R  D      [Pearson Correlation] [Pearson correlatie] [2010-12-19 10:06:34] [ecfb965f5669057f3ac5b58964283289] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
62.027
56.493
65.566
62.653
53.470
59.600
42.542
42.018
44.038
44.988
43.309
26.843
69.770
64.886
79.354
63.025
54.003
55.926
45.629
40.361
43.039
44.570
43.269
25.563
68.707
60.223
74.283
61.232
61.531
65.305
51.699
44.599
35.221
55.066
45.335
28.702
69.517
69.240
71.525
77.740
62.107
65.450
51.493
43.067
49.172
54.483
38.158
27.898
58.648
56.000
62.381
59.849
48.345
55.376
45.400
38.389
44.098
48.290
41.267
31.238
Dataseries Y:
Download CSV
Histogram 
63.152
60.106
72.616
73.159
68.848
77.056
62.246
60.777
64.513
58.353
56.511
44.554
71.414
65.719
80.997
69.826
65.386
75.589
65.520
59.003
63.961
59.716
57.520
42.886
69.805
64.656
80.353
71.321
76.577
81.580
71.127
63.478
48.152
69.236
57.038
43.621
69.551
72.009
72.140
81.519
73.310
80.406
70.697
59.328
68.281
70.041
51.244
46.538
61.443
62.256
73.117
74.155
65.191
77.889
68.688
59.983
65.470
65.089
54.795
47.123

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112249&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112249&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112249&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean52.566266666666765.4439166666667
Biased Variance165.98916632888993.3867756430555
Biased Standard Deviation12.88367829188899.66368333727133
Covariance109.370960937853
Correlation0.863813976906626
Determination0.746174586699241
T-Test13.0576995832223
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom58
Number of Observations60

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 52.5662666666667 & 65.4439166666667 \tabularnewline
Biased Variance & 165.989166328889 & 93.3867756430555 \tabularnewline
Biased Standard Deviation & 12.8836782918889 & 9.66368333727133 \tabularnewline
Covariance & 109.370960937853 \tabularnewline
Correlation & 0.863813976906626 \tabularnewline
Determination & 0.746174586699241 \tabularnewline
T-Test & 13.0576995832223 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 58 \tabularnewline
Number of Observations & 60 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112249&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]52.5662666666667[/C][C]65.4439166666667[/C][/ROW]
[ROW][C]Biased Variance[/C][C]165.989166328889[/C][C]93.3867756430555[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]12.8836782918889[/C][C]9.66368333727133[/C][/ROW]
[ROW][C]Covariance[/C][C]109.370960937853[/C][/ROW]
[ROW][C]Correlation[/C][C]0.863813976906626[/C][/ROW]
[ROW][C]Determination[/C][C]0.746174586699241[/C][/ROW]
[ROW][C]T-Test[/C][C]13.0576995832223[/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]58[/C][/ROW]
[ROW][C]Number of Observations[/C][C]60[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112249&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112249&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
Mean52.566266666666765.4439166666667
Biased Variance165.98916632888993.3867756430555
Biased Standard Deviation12.88367829188899.66368333727133
Covariance109.370960937853
Correlation0.863813976906626
Determination0.746174586699241
T-Test13.0576995832223
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom58
Number of Observations60


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')