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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 computationFri, 11 Apr 2014 10:43:01 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Apr/11/t1397227417ersw9q87iruu93g.htm/, Retrieved Fri, 17 May 2024 04:59:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234428, Retrieved Fri, 17 May 2024 04:59:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact205

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 
53
46
46
41
41
44
44
50
50
61
61
53
53
56
56
50
50
58
58
50
50
38
38
26
26
18
18
24
24
29
29
40
40
40
40
53
53
44
44
49
49
50
50
49
49
49
49
35
35
36
36
33
33
32
32
36
36
42
42
44
44
42
42
37
37
38
38
41
41
53
53
54
54
53
53
45
45
45
45
44
44
43
43
52
52
55
55
55
55
50
49
51
51
55
55
49
49
40
40
47
47
45
Dataseries Y:
Download CSV
Histogram 
6537.88
6663.85
6036.54
6112.61
6863.63
6599.81
7116.87
7138.95
6979.36
6688.86
6963.35
7746.64
7833.88
7898.83
8302.58
8267.41
8259.88
8661.12
7840.05
7282.38
6302.57
6186.65
6810.29
7366.4
8266.44
8635.17
8284.28
8872.91
9574.48
11161
13126.95
15152.96
16167.26
15836
13855.39
13443.79
13762.44
13452.82
14384.51
15281.26
15633.24
16099.4
15729.94
16556.65
16613.26
16660.44
16266.13
17095.35
17181.9
17334.63
18114.05
18632.33
19437.08
20442.3
21540.8
21892.61
22738.8
23221.83
23003.18
23462.63
24431.7
25564.9
25199.86
24907.28
25995.71
26921.91
28120.33
28694.04
28294.53
28740.74
27923.33
28953.24
30784.2
31805.07
32624.24
33453.3
34544.05
35478.82
35755.71
35257.76
36029.22
36540.37
37557.46
38125.12
39113.65
40383.14
41691.95
43215.86
44494.65
44471.56
44832.35
45660.06
46968.24
48094.38
48910
49310.56
48707.74
46927.16
47709.96
48239.6
49231.18
49797

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' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234428&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' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234428&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234428&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' @ wold.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean44.57843137254922733.6914705882
Biased Variance81.1262014609765196512440.452505
Biased Standard Deviation9.0070084634675814018.2894980987
Covariance28577.4571607455
Correlation0.224114104264692
Determination0.0502271317303654
T-Test2.29963711571525
p-value (2 sided)0.0235475876894498
p-value (1 sided)0.0117737938447249
Degrees of Freedom100
Number of Observations102

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 44.578431372549 & 22733.6914705882 \tabularnewline
Biased Variance & 81.1262014609765 & 196512440.452505 \tabularnewline
Biased Standard Deviation & 9.00700846346758 & 14018.2894980987 \tabularnewline
Covariance & 28577.4571607455 \tabularnewline
Correlation & 0.224114104264692 \tabularnewline
Determination & 0.0502271317303654 \tabularnewline
T-Test & 2.29963711571525 \tabularnewline
p-value (2 sided) & 0.0235475876894498 \tabularnewline
p-value (1 sided) & 0.0117737938447249 \tabularnewline
Degrees of Freedom & 100 \tabularnewline
Number of Observations & 102 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234428&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]44.578431372549[/C][C]22733.6914705882[/C][/ROW]
[ROW][C]Biased Variance[/C][C]81.1262014609765[/C][C]196512440.452505[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]9.00700846346758[/C][C]14018.2894980987[/C][/ROW]
[ROW][C]Covariance[/C][C]28577.4571607455[/C][/ROW]
[ROW][C]Correlation[/C][C]0.224114104264692[/C][/ROW]
[ROW][C]Determination[/C][C]0.0502271317303654[/C][/ROW]
[ROW][C]T-Test[/C][C]2.29963711571525[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0235475876894498[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0117737938447249[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]100[/C][/ROW]
[ROW][C]Number of Observations[/C][C]102[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234428&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234428&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
Mean44.57843137254922733.6914705882
Biased Variance81.1262014609765196512440.452505
Biased Standard Deviation9.0070084634675814018.2894980987
Covariance28577.4571607455
Correlation0.224114104264692
Determination0.0502271317303654
T-Test2.29963711571525
p-value (2 sided)0.0235475876894498
p-value (1 sided)0.0117737938447249
Degrees of Freedom100
Number of Observations102


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')