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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 computationThu, 21 Nov 2013 03:02:17 -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/2013/Nov/21/t1385020953c5h80snac3jhlq4.htm/, Retrieved Fri, 03 May 2024 14:54:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=226786, Retrieved Fri, 03 May 2024 14:54:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [] [2013-11-21 08:02:17] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100
170
76
64
86
71
58
68
180
72
55
131
116
60
67
60
81
64
63
95
86
69
68
172
170
64
181
74
89
88
159
79
91
51
43
142
46
52
44
154
40
160
68
102
51
133
177
349
285
231
130
Dataseries Y:
Download CSV
Histogram 
8
10
8
7
8
8
8
9
8
8
8
12
8
7
6
7
8
7
10
11
8
8
7
9
8
8
9
7
9
8
7
8
7
8
7
6
6
6
7
6
7
5
7
6
8
8
9
8
7
11
7

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'Sir Maurice George Kendall' @ kendall.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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226786&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226786&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226786&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'Sir Maurice George Kendall' @ kendall.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean105.5882352941187.80392156862745
Biased Variance3969.73241061131.80469050365244
Biased Standard Deviation63.00581251449191.3433876967028
Covariance17.0976470588235
Correlation0.198040581561741
Determination0.0392200719453126
T-Test1.41429586707632
p-value (2 sided)0.163597987115322
p-value (1 sided)0.0817989935576612
Degrees of Freedom49
Number of Observations51

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 105.588235294118 & 7.80392156862745 \tabularnewline
Biased Variance & 3969.7324106113 & 1.80469050365244 \tabularnewline
Biased Standard Deviation & 63.0058125144919 & 1.3433876967028 \tabularnewline
Covariance & 17.0976470588235 \tabularnewline
Correlation & 0.198040581561741 \tabularnewline
Determination & 0.0392200719453126 \tabularnewline
T-Test & 1.41429586707632 \tabularnewline
p-value (2 sided) & 0.163597987115322 \tabularnewline
p-value (1 sided) & 0.0817989935576612 \tabularnewline
Degrees of Freedom & 49 \tabularnewline
Number of Observations & 51 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226786&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]105.588235294118[/C][C]7.80392156862745[/C][/ROW]
[ROW][C]Biased Variance[/C][C]3969.7324106113[/C][C]1.80469050365244[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]63.0058125144919[/C][C]1.3433876967028[/C][/ROW]
[ROW][C]Covariance[/C][C]17.0976470588235[/C][/ROW]
[ROW][C]Correlation[/C][C]0.198040581561741[/C][/ROW]
[ROW][C]Determination[/C][C]0.0392200719453126[/C][/ROW]
[ROW][C]T-Test[/C][C]1.41429586707632[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.163597987115322[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0817989935576612[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]49[/C][/ROW]
[ROW][C]Number of Observations[/C][C]51[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226786&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226786&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
Mean105.5882352941187.80392156862745
Biased Variance3969.73241061131.80469050365244
Biased Standard Deviation63.00581251449191.3433876967028
Covariance17.0976470588235
Correlation0.198040581561741
Determination0.0392200719453126
T-Test1.41429586707632
p-value (2 sided)0.163597987115322
p-value (1 sided)0.0817989935576612
Degrees of Freedom49
Number of Observations51


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')