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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 computationThu, 27 Sep 2012 04:26:59 -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/2012/Sep/27/t1348734853zp00afy8felq0xv.htm/, Retrieved Mon, 29 Apr 2024 15:01:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=170020, Retrieved Mon, 29 Apr 2024 15:01:21 +0000
QR Codes:

Original text written by user:Here I have correlated height (m) in the y-axis versus weight (kg) in the x-axis. The output is a Pearson correlation of r=0.63 and the P-value is 3.83 x 10-6 (essentially 3.83 with the decimal place moved down by 6 places - very low indeed so just state this as 'P<0.001'.
IsPrivate?No (this computation is public)
User-defined keywordsExample of output of correlation calculation, using class height and weight (all data are anonymised)
Estimated Impact204

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Height v weight] [2012-09-27 08:26:59] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1.69
1.68
1.63
1.61
1.87
1.83
1.61
1.69
1.76
1.73
1.84
1.71
1.62
1.6
1.84
1.59
1.66
1.78
1.74
1.81
1.89
1.75
1.78
1.8
1.71
1.69
1.89
1.88
1.86
1.9
1.83
1.76
1.85
1.72
1.81
1.9
1.7
1.71
1.88
1.82
1.83
1.67
1.9
1.79
1.76
Dataseries Y:
Download CSV
Histogram 
62.6
61.6
63.4
46.5
81.7
82.5
55.5
68.8
65.3
68
95
95
53.6
48.8
84.7
69.3
53.5
91.8
75.8
89
115.8
72
74.5
72.5
72.6
72.5
81
76.2
88
72.8
82
57.3
68
62.1
73.9
84.2
58.7
63
76.6
56
56.4
63.4
83.5
59.8
76.4

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' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=170020&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=170020&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=170020&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' @ jenkins.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean1.7637777777777871.8133333333333
Biased Variance0.00843683950617284191.648711111111
Biased Standard Deviation0.091852270010995613.8437246112132
Covariance0.817016666666667
Correlation0.628243832010604
Determination0.394690312459368
T-Test5.29509369213878
p-value (2 sided)3.83102897894005e-06
p-value (1 sided)1.91551448947003e-06
Degrees of Freedom43
Number of Observations45

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 1.76377777777778 & 71.8133333333333 \tabularnewline
Biased Variance & 0.00843683950617284 & 191.648711111111 \tabularnewline
Biased Standard Deviation & 0.0918522700109956 & 13.8437246112132 \tabularnewline
Covariance & 0.817016666666667 \tabularnewline
Correlation & 0.628243832010604 \tabularnewline
Determination & 0.394690312459368 \tabularnewline
T-Test & 5.29509369213878 \tabularnewline
p-value (2 sided) & 3.83102897894005e-06 \tabularnewline
p-value (1 sided) & 1.91551448947003e-06 \tabularnewline
Degrees of Freedom & 43 \tabularnewline
Number of Observations & 45 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=170020&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]1.76377777777778[/C][C]71.8133333333333[/C][/ROW]
[ROW][C]Biased Variance[/C][C]0.00843683950617284[/C][C]191.648711111111[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]0.0918522700109956[/C][C]13.8437246112132[/C][/ROW]
[ROW][C]Covariance[/C][C]0.817016666666667[/C][/ROW]
[ROW][C]Correlation[/C][C]0.628243832010604[/C][/ROW]
[ROW][C]Determination[/C][C]0.394690312459368[/C][/ROW]
[ROW][C]T-Test[/C][C]5.29509369213878[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]3.83102897894005e-06[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.91551448947003e-06[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]43[/C][/ROW]
[ROW][C]Number of Observations[/C][C]45[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=170020&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=170020&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
Mean1.7637777777777871.8133333333333
Biased Variance0.00843683950617284191.648711111111
Biased Standard Deviation0.091852270010995613.8437246112132
Covariance0.817016666666667
Correlation0.628243832010604
Determination0.394690312459368
T-Test5.29509369213878
p-value (2 sided)3.83102897894005e-06
p-value (1 sided)1.91551448947003e-06
Degrees of Freedom43
Number of Observations45


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')