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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 computationMon, 20 Dec 2010 15:29:16 +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/20/t1292858844olrsuoro91epe8j.htm/, Retrieved Fri, 03 May 2024 18:38:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112998, Retrieved Fri, 03 May 2024 18:38:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Pearson Correlati...] [2010-12-20 15:29:16] [55fca7c82a53ae69fe96aa1750b06058] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
85.334492
86.09449414
96.57199043
94.71639434
86.73119155
87.75563173
96.25953607
95.56006558
89.92194836
90.26424442
98.85533083
95.80330025
91.86548922
91.56037318
100.8626506
100.4556201
94.66315636
94.27859711
103.5047587
103.2146892
96.10376732
95.21767635
105.2941157
104.968819
99.04979293
100.4414598
111.4468631
110.7535953
105.6477558
105.3631224
115.0971273
115.1088249
106.8840226
108.3580626
116.2410156
116.4577372
109.359449
109.4105199
118.4803659
120.3925104
112.3933786
111.7691161
121.5416059
122.3620511
114.7979273
115.2853501
124.8763726
124.9793051
118.463543
120.8677241
129.1531371
129.05294
122.3768726
121.9853848
132.3042669
135.9430835
Dataseries Y:
Download CSV
Histogram 
108.3286119
96.4958159
75.71815718
143.3786686
100.6490265
97.66865079
79.02488573
129.6915167
103.567889
98.32535885
71.43552311
140.3950954
83.01795245
112.7995324
73.98963731
130.2521008
107.5268817
93.7
82.6040555
112.0155039
107.4394464
97.69189479
74.28571429
130.9171598
106.1016949
97.44408946
75.57377049
144.9023861
95.35928144
96.9126112
80.02159827
133.4008097
98.63429439
102.1538462
81.07429719
126.0681115
105.5009823
97.76536313
76.33333333
128.4466625
101.7484216
105.4892601
72.80542986
122.0633934
107.6374745
97.16177862
69.32814021
142.2050562
98.91358025
100.6989516
75.75607338
139.3324607
94.59840301
112.1648461
79.8583444
132.7605322

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=112998&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=112998&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112998&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
Mean107.366118144107102.663113521964
Biased Variance167.661520393847441.129559060172
Biased Standard Deviation12.948417679154721.0030845129989
Covariance11.0063938650911
Correlation0.0397484257134597
Determination0.00157993734669843
T-Test0.292321099025175
p-value (2 sided)0.771161352871245
p-value (1 sided)0.385580676435622
Degrees of Freedom54
Number of Observations56

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 107.366118144107 & 102.663113521964 \tabularnewline
Biased Variance & 167.661520393847 & 441.129559060172 \tabularnewline
Biased Standard Deviation & 12.9484176791547 & 21.0030845129989 \tabularnewline
Covariance & 11.0063938650911 \tabularnewline
Correlation & 0.0397484257134597 \tabularnewline
Determination & 0.00157993734669843 \tabularnewline
T-Test & 0.292321099025175 \tabularnewline
p-value (2 sided) & 0.771161352871245 \tabularnewline
p-value (1 sided) & 0.385580676435622 \tabularnewline
Degrees of Freedom & 54 \tabularnewline
Number of Observations & 56 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112998&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]107.366118144107[/C][C]102.663113521964[/C][/ROW]
[ROW][C]Biased Variance[/C][C]167.661520393847[/C][C]441.129559060172[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]12.9484176791547[/C][C]21.0030845129989[/C][/ROW]
[ROW][C]Covariance[/C][C]11.0063938650911[/C][/ROW]
[ROW][C]Correlation[/C][C]0.0397484257134597[/C][/ROW]
[ROW][C]Determination[/C][C]0.00157993734669843[/C][/ROW]
[ROW][C]T-Test[/C][C]0.292321099025175[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.771161352871245[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.385580676435622[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]54[/C][/ROW]
[ROW][C]Number of Observations[/C][C]56[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112998&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112998&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
Mean107.366118144107102.663113521964
Biased Variance167.661520393847441.129559060172
Biased Standard Deviation12.948417679154721.0030845129989
Covariance11.0063938650911
Correlation0.0397484257134597
Determination0.00157993734669843
T-Test0.292321099025175
p-value (2 sided)0.771161352871245
p-value (1 sided)0.385580676435622
Degrees of Freedom54
Number of Observations56


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')