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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 computationSun, 17 Apr 2011 16:03:41 +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/2011/Apr/17/t1303056013t8ef581udl75wn7.htm/, Retrieved Thu, 09 May 2024 16:11:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=120610, Retrieved Thu, 09 May 2024 16:11:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact232

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [Lack of correlati...] [2011-04-17 16:03:41] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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23026
22927
22838
22686
22799
22820
22835
22854
22650
22657
22744
22664
22688
22447
22044
21796
21400
21470
21569
21711
21850
21943
21959
22008
22044
22024
22047
22067
22106
22005
21909
21793
21775
21830
21814
21802
21851
21812
21780
21771
21757
21759
21638
21510
21411
21385
21490
19065
19919
20919
20912
20913
20810
20808
20746
20601
20383
20091
20099
19896
19793
19421
19187
18969
18708
18566
18200
18200
17013
16998
16894
16937
16952
16882
16864
16944
16987
17060
17143
17218
17280
17278
17310
17389
17502
17609
17816
17982
17996
18247
18489
18510
18670
18823
18967
18946
19275
19546
19514
19836
19731
20165
20448
20624
20969
21135
21316
21642
21743
22021
22144
22416
22454
22584
22676
22878
22905
23049
23288
23442
23570
23791
23769
23921
23353
24162
24407
24552
24782
24783
25071
24496
25156
25228
25384
25740
25860
23791
24306
25278
24727
25568
25672
25405
25404
25858
26160
26088
26192
26177
26286
25606
26227
26143
26084
26119
26038
26038
26031
26010
25946
25088
25670
25425
25338
25157
25029
24876
24851
24747
24523
24301
24182
24085
23961
23699
23850
23669
23340
23394
23227
23263
23253
23239
23206
23131
23083
23088
22953
22955
22845
22834
22848
22784
22769
22741
22625
20344
20832
21083
21242
21287
21184
21044
20872
20819
20698
20424
20249
20151
19898
19652
19516
19416
19293
19015
18971
18902
18778
18622
18574
18480
18337
18279
18327
18343
18405
18464
18051
18591
18774
18859
18915
18463
18668
18836
19251
16875
17379
17859
18118
18373
18668
Dataseries Y:
Download CSV
Histogram 
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0.0004593573
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0.0004685962
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0.0005344337
0.0005154457
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0.0006371907
0.0005808047
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0.0004292553
0.0004442501
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0.0003197241
0.0003321938
0.0003321938
0.0003321938
0.0003171991
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0.0003321941
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0.0003505026
0.0003598743
0.0003598743
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0.0003748693
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0.0004123562
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0.0004873299
0.0004873299
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0.0004590418
0.0005433873
0.0004590418
0.0005433873
0.0005339461
0.0005153584
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0.0005342754
0.0005343449
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0.0005154457
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0.0004404708
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0.0004878884
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0.0003454042
0.000335963
0.0003264758
0.0003317982
0.0003316599
0.0003260369
0.0003167043
0.0003017095
0.0003111117
0.000296092
0.0002961613
0.0002905632
0.0003085424
0.0003010955
0.0002920467
0.0003016361

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'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120610&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]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=120610&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120610&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'Herman Ole Andreas Wold' @ www.yougetit.org






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean21564.43032786890.000423103434836066
Biased Variance6970087.310719568.79791719583547e-09
Biased Standard Deviation2640.092292083669.3797213156018e-05
Covariance0.121857381666017
Correlation0.490071272426121
Determination0.240169852057358
T-Test8.7459837821133
p-value (2 sided)4.44089209850063e-16
p-value (1 sided)2.22044604925031e-16
Degrees of Freedom242
Number of Observations244

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 21564.4303278689 & 0.000423103434836066 \tabularnewline
Biased Variance & 6970087.31071956 & 8.79791719583547e-09 \tabularnewline
Biased Standard Deviation & 2640.09229208366 & 9.3797213156018e-05 \tabularnewline
Covariance & 0.121857381666017 \tabularnewline
Correlation & 0.490071272426121 \tabularnewline
Determination & 0.240169852057358 \tabularnewline
T-Test & 8.7459837821133 \tabularnewline
p-value (2 sided) & 4.44089209850063e-16 \tabularnewline
p-value (1 sided) & 2.22044604925031e-16 \tabularnewline
Degrees of Freedom & 242 \tabularnewline
Number of Observations & 244 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=120610&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]21564.4303278689[/C][C]0.000423103434836066[/C][/ROW]
[ROW][C]Biased Variance[/C][C]6970087.31071956[/C][C]8.79791719583547e-09[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]2640.09229208366[/C][C]9.3797213156018e-05[/C][/ROW]
[ROW][C]Covariance[/C][C]0.121857381666017[/C][/ROW]
[ROW][C]Correlation[/C][C]0.490071272426121[/C][/ROW]
[ROW][C]Determination[/C][C]0.240169852057358[/C][/ROW]
[ROW][C]T-Test[/C][C]8.7459837821133[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]4.44089209850063e-16[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]2.22044604925031e-16[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]242[/C][/ROW]
[ROW][C]Number of Observations[/C][C]244[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=120610&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=120610&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
Mean21564.43032786890.000423103434836066
Biased Variance6970087.310719568.79791719583547e-09
Biased Standard Deviation2640.092292083669.3797213156018e-05
Covariance0.121857381666017
Correlation0.490071272426121
Determination0.240169852057358
T-Test8.7459837821133
p-value (2 sided)4.44089209850063e-16
p-value (1 sided)2.22044604925031e-16
Degrees of Freedom242
Number of Observations244


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')