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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 computationSat, 17 Dec 2011 07:56:24 -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/2011/Dec/17/t1324126596frdyhnqw8m8pbrk.htm/, Retrieved Tue, 16 Apr 2024 23:49:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=156239, Retrieved Tue, 16 Apr 2024 23:49:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact91

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [] [2010-12-05 18:56:24] [b98453cac15ba1066b407e146608df68]
- RMPD  [Pearson Correlation] [Workshop 10 Corre...] [2011-12-09 17:37:08] [de8512d9b386046939a89973b76869e3]
- R  D      [Pearson Correlation] [] [2011-12-17 12:56:24] [43f1c1fe5c2aaa4d7bd6f731e1a494da] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
140824
110459
105079
112098
43929
76173
187326
22807
144408
66485
79089
81625
68788
103297
69446
114948
167949
125081
125818
136588
112431
103037
82317
118906
83515
104581
103129
83243
37110
113344
139165
86652
112302
69652
119442
69867
101629
70168
31081
103925
92622
79011
93487
64520
93473
114360
33032
96125
151911
89256
95671
5950
149695
32551
31701
100087
169707
150491
120192
95893
151715
176225
59900
104767
114799
72128
143592
89626
131072
126817
81351
22618
88977
92059
81897
108146
126372
249771
71154
71571
55918
160141
38692
102812
56622
15986
123534
108535
93879
144551
56750
127654
65594
59938
146975
143372
168553
183500
165986
184923
140358
149959
57224
43750
48029
104978
100046
101047
197426
160902
147172
109432
1168
83248
25162
45724
110529
855
101382
14116
89506
135356
116066
144244
8773
102153
117440
104128
134238
134047
279488
79756
66089
102070
146760
154771
165933
64593
92280
67150
128692
124089
125386
37238
140015
150047
154451
156349
0
6023
0
0
0
0
84601
68946
0
0
1644
6179
3926
52789
0
100350
Dataseries Y:
Download CSV
Histogram 
270018
179444
222373
218443
162874
70849
498732
33186
207822
213274
296074
237633
164107
358752
222781
369889
305704
322896
176082
263411
271965
425544
179306
189897
219420
207280
267198
270750
155915
327474
278019
204039
318563
97717
369331
273950
422946
215710
115469
336047
324178
166266
195153
173510
153778
455168
78800
208051
334657
175523
213060
24188
372238
65029
101097
279012
302218
323485
339837
252529
370483
303406
233632
264889
228595
216027
187965
237323
232765
175699
239314
73566
242585
187167
191920
359644
341637
206059
201783
182231
153613
447353
145943
280343
80953
150216
156923
365370
318651
179797
251466
254506
185890
263577
314255
189252
222504
285198
368878
397681
287015
285330
186856
43287
185468
219475
259692
301614
121726
154165
306952
297982
23623
195817
61857
163766
384053
21054
252805
31961
311281
240153
174892
152043
38214
198094
353021
196269
403932
316105
396725
187992
102424
283950
401260
137843
383703
157429
236370
282399
217478
366774
236660
173260
323545
168994
246745
301703
1
14688
98
455
0
0
233143
368328
0
203
7199
46660
17547
116678
969
199726

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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156239&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156239&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156239&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'Gertrude Mary Cox' @ cox.wessa.net






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean94780.4451219512219190.067073171
Biased Variance2688672457.3567412504236866.8431
Biased Standard Deviation51852.4103331441111822.345114217
Covariance4141668138.55892
Correlation0.709939774501961
Determination0.504014483419895
T-Test12.8305276877407
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom162
Number of Observations164

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 94780.4451219512 & 219190.067073171 \tabularnewline
Biased Variance & 2688672457.35674 & 12504236866.8431 \tabularnewline
Biased Standard Deviation & 51852.4103331441 & 111822.345114217 \tabularnewline
Covariance & 4141668138.55892 \tabularnewline
Correlation & 0.709939774501961 \tabularnewline
Determination & 0.504014483419895 \tabularnewline
T-Test & 12.8305276877407 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 162 \tabularnewline
Number of Observations & 164 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156239&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]94780.4451219512[/C][C]219190.067073171[/C][/ROW]
[ROW][C]Biased Variance[/C][C]2688672457.35674[/C][C]12504236866.8431[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]51852.4103331441[/C][C]111822.345114217[/C][/ROW]
[ROW][C]Covariance[/C][C]4141668138.55892[/C][/ROW]
[ROW][C]Correlation[/C][C]0.709939774501961[/C][/ROW]
[ROW][C]Determination[/C][C]0.504014483419895[/C][/ROW]
[ROW][C]T-Test[/C][C]12.8305276877407[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]162[/C][/ROW]
[ROW][C]Number of Observations[/C][C]164[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156239&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156239&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
Mean94780.4451219512219190.067073171
Biased Variance2688672457.3567412504236866.8431
Biased Standard Deviation51852.4103331441111822.345114217
Covariance4141668138.55892
Correlation0.709939774501961
Determination0.504014483419895
T-Test12.8305276877407
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom162
Number of Observations164


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')