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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, 02 Nov 2009 06:02:46 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/02/t1257167040o4p3tq7r2wpeknn.htm/, Retrieved Fri, 03 May 2024 19:05:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=52554, Retrieved Fri, 03 May 2024 19:05:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Pearson Correlation] [WS5-Pearson Corre...] [2009-11-02 13:02:46] [0cc924834281808eda7297686c82928f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
-1345.524047
-2903.542911
426.0061823
128.1400331
-360.1263768
-259.1728883
-851.6235307
469.1211691
2334.282666
-64.10234394
2157.52892
733.142615
250.1555364
-1624.55119
1808.534593
2905.586023
1848.615216
655.7679328
1162.523228
1123.254495
2741.764052
400.2289131
1425.329685
1570.489633
719.8782672
-1347.917082
745.7103047
1403.037429
546.7694751
-3489.706533
-2062.764672
-2280.596458
-1467.803967
-942.9943854
-886.3881872
-1996.031094
-727.0034212
-4770.786129
-2052.208885
82.89190751
-2652.026713
-3341.779671
-1548.248651
-2073.976825
-671.6197169
-996.3949052
-1187.367253
-2360.1001
-1662.506024
-5020.72902
-1908.497264
-118.53264
-2970.561859
-1405.816092
-1646.800071
-2214.467019
-665.0835758
-844.221019
-1508.620238
-946.0127792
-1476.407844
-2652.22204
-492.9050182
1170.670463
-1799.745861
-362.6308353
-545.7584742
-1249.361082
287.2918716
305.302748
-1730.877381
425.2830983
-804.554091
-2345.11198
1234.432456
-187.8556572
147.147942
459.244866
278.0192908
147.6453824
2533.081024
129.2296303
1944.763989
1985.781554
410.3650286
-1545.498547
146.4636974
1225.492132
958.918742
520.7373862
1099.749254
64.93192921
3521.043053
610.6412411
2210.921351
1841.389285
1973.5552
-552.013028
1098.968101
3297.288254
481.756705
995.6513386
3233.046931
3195.216694
3279.56372
5136.845895
4246.561412
4541.772999
4129.559065
617.9107561
3309.055684
3685.163193
-1679.698063
-1579.335244
-1534.49105
-2274.367558
-1549.988757
-1364.544547
-1420.58485
-195.0641937
Dataseries Y:
Download CSV
Histogram 
-9.950226456
-50.34292536
-6.014069555
-16.96378285
-30.80492445
38.72826771
-8.137816864
27.54351825
19.61109823
33.58231736
87.90010911
23.6982651
19.50621454
-155.5096355
-191.6906481
36.5201684
-125.4821252
-2.882323942
-88.03410605
-9.502682971
-29.73106637
-16.32715355
-56.49376266
59.23658854
56.89313054
-45.58155181
-35.39887115
-95.16443446
-32.37235783
83.251308
205.2927982
180.0921499
-52.09798504
-48.03094912
-216.5252184
-246.9460531
204.2802909
-86.90284266
-172.6419936
40.47318523
-572.696242
144.6375007
42.23202084
-243.0953917
-25.0048854
-140.55699
-198.2124341
-445.4037679
62.53645493
-129.1123364
-238.8775543
-53.8696505
-271.4195919
-38.57712427
-135.7379016
-116.4300565
-517.306661
-128.7052112
-168.687742
-387.9452614
-224.4330961
-132.0323207
-562.1477765
183.175254
-472.5757885
-169.1114404
-181.8014711
-214.515754
-245.8199438
9.420155311
-717.8145616
-246.3604598
74.80515564
87.19718014
88.97345562
186.4997702
-262.0247036
-235.8605575
292.0422345
88.25185206
86.2058235
276.188136
181.266754
142.4727584
269.3188358
310.6470922
-400.7473563
131.5714845
-423.2496727
159.4151739
394.0165162
172.920152
709.4971541
-2.788318665
218.4214259
-103.4524387
514.614897
-148.33898
495.5410584
-66.92044222
198.0749184
4.591126846
305.3890808
134.2688456
232.0912474
528.1506303
196.975153
-42.99672098
144.8522984
99.45454314
138.1478089
208.6379438
66.08000411
276.3296979
213.9395174
98.8189303
150.4010864
445.3222469
351.7020638
262.4552631

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=52554&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=52554&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=52554&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean-2.66666605406215e-09-2.9999983654679e-10
Biased Variance3744349.2180752554317.50569887
Biased Standard Deviation1935.03209742765233.061162999909
Covariance166814.083486611
Correlation0.366809307021400
Determination0.134549067717519
T-Test4.28311884496443
p-value (2 sided)3.776940766409e-05
p-value (1 sided)1.8884703832045e-05
Degrees of Freedom118
Number of Observations120

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & -2.66666605406215e-09 & -2.9999983654679e-10 \tabularnewline
Biased Variance & 3744349.21807525 & 54317.50569887 \tabularnewline
Biased Standard Deviation & 1935.03209742765 & 233.061162999909 \tabularnewline
Covariance & 166814.083486611 \tabularnewline
Correlation & 0.366809307021400 \tabularnewline
Determination & 0.134549067717519 \tabularnewline
T-Test & 4.28311884496443 \tabularnewline
p-value (2 sided) & 3.776940766409e-05 \tabularnewline
p-value (1 sided) & 1.8884703832045e-05 \tabularnewline
Degrees of Freedom & 118 \tabularnewline
Number of Observations & 120 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=52554&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]-2.66666605406215e-09[/C][C]-2.9999983654679e-10[/C][/ROW]
[ROW][C]Biased Variance[/C][C]3744349.21807525[/C][C]54317.50569887[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]1935.03209742765[/C][C]233.061162999909[/C][/ROW]
[ROW][C]Covariance[/C][C]166814.083486611[/C][/ROW]
[ROW][C]Correlation[/C][C]0.366809307021400[/C][/ROW]
[ROW][C]Determination[/C][C]0.134549067717519[/C][/ROW]
[ROW][C]T-Test[/C][C]4.28311884496443[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]3.776940766409e-05[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.8884703832045e-05[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]118[/C][/ROW]
[ROW][C]Number of Observations[/C][C]120[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=52554&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=52554&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
Mean-2.66666605406215e-09-2.9999983654679e-10
Biased Variance3744349.2180752554317.50569887
Biased Standard Deviation1935.03209742765233.061162999909
Covariance166814.083486611
Correlation0.366809307021400
Determination0.134549067717519
T-Test4.28311884496443
p-value (2 sided)3.776940766409e-05
p-value (1 sided)1.8884703832045e-05
Degrees of Freedom118
Number of Observations120


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')