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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, 05 Nov 2012 07:48:38 -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/2012/Nov/05/t1352119734y8ozdgpbqryvw7o.htm/, Retrieved Sat, 20 Apr 2024 11:57:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=186020, Retrieved Sat, 20 Apr 2024 11:57:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact132

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [ws7/2] [2011-11-24 10:28:55] [8ae0a4da1b3ee81f40dbba5e42914d07]
- RMPD  [Pearson Correlation] [correlation Yt en...] [2011-11-24 12:50:00] [75512e061a94450f738c2449abbaac12]
-    D    [Pearson Correlation] [correlatie Yt en ...] [2011-11-24 12:57:28] [75512e061a94450f738c2449abbaac12]
- R  D      [Pearson Correlation] [WS7 - 2] [2012-11-05 12:44:22] [fe055a25191a04e375a94ef97fddf389]
-    D          [Pearson Correlation] [WS7 - 3] [2012-11-05 12:48:38] [bb6586829c319b85526f2aafa1a31f73] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
22274
14819
15136
13704
19638
7551
8019
6509
6634
11166
7508
4275
4944
5441
1689
1522
1416
1594
1909
2599
1262
1199
4404
1166
1122
886
778
4436
1890
3107
1038
300
988
2008
1522
1336
976
798
869
1260
578
2359
736
1690
1201
813
778
687
1270
671
1559
489
773
629
637
277
776
1651
377
222
1068
399
547
668
451
724
853
434
730
612
558
859
311
318
312
343
710
273
259
1274
625
245
235
250
NA
303
250
403
441
1507
388
530
107
868
NA
753
62
346
478
292
Dataseries Y:
Download CSV
Histogram 
72772
45104
44525
41169
31118
28435
22162
20202
17773
17094
15153
11218
10796
9594
9309
8556
8041
7639
6884
6642
6321
6216
5865
5799
5695
5644
5446
5395
5363
5338
5160
5091
5057
5039
4880
4735
4693
4653
4586
4398
3974
3858
3826
3819
3556
3372
3193
3126
3104
2967
2848
2748
2649
2625
2572
2548
2477
2442
2392
2372
2346
2251
2230
2225
2220
2205
2193
2116
2102
2099
2096
2064
2036
1920
1813
1776
1752
1738
1729
1685
1684
1549
1533
1528
1489
1456
1393
1370
1357
1292
1278
1256
1219
1217
1187
1187
1182
1157
1156
1155

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=186020&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=186020&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=186020&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
Mean2322.96938775516781.5612244898
Biased Variance16125237.5806955118244497.552374
Biased Standard Deviation4015.6241831993610874.0285797111
Covariance41622640.0689038
Correlation0.943477941744035
Determination0.890150626557561
T-Test27.8912883366229
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom96
Number of Observations98

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 2322.9693877551 & 6781.5612244898 \tabularnewline
Biased Variance & 16125237.5806955 & 118244497.552374 \tabularnewline
Biased Standard Deviation & 4015.62418319936 & 10874.0285797111 \tabularnewline
Covariance & 41622640.0689038 \tabularnewline
Correlation & 0.943477941744035 \tabularnewline
Determination & 0.890150626557561 \tabularnewline
T-Test & 27.8912883366229 \tabularnewline
p-value (2 sided) & 0 \tabularnewline
p-value (1 sided) & 0 \tabularnewline
Degrees of Freedom & 96 \tabularnewline
Number of Observations & 98 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=186020&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]2322.9693877551[/C][C]6781.5612244898[/C][/ROW]
[ROW][C]Biased Variance[/C][C]16125237.5806955[/C][C]118244497.552374[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]4015.62418319936[/C][C]10874.0285797111[/C][/ROW]
[ROW][C]Covariance[/C][C]41622640.0689038[/C][/ROW]
[ROW][C]Correlation[/C][C]0.943477941744035[/C][/ROW]
[ROW][C]Determination[/C][C]0.890150626557561[/C][/ROW]
[ROW][C]T-Test[/C][C]27.8912883366229[/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]96[/C][/ROW]
[ROW][C]Number of Observations[/C][C]98[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=186020&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=186020&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
Mean2322.96938775516781.5612244898
Biased Variance16125237.5806955118244497.552374
Biased Standard Deviation4015.6241831993610874.0285797111
Covariance41622640.0689038
Correlation0.943477941744035
Determination0.890150626557561
T-Test27.8912883366229
p-value (2 sided)0
p-value (1 sided)0
Degrees of Freedom96
Number of Observations98


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')