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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 computationSat, 20 Oct 2007 07:33:09 -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/2007/Oct/20/pf033jtg6fnptnh1192890657.htm/, Retrieved Thu, 02 May 2024 22:58:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1158, Retrieved Thu, 02 May 2024 22:58:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsQ4 juist
Estimated Impact437

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Pearson Correlation] [Q4 Clothing produ...] [2007-10-20 14:33:09] [1a83104d28786df2e24859e2e02dc234] [Current]
F    D    [Pearson Correlation] [Q4 - Clothing pro...] [2008-10-15 17:49:05] [a57f5cc542637534b8bb5bcb4d37eab1]
F R  D      [Pearson Correlation] [Correlatie Huurpr...] [2008-10-20 16:19:38] [a57f5cc542637534b8bb5bcb4d37eab1]
F R  D      [Pearson Correlation] [Correlatie Gasoli...] [2008-10-20 16:22:41] [a57f5cc542637534b8bb5bcb4d37eab1]
F R  D      [Pearson Correlation] [Correlatie Eurosu...] [2008-10-20 16:24:31] [a57f5cc542637534b8bb5bcb4d37eab1]
F R  D      [Pearson Correlation] [Correlatie Huurpr...] [2008-10-20 16:26:07] [a57f5cc542637534b8bb5bcb4d37eab1]
-    D    [Pearson Correlation] [Q4: Is Clothing P...] [2008-10-17 12:28:27] [1e1d8320a8a1170c475bf6e4ce119de6]
F    D    [Pearson Correlation] [Overeenkomst prod...] [2008-10-17 15:01:56] [cf45c678b7899ee33d7b061948f80651]
F    D    [Pearson Correlation] [Correlatie 2] [2008-10-17 21:21:18] [8b0d202c3a0c4ea223fd8b8e731dacd8]
-    D    [Pearson Correlation] [Correlatie kledin...] [2008-10-18 14:06:45] [d32f94eec6fe2d8c421bd223368a5ced]
F    D    [Pearson Correlation] [Kledij geassociee...] [2008-10-18 16:21:36] [93834488277b53a4510bfd06084ae13b]
- RM D    [Percentiles] [Percentiles] [2008-10-18 17:01:55] [b943bd7078334192ff8343563ee31113]
F RM D      [Back to Back Histogram] [Tijdreeks 1 met 2] [2008-10-20 17:26:39] [b943bd7078334192ff8343563ee31113]
F RM D      [Back to Back Histogram] [Tijdreeks 1 met 3] [2008-10-20 17:41:00] [b943bd7078334192ff8343563ee31113]
F RM D      [Back to Back Histogram] [Tijdreeks 1 met 4] [2008-10-20 17:46:37] [b943bd7078334192ff8343563ee31113]
F RMPD      [Pearson Correlation] [Pearson Tijdreeks...] [2008-10-20 18:23:11] [b943bd7078334192ff8343563ee31113]
F RMPD      [Pearson Correlation] [Pearson Tijdreeks...] [2008-10-20 18:28:48] [b943bd7078334192ff8343563ee31113]
F    D    [Pearson Correlation] [Correlation] [2008-10-19 08:50:37] [4396f984ebeab43316cd6baa88a4fd40]
F    D    [Pearson Correlation] [Investigating Ass...] [2008-10-19 09:20:55] [6743688719638b0cb1c0a6e0bf433315]
F    D    [Pearson Correlation] [Task 1 - Q4 - Clo...] [2008-10-19 11:11:01] [33f4701c7363e8b81858dafbf0350eed]
F    D    [Pearson Correlation] [Reproduction Task...] [2008-10-19 13:30:40] [86761fc994bdf34e4f4ab5b8e1d9e1c3]
-    D    [Pearson Correlation] [Controle: associa...] [2008-10-19 16:08:41] [5e74953d94072114d25d7276793b561e]
F    D    [Pearson Correlation] [Pearson] [2008-10-19 17:26:00] [8d78428855b119373cac369316c08983]
F    D    [Pearson Correlation] [Q4 Correlation ] [2008-10-19 17:45:45] [2bd2ad6af3eef3a703e9ec23e39bd695]
F    D    [Pearson Correlation] [Q4 Correlatie tus...] [2008-10-19 18:15:30] [cf9c64468d04c2c4dd548cc66b4e3677]
F    D    [Pearson Correlation] [Q5 Correlatie tus...] [2008-10-19 19:23:19] [cf9c64468d04c2c4dd548cc66b4e3677]
F    D      [Pearson Correlation] [Q10 assosications...] [2008-10-20 21:55:17] [cf9c64468d04c2c4dd548cc66b4e3677]
F    D      [Pearson Correlation] [Q10 assosications...] [2008-10-20 22:02:21] [cf9c64468d04c2c4dd548cc66b4e3677]
F    D        [Pearson Correlation] [Q10 assosications...] [2008-10-20 22:07:33] [cf9c64468d04c2c4dd548cc66b4e3677]
F    D        [Pearson Correlation] [Q10 assosications...] [2008-10-20 22:13:26] [cf9c64468d04c2c4dd548cc66b4e3677]
-    D          [Pearson Correlation] [Q10 assosications...] [2008-10-20 22:22:07] [cf9c64468d04c2c4dd548cc66b4e3677]
F    D          [Pearson Correlation] [Q10 assosications...] [2008-10-20 22:22:07] [cf9c64468d04c2c4dd548cc66b4e3677]
F    D            [Pearson Correlation] [Q10 assosications...] [2008-10-20 22:29:16] [cf9c64468d04c2c4dd548cc66b4e3677]
F RM D    [Percentiles] [Q6 80% confidence...] [2008-10-19 19:35:43] [cf9c64468d04c2c4dd548cc66b4e3677]
F    D    [Pearson Correlation] [Q4 Pearson Correl...] [2008-10-20 09:27:17] [38f43994ada0e6172896e12525dcc585]
F    D    [Pearson Correlation] [q4 correlation pr...] [2008-10-20 12:10:23] [dd679c9a7f849ed0333823e9c020c5a6]
F    D    [Pearson Correlation] [Correlatie produc...] [2008-10-20 13:14:29] [1d988b04e8982749ec309eda662241b4]
F R  D    [Pearson Correlation] [Correlatie produc...] [2008-10-20 13:15:37] [a7f04e0e73ce3683561193958d653479]
F    D    [Pearson Correlation] [Samenhang prijs -...] [2008-10-20 13:47:23] [1376d48f59a7212e8dd85a587491a69b]
F    D    [Pearson Correlation] [Q4 associatie pri...] [2008-10-20 13:48:21] [e562c84ebfc887cc5a7a99782625ca3b]
F    D    [Pearson Correlation] [Workshop 2] [2008-10-20 14:05:39] [b990da0cb3aa26f81c0c422f8ba66d53]
-    D    [Pearson Correlation] [Correlation Produ...] [2008-10-20 14:18:02] [43d870b30ac8a7afeb5de9ee11dcfc1a]
F R PD    [Pearson Correlation] [Q4 Relatie tussen...] [2008-10-20 14:39:45] [74be16979710d4c4e7c6647856088456]
F    D    [Pearson Correlation] [Q4: associatie pr...] [2008-10-20 15:24:39] [82d201ca7b4e7cd2c6f885d29b5b6937]
- R  D    [Pearson Correlation] [taak 1 vraag 4 Ko...] [2008-10-20 15:27:46] [f21e40d80585aedc38277df87deba3c6]
F R  D    [Pearson Correlation] [taak 1 vraag 4 Ko...] [2008-10-20 15:27:46] [f21e40d80585aedc38277df87deba3c6]
F           [Pearson Correlation] [Pearson correlati...] [2008-10-20 17:31:07] [e242ef2117cdd06cb7827a9ae01189a0]
F    D    [Pearson Correlation] [Q4 Clothing produ...] [2008-10-20 16:19:16] [fe7291e888d31b8c4db0b24d6c0f75c6]
F           [Pearson Correlation] [back to back hist...] [2008-10-20 16:57:07] [b635de6fc42b001d22cbe6e730fec936]

[Truncated]
Feedback Forum
2008-10-22 13:12:50 [Ellen Smolders] [reply] 
De student heeft de juiste grafiek ingevoegd en het antwoord is correct. Er is een minimale positieve correlatie tussen de prijzen van kleding en de productie. De redenering van de student klopt niet, het klopt wel dat de prijs geen invloed heeft op de productie maar waarschijnlijk andersoms. Om de werkelijke correlatie te berekenen had de student best de datasetuiteengehaald en het verband berekent tussen de hoge prijzen en de productie en de lage prijzen en de productie.
2008-10-23 13:33:45 [Peter Smolders] [reply] 
Ze heeft de oefening juist gereproduceerd, en een conclusie geformuleerd over de correlatie, maar haar conclusie is niet helemaal correct. Het had juister geweest wanneer de student de datareeksen had opgesplitst en een aparte berekening had gemaakt voor de productie van lage prijzen en voor de productie van hoge prijzen. Maar dit had de student bijna niet kunnen weten op het moment dat zij de oefening maakte.
2008-10-26 13:26:57 [Natascha Meeus] [reply] 
De correlatie is hier slecht 0,28. Er is dus een zeer zwakke correlatie. Er is geen lineair verband tussen deze twee. Als de student dan de redenering maakt dat een prijsstijging niet veel effect zal hebben dan is dit correct.
2008-10-26 14:50:42 [Steven Hulsmans] [reply] 
Indien we een rechte zouden trekken zouden er vooral veel groeperingen liggen boven en onder de grafiek. Dit wijst op een zeer zwakke correlatie, aangezien er vooral veel op de grafiek zouden moeten liggen eer we spreken van een sterke correlatie. Het antwoord van de student is hier dus juist geformuleerd. De beste oplossing was echter om de dataset uit mekaar te halen en zo meerdere berekeningen uit te voeren: namelijk de berekening voor hoge prijzen en deze voor lage prijzen. Zo zou het probleem van de 'onbrekende blokken' ook opgelost zijn.
2008-10-27 18:23:11 [Jeroen Aerts] [reply] 
De student heeft inderdaad het correcte antwoord gegeven maar is niet volledig geweest. Want wanneer je de datasets uit elkaar haalt en een berekening maakt voor de hoge en lage prijzen om de correcte correlatie te zien, maar dat kon de student niet weten op het moment dat hij de oefening maakte.
2008-10-27 18:52:40 [Michaël De Kuyer] [reply] 
Ik sluit me aan bij Peter en Ellen. Het is inderdaad zo dat de studente had kunnen vermelden dat men de datareeks beter uit elkaar zou halen voor een grondigere analyse.
2008-10-27 19:54:12 [Evelyn Ongena] [reply] 
Ook ik sluit me aan bij wat hierboven is vermeld.
2008-10-27 20:14:12 [Dries Van Gheluwe] [reply] 
Zoals besproken in de les was het hier beter geweest dat er een andere berekening zou gemaakt worden voor productie onder lage en hoge prijzen
2008-10-28 06:52:03 [An De Koninck] [reply] 
Vraag 4 werd goed beantwoord. Het resultaat van een zwak lineair verband werd goed uitgelegd, dit betekent dat de grafiek goed geïnterpreteerd werd.
2008-10-28 07:17:39 [Evelyne Slegers] [reply] 
In de grafiek is te zien dat er sprake is van zeer lichte correlatie. De punten liggen niet op een rechte. Moest de student de twee datasets uit elkaar gehaald hebben dan zouden we merken dat er wel sprake is van correlatie.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
109,20
88,60
94,30
98,30
86,40
80,60
104,10
108,20
93,40
71,90
94,10
94,90
96,40
91,10
84,40
86,40
88,00
75,10
109,70
103,00
82,10
68,00
96,40
94,30
90,00
88,00
76,10
82,50
81,40
66,50
97,20
94,10
80,70
70,50
87,80
89,50
99,60
84,20
75,10
92,00
80,80
73,10
99,80
90,00
83,10
72,40
78,80
87,30
91,00
80,10
73,60
86,40
74,50
71,20
92,40
81,50
85,30
69,90
84,20
90,70
100,30
Dataseries Y:
Download CSV
Histogram 
99,90
99,80
99,80
100,30
99,90
99,90
100,00
100,10
100,10
100,20
100,30
100,60
100,00
100,10
100,20
100,00
100,10
100,10
100,10
100,50
100,50
100,50
96,30
96,30
96,80
96,80
96,90
96,80
96,80
96,80
96,80
97,00
97,00
97,00
96,80
96,90
97,20
97,30
97,30
97,20
97,30
97,30
97,30
97,30
97,30
97,30
98,10
96,80
96,80
96,80
96,80
96,80
96,80
96,80
96,80
96,80
96,80
96,80
96,90
97,10
97,10

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1158&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1158&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1158&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean86.893442622950898.111475409836
Biased Variance109.8917602794952.39249126578877
Biased Standard Deviation10.48292708548021.54676800645370
Covariance4.73174316939891
Correlation0.287034985095086
Determination0.0823890826685364
T-Test2.30160903402757
p-value (2 sided)0.0249057450545596
p-value (1 sided)0.0124528725272798
Degrees of Freedom59
Number of Observations61

\begin{tabular}{lllllllll}
\hline
Pearson Product Moment Correlation - Ungrouped Data \tabularnewline
Statistic & Variable X & Variable Y \tabularnewline
Mean & 86.8934426229508 & 98.111475409836 \tabularnewline
Biased Variance & 109.891760279495 & 2.39249126578877 \tabularnewline
Biased Standard Deviation & 10.4829270854802 & 1.54676800645370 \tabularnewline
Covariance & 4.73174316939891 \tabularnewline
Correlation & 0.287034985095086 \tabularnewline
Determination & 0.0823890826685364 \tabularnewline
T-Test & 2.30160903402757 \tabularnewline
p-value (2 sided) & 0.0249057450545596 \tabularnewline
p-value (1 sided) & 0.0124528725272798 \tabularnewline
Degrees of Freedom & 59 \tabularnewline
Number of Observations & 61 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1158&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]86.8934426229508[/C][C]98.111475409836[/C][/ROW]
[ROW][C]Biased Variance[/C][C]109.891760279495[/C][C]2.39249126578877[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]10.4829270854802[/C][C]1.54676800645370[/C][/ROW]
[ROW][C]Covariance[/C][C]4.73174316939891[/C][/ROW]
[ROW][C]Correlation[/C][C]0.287034985095086[/C][/ROW]
[ROW][C]Determination[/C][C]0.0823890826685364[/C][/ROW]
[ROW][C]T-Test[/C][C]2.30160903402757[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]0.0249057450545596[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]0.0124528725272798[/C][/ROW]
[ROW][C]Degrees of Freedom[/C][C]59[/C][/ROW]
[ROW][C]Number of Observations[/C][C]61[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1158&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1158&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
Mean86.893442622950898.111475409836
Biased Variance109.8917602794952.39249126578877
Biased Standard Deviation10.48292708548021.54676800645370
Covariance4.73174316939891
Correlation0.287034985095086
Determination0.0823890826685364
T-Test2.30160903402757
p-value (2 sided)0.0249057450545596
p-value (1 sided)0.0124528725272798
Degrees of Freedom59
Number of Observations61


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')