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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 07:22:11 -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/20/30u76j2iqumdtuj1192890044.htm/, Retrieved Thu, 02 May 2024 17:22:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1094, Retrieved Thu, 02 May 2024 17:22:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsQ3 juist
Estimated Impact488

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] [Q3 Clothing produ...] [2007-10-20 14:22:11] [1a83104d28786df2e24859e2e02dc234] [Current]
F    D    [Pearson Correlation] [Q3 - Clothing pro...] [2008-10-15 17:45:30] [a57f5cc542637534b8bb5bcb4d37eab1]
F    D    [Pearson Correlation] [Correlatie kledij...] [2008-10-15 18:29:08] [8f802de8cb3f2f7005fd796d72a00b6d]
- R  D    [Pearson Correlation] [clothing prod ass...] [2008-10-17 11:56:13] [3d2d096cc21c6f80db3dd7b8e12effce]
- R  D    [Pearson Correlation] [Tot prod associat...] [2008-10-17 12:04:32] [3d2d096cc21c6f80db3dd7b8e12effce]
- R  D    [Pearson Correlation] [clothing and inve...] [2008-10-17 12:07:40] [3d2d096cc21c6f80db3dd7b8e12effce]
-    D    [Pearson Correlation] [Q3: Is Clothing P...] [2008-10-17 12:22:55] [1e1d8320a8a1170c475bf6e4ce119de6]
-    D    [Pearson Correlation] [Pearson Correlation] [2008-10-17 13:16:06] [252acdb58d8522ab27f61fa1e87b5efe]
F    D      [Pearson Correlation] [Verband tussen pr...] [2008-10-20 13:40:55] [1376d48f59a7212e8dd85a587491a69b]
F    D    [Pearson Correlation] [Overeenkomst tota...] [2008-10-17 14:47:32] [cf45c678b7899ee33d7b061948f80651]
-    D    [Pearson Correlation] [Relatie aantal ge...] [2008-10-17 17:40:27] [c45c87b96bbf32ffc2144fc37d767b2e]
-    D      [Pearson Correlation] [relatie aantal ge...] [2008-10-17 17:44:05] [c45c87b96bbf32ffc2144fc37d767b2e]
-    D      [Pearson Correlation] [relatie aantal ge...] [2008-10-17 17:46:26] [c45c87b96bbf32ffc2144fc37d767b2e]
-    D    [Pearson Correlation] [investigating ass...] [2008-10-17 18:17:39] [ec1c727838a7caf353f22e99d242fe74]
F RM D    [Kendall tau Rank Correlation] [investigating ass...] [2008-10-17 19:07:36] [cbd3d88cd5aad6543e769146e7e26b0c]
F    D    [Pearson Correlation] [investigating ass...] [2008-10-17 19:17:41] [cbd3d88cd5aad6543e769146e7e26b0c]
F RM        [Kendall tau Rank Correlation] [investigating ass...] [2008-10-17 19:35:42] [cbd3d88cd5aad6543e769146e7e26b0c]
F    D    [Pearson Correlation] [Correlatie] [2008-10-17 21:12:26] [8b0d202c3a0c4ea223fd8b8e731dacd8]
- R  D    [Pearson Correlation] [Q3] [2008-10-18 11:21:34] [529a65e524c481ca1098665a9566b89f]
- R  D    [Pearson Correlation] [Q4] [2008-10-18 11:25:59] [529a65e524c481ca1098665a9566b89f]
F R  D    [Pearson Correlation] [Q5] [2008-10-18 11:29:27] [529a65e524c481ca1098665a9566b89f]
- RM D    [Percentiles] [Q6] [2008-10-18 11:33:35] [529a65e524c481ca1098665a9566b89f]
- RMPD    [Harrell-Davis Quantiles] [Q7] [2008-10-18 11:43:23] [529a65e524c481ca1098665a9566b89f]
-    D    [Pearson Correlation] [Correlatie kledin...] [2008-10-18 13:48:33] [d32f94eec6fe2d8c421bd223368a5ced]
-    D    [Pearson Correlation] [Pearson correlati...] [2008-10-18 16:08:45] [b943bd7078334192ff8343563ee31113]
F    D    [Pearson Correlation] [Correlation] [2008-10-19 08:41:50] [4396f984ebeab43316cd6baa88a4fd40]
F    D    [Pearson Correlation] [Investigating Ass...] [2008-10-19 09:13:09] [6743688719638b0cb1c0a6e0bf433315]
F    D    [Pearson Correlation] [Task 1 - Q3 - Clo...] [2008-10-19 10:54:35] [33f4701c7363e8b81858dafbf0350eed]
- RM D    [Kendall tau Rank Correlation] [Q3 association] [2008-10-19 12:01:15] [e5d91604aae608e98a8ea24759233f66]
- RM D    [Spearman Rank Correlation] [Q3: Spearman] [2008-10-19 12:23:25] [e5d91604aae608e98a8ea24759233f66]
F    D    [Pearson Correlation] [Reproduction Q2] [2008-10-19 13:09:35] [86761fc994bdf34e4f4ab5b8e1d9e1c3]
-    D    [Pearson Correlation] [Controle: Associa...] [2008-10-19 15:53:38] [5e74953d94072114d25d7276793b561e]
F    D    [Pearson Correlation] [Pearson] [2008-10-19 16:47:00] [8d78428855b119373cac369316c08983]
- RM D    [Kendall tau Rank Correlation] [Kendall Tau Rank] [2008-10-19 16:51:45] [8d78428855b119373cac369316c08983]
F    D    [Pearson Correlation] [Q3 Correlatie Tot...] [2008-10-19 17:07:54] [cf9c64468d04c2c4dd548cc66b4e3677]
-    D    [Pearson Correlation] [Clothing Producti...] [2008-10-19 19:22:05] [988ab43f527fc78aae41c84649095267]
-    D    [Pearson Correlation] [Is Clothing Produ...] [2008-10-19 19:51:15] [988ab43f527fc78aae41c84649095267]
F    D    [Pearson Correlation] [Is there a relati...] [2008-10-19 19:53:05] [988ab43f527fc78aae41c84649095267]
- RM D    [Percentiles] [: Compute a and b...] [2008-10-19 19:55:16] [988ab43f527fc78aae41c84649095267]
- RMPD    [Harrell-Davis Quantiles] [Compute the 95% C...] [2008-10-19 19:58:52] [988ab43f527fc78aae41c84649095267]
-   PD      [Harrell-Davis Quantiles] [Compute the 95% C...] [2008-10-20 15:16:26] [988ab43f527fc78aae41c84649095267]
- RMPD      [Univariate Data Series] [actual values of ...] [2008-10-20 15:34:58] [988ab43f527fc78aae41c84649095267]
-   PD      [Harrell-Davis Quantiles] [New 95%] [2008-10-20 15:40:05] [988ab43f527fc78aae41c84649095267]
- RMPD      [Central Tendency] [Frankrijk/Uitvoer ] [2008-10-20 15:56:26] [988ab43f527fc78aae41c84649095267]
- RMPD      [Central Tendency] [Luxemburg/Uitvoer] [2008-10-20 15:59:18] [988ab43f527fc78aae41c84649095267]
- RMPD      [Central Tendency] [Nederland.Uitvoer] [2008-10-20 16:01:01] [988ab43f527fc78aae41c84649095267]
- RMPD      [Central Tendency] [Duitsland.Uitvoer] [2008-10-20 16:03:46] [988ab43f527fc78aae41c84649095267]
F    D    [Pearson Correlation] [Q3 Pearson Correl...] [2008-10-20 09:12:24] [38f43994ada0e6172896e12525dcc585]
F    D    [Pearson Correlation] [Q3 correlation] [2008-10-20 11:58:00] [dd679c9a7f849ed0333823e9c020c5a6]

[Truncated]
Feedback Forum
2008-10-22 13:07:24 [Ellen Smolders] [reply] 
De student heeft de juiste grafiek ingevoegd en heeft het juiste antwoord gegeven, namelijk dat er een gemiddeld positieve correlatie van 57% is tussen de totale productie en de productie van kleding.
2008-10-23 11:10:17 [Bas van Keken] [reply] 
De assen zijn goed weergegeven. Een toevoeging op de figuur zou een doorgetrokke rechte kunnen zijn. Dit kunt u ook in uw document plaatsen bij de uitleg van deze blog. Dat zou uw cijfermatige conclusie visueel kunnen ondersteunen.
2008-10-23 13:26:43 [Peter Smolders] [reply] 
De oefening is volledig correct uitgevoerd. Een kleine opmerking wel ivm de conclusie, waar de student zegt dat 57% eerder veel is, denk ik toch dat dit meer gemiddeld is. Voor het overige heb ik weinig op deze opdracht aan te merken.
2008-10-26 13:23:29 [Natascha Meeus] [reply] 
Ik ga akkoord met Peter. De oefening is correct uitgevoerd, maar ik vind dat we ook eerder van eenmatig verband kunnen spreken dan van een sterk verband.
2008-10-26 14:28:02 [Elias Van Deun] [reply] 
@ senne dierckx: de berekening is correct, duidelijke uitleg. Het was wel beter geweest dat je 'gematigde correlatie' had geantwoord.
2008-10-26 14:44:21 [Steven Hulsmans] [reply] 
Goede grafiek, juiste assen benoemd en ook een goeie uitleg. De correlatie is inderdaad ongeveer 57%, maar ik vind het zelf toch niet echt een heel erg sterke correlatie. Misschien is er toch eerder sprake van een gemiddelde correlatie?
2008-10-26 21:02:50 [Stéphanie Thijs] [reply] 
'Ook hier komen we hetzelfde correlatiepercentage uit: 56,5% . Er bestaat dus een correlatie tussen beide datasets, ze zijn gemiddeld afhankelijk van elkaar. Ook andere gegevens kunnen een invloed hebben op de datasets.'

Dit was het letterlijke antwoord. Er wordt van gemiddelde correlatie gesproken, niet 'sterk' of 'veel'.
2008-10-27 18:08:14 [Jeroen Aerts] [reply] 
Juiste berekening, spijtig dat je geen eigen conclusie hebt geschreven maar die van het voorbeeld hebt overgenomen. Dat antwoord is uiteraard juist, maar dat vermeld je niet.
2008-10-27 18:50:32 [Michaël De Kuyer] [reply] 
Misschien had je aan deze vraag nog kunnen toevoegen dat de spreiding van beide tijdreeksen gelijk loopt.
2008-10-27 19:52:35 [Evelyn Ongena] [reply] 
deze vraag is correct beantwoord, hoewle er inderdaad discussie mogelijk is over de correlatie. Een correlatie van 57% is volgens mij gemiddeld.
2008-10-27 20:07:33 [Dries Van Gheluwe] [reply] 
Correct antwoord op deze vraag
2008-10-28 06:49:56 [An De Koninck] [reply] 
Vraag 3 is nogal vaag beantwoord. De student had kunnen uitleggen wat correlatie juist is en wat het uitdrukt. Er is dus sprake van een positieve correlatie, wat betekent dat er een onderling verband bestaat. Als de productie van kleding stijgt, zal de totale productie dus ook stijgen.
2008-10-28 07:00:33 [Evelyne Slegers] [reply] 
Volgens mij is hier wel sprake van een sterke correlatie, in tegenstelling tot de bewering van de student. De punten liggen min of meer op een rechte. Er is dus wel een sterk oorzakelijk verband tussen de twee datasets.

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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 
110,40
96,40
101,90
106,20
81,00
94,70
101,00
109,40
102,30
90,70
96,20
96,10
106,00
103,10
102,00
104,70
86,00
92,10
106,90
112,60
101,70
92,00
97,40
97,00
105,40
102,70
98,10
104,50
87,40
89,90
109,80
111,70
98,60
96,90
95,10
97,00
112,70
102,90
97,40
111,40
87,40
96,80
114,10
110,30
103,90
101,60
94,60
95,90
104,70
102,80
98,10
113,90
80,90
95,70
113,20
105,90
108,80
102,30
99,00
100,70
115,50

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1094&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1094&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1094&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Pearson Product Moment Correlation - Ungrouped Data
StatisticVariable XVariable Y
Mean86.8934426229508100.908196721311
Biased Variance109.89176027949564.2309164203171
Biased Standard Deviation10.48292708548028.01441928153981
Covariance48.2815546448088
Correlation0.565259717157914
Determination0.319518547841445
T-Test5.2633941884171
p-value (2 sided)2.07228182791397e-06
p-value (1 sided)1.03614091395698e-06
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 & 100.908196721311 \tabularnewline
Biased Variance & 109.891760279495 & 64.2309164203171 \tabularnewline
Biased Standard Deviation & 10.4829270854802 & 8.01441928153981 \tabularnewline
Covariance & 48.2815546448088 \tabularnewline
Correlation & 0.565259717157914 \tabularnewline
Determination & 0.319518547841445 \tabularnewline
T-Test & 5.2633941884171 \tabularnewline
p-value (2 sided) & 2.07228182791397e-06 \tabularnewline
p-value (1 sided) & 1.03614091395698e-06 \tabularnewline
Degrees of Freedom & 59 \tabularnewline
Number of Observations & 61 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1094&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]100.908196721311[/C][/ROW]
[ROW][C]Biased Variance[/C][C]109.891760279495[/C][C]64.2309164203171[/C][/ROW]
[ROW][C]Biased Standard Deviation[/C][C]10.4829270854802[/C][C]8.01441928153981[/C][/ROW]
[ROW][C]Covariance[/C][C]48.2815546448088[/C][/ROW]
[ROW][C]Correlation[/C][C]0.565259717157914[/C][/ROW]
[ROW][C]Determination[/C][C]0.319518547841445[/C][/ROW]
[ROW][C]T-Test[/C][C]5.2633941884171[/C][/ROW]
[ROW][C]p-value (2 sided)[/C][C]2.07228182791397e-06[/C][/ROW]
[ROW][C]p-value (1 sided)[/C][C]1.03614091395698e-06[/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=1094&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1094&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
Mean86.8934426229508100.908196721311
Biased Variance109.89176027949564.2309164203171
Biased Standard Deviation10.48292708548028.01441928153981
Covariance48.2815546448088
Correlation0.565259717157914
Determination0.319518547841445
T-Test5.2633941884171
p-value (2 sided)2.07228182791397e-06
p-value (1 sided)1.03614091395698e-06
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')