Chapitre V : Coefficients de corrélation et tests
Il existe plusieurs mesures de liaison entre variables quantitatives continues. Nous utiliserons le coefficient de corrélation de Pearson.
Cours 12 : Corrélation et régression
Test sur le coefficient de corrélation de Pearson. zéro; pouvoir faire des tests d'hypothèses sur la pente de la régression.
Test de corrélation simple Et test de Normalité
La corrélation de Pearson qui est un test paramétrique
La corrélation linéaire Tests visant à mettre en évidence une
5 déc. 2019 Le test de corrélation linéaire de Pearson. Le test de corrélation de rangs de Spearman. Les limites des tests de corrélation.
[0:01] Terminons cette série de chapitres sur les tests statistiques en
[0:11] Le test de nullité d'un coefficient de corrélation n'a pas de de Pearson ce d'autant plus que l'autre variable ici
Test Statistique Student
https://dept-info.labri.fr/~beurton/Enseignement/Stat/2014-2015/Cours2.pdf
Coefficient de corrélation et prise de décision
Le coefficient de corrélation p de Bravais-Pearson (noté p) permet de prendre en compte l'interprétation s'appuie souvent sur le résultat du test entre ...
The Mantel Test versus Pearsons Correlation Analysis: Assessment
Then we use fish and zooplankton biomass data from Lake Erie (North American Great. Lakes) to show that Pearson's correlation statistic may be nonsignificant
Analyse de corrélation
4.2 Corrélation partielle d'ordre 1 basé sur le r de Pearson . Dans ce cas : la distribution sous H0 de la statistique du test que.
ÉTUDE DE LA RELATION ENTRE DEUX VARIABLES (le coefficient
Le coefficient de corrélation de Bravais-Pearson est un indice statistique qui exprime l'intensité et le sens (positif ou négatif) de la relation linéaire entre
CHAPTER 8 Correlation and Regression— Pearson and Spearman
OVERVIEW—PEARSON CORRELATION Regression involves assessing the correlation between two variables Before proceeding let us deconstruct the word correlation: The prefix co means two—hence correlation is about the relationship between two things Regression is about statistically assessing the correlation between two continuous variables
Tests Non Paramétriques - univ-amufr
V Corrélation Test de Spearman Principe Coefficient de corrélation de Pearson Calcul du coefficient de corrélation pour les rangs 1 Paramétrique?
What Is The Pearson Correlation coefficient?
The Pearson correlation coefficient (r) is the most widely used correlation coefficient and is known by many names: 1. Pearson’s r 2. Bivariate correlation 3. Pearson product-moment correlation coefficient (PPMCC) 4. The correlation coefficient The Pearson correlation coefficient is a descriptive statistic, meaning that it summarizes the characteri...
Visualizing The Pearson Correlation Coefficient
Another way to think of the Pearson correlation coefficient (r) is as a measure of how close the observations are to a line of best fit. The Pearson correlation coefficient also tells you whether the slope of the line of best fit is negative or positive. When the slope is negative,r is negative. When the slope is positive, ris positive. When ris 1 ...
When to Use The Pearson Correlation Coefficient
The Pearson correlation coefficient (r) is one of several correlation coefficients that you need to choose between when you want to measure a correlation. The Pearson correlation coefficient is a good choice when all of the following are true: 1. Both variables are quantitative: You will need to use a different method if either of the variables is ...
Calculating The Pearson Correlation Coefficient
Below is a formula for calculating the Pearson correlation coefficient (r): The formula is easy to use when you follow the step-by-step guide below. You can also use software such as R or Excel to calculate the Pearson correlation coefficient for you.
Testing For The Significance of The Pearson Correlation Coefficient
The Pearson correlation coefficient can also be used to test whether the relationship between two variables is significant. The Pearson correlation of the sample is r. It is an estimate of rho (?), the Pearson correlation of the population. Knowing r and n (the sample size), we can infer whether ? is significantly different from 0. 1. Null hypothes...
What is Pearson correlation?
Pearson correlation measures the existence (given by a p-value) and strength (given by the coefficient r between -1 and +1) of a linear relationship between two variables (Samuels, & Gilchrist, 2015).
How do you measure a linear correlation?
The Pearson correlation coefficient (r) is the most common way of measuring a linear correlation. It is a number between –1 and 1 that measures the strength and direction of the relationship between two variables. When one variable changes, the other variable changes in the same direction. The longer the baby, the heavier their weight.
What are the pretest criteria for the Spearman correlation?
Spearman’s rho is a nonparametric (pronounced non-pair-uh-metric) test, meaning that the data are not expected to be normally distributed, and hence the pretest criteria for the Pearson regression (normality, linearity, and homoscedasticity) are not pertinent when it comes to running the Spearman correlation. Since each item is only present once
What is a bivariate correlation?
Correlation involving two variables, sometimes referred to as bivariate correlation, is notated using a lowercase rand has a value between ?1 and +1. Correlations have two primary attributes: direction and strength. Directionis indicated by the sign of the rvalue: ? or +.
COV(X,Y) =E{[X-E(X)][Y-E(Y)]}?????
COV(X,Y) =E[XY]-E[X]E[Y]?????
COV(X,X) =E{[X-E(X)][X-E(X)]}
=E{[X-E(X)]2} =V(X) >0E[X] +E[Y]?
COV(X,Y)
X,Yindependants⇒COV(X,Y) = 0
??????E[X×Y] =E[X]×E[Y]??Sxy=∑
n i=1(xi-¯x)(yi-¯y) n nCOV(X,Y)?
COV(X,Y) =∑
n i=1(xi-¯x)(yi-¯y) n-1=∑ n i=1xiyi-n¯x¯y n-1????? r xy=COV(X,Y)V(X)×V(Y)
COV(X,Y)
x×σy ???????X??Y? V(X x+Y y)0)r 1 V(X xY y)0)r+1ˆr=∑
n i=1(xi-¯x)(yi-¯y) n n i=1(yi-¯y)2?????ˆr=∑xiyi-n¯x¯y
y2i-n¯y2????? crx??????cry? ??? ??????? ??X??????Y? cr xi=xi-¯x s xˆr=1
n n i=1cr xi×cryi??????E[ˆr] =r-r(1-r2)
2n 1-n-1 n-2(1-ˆr2)??????102138444??197200?
543169.291?
H0:r= 0
H1:r̸= 0
t=ˆr 1^r2 n2??????R.C.:|t|> t1
2 (n-2) ??t1 2 210:94752
282= 15.1171
pˆz=1
2 ln1 + ˆr1-ˆr??????
2 ln1+r 1r+r2(n1)? ?? ? ? ??
E[ˆz]≈1
2 ln1 +r 1-rV[ˆz]≈1
n-3ˆr=e2^z-1
e2^z+ 1??????
z1,2= ˆz±u1
2 1 n-3?????? 2 ln1+0.947510.9475= 1.8072
1283= 0.2
r1=e21.4152-1
e21.4152+ 1= 0.8886
r2=e22.1992-1
e22.1992+ 1= 0.9757
[0.8886; 0.9757] 2 ln1+r0 H0:z=z0
U=ˆz-z0
1 n-3?????? ?? ??????5% H0:r= 0.9
H1:r >0.9
2 ln1+0.910.9= 1.4722
28-3 = 1.6750
??????? ???????u0.95= 1.6449 H0:r1=r2
H1:r1̸=r2
D= ˆz1-ˆz2??????
E[D] = 0
V[D] =1
n 1-3+1 n 2-3R.C.:U=|ˆz1-ˆz2|
1 n 13+1 n23≥u1
2 153+1203= 0.1422
p0.1422=0.3652
0.3770= 0.2771
H0:r1=r2=···=rK
2=K∑
k=1(nk-3)ˆz2k-[∑K k=1(nk-3)ˆzk]2 K k=1(nk-3)?????? ?????? ??ˆrk???????ˆzk=1 2 ln1+^rk 1^rk? ???? ??????? ?????A=∑ k(nk-3)ˆzk= 3178.7259?B=∑ k(nk-3) = 28?C=∑ k(nk-3)ˆz2k=113.6718?
B = 0.1459? A= [(15-3)×0.6417 + (20-3)×0.5372]2= 283.3678B= (15-3) + (20-3) = 29
C= (15-3)×0.64172+ (20-3)×0.53722= 9.8481
B H0:ryx=ryz
(n-1)(1 + ˆrxz) 2 n1 n3|R|+ ¯r2(1-ˆrxz)3?????? ??¯r= (ˆryx+ ˆryz)/2?|R|= 1-ˆr2yx-ˆr2yz-ˆr2xz+ 2ˆryxˆryzˆrxz ????? ??????? ???n= 28?B= (n-1)(1 + ˆrxz= 52.5838
|R|= 1-ˆr2yx-ˆr2yz-ˆr2xz+ 2ˆryxˆryzˆrxz= 0.0191¯r= (ˆryx+ ˆryz)/2 = 0.8898
C= (1-ˆrxz)3= 0.0001
B 2 2725
0.0191+0.88980.0001= 0.1448
H0:rxy=rzw
H1:rxy̸=rzw
n-32-2¯s??????
ˆz=1
2 ln1+^r¯s=ψ
(1r2)2?¯r=^r12+^r34
2ψ= 0.5{[(ˆr13-ˆr23¯r)(ˆr24-ˆr23¯r)] + [(ˆr14-ˆr13¯r)(ˆr23-ˆr13¯r)] + [(ˆr13-ˆr14¯r)(ˆr24-ˆr14¯r)] + [(ˆr14-
ˆr24¯r)(ˆr23-ˆr24¯r)]}
ˆr12= 0.3??ˆr34= 0.4?
r pb=¯y1-¯y0 s n 1n0 n(n-1)????? ???????s2n1=1 n1∑ n i=1(yi-¯y)2? t r=rpb 1r2pb n1+n02?????
?????tc???? ??? ??? ?? ??????? ? ?(n1+n0-2)?????? ?? ??????? t c=y1-y0 s s2=(n11)s2
1+(n01)s2
0 n1+n02(1
n 1+1 n 0)? ????s2j=1 n j1∑ nj ?s1= 0.071?s0= 0.061??20+152(1
20 +1 15 ) = 0.0005 ????tc=1.7331.589 pˆrb=¯y1-¯y0
s n1×n1×n0 n2×λn1/n?????
s 2n1=1 n1∑ ????n1/n= 23/28 = 0.8214?λ=fN(0.9208) =1
2πe0:92082
2 = 0.2611ˆrb= 0.9481
1^r2b n2= 15.2016 n1n0(n-1)
2n1/n×n3?????
n1n0(n-1)
2n1/nn3≥1.25
ϕ=ad-bc
(a+b)(c+d)(a+c)(b+d)????? a+b n ??a+c n S i=Rang(Yi)? n i=1(Ri-¯R)(Si-¯S) i(Si-¯S)2?????¯S=¯R=n+1
2ˆρ=12∑n
i=1RiSi n(n2-1)-3(n+ 1) n-1????? ?? ?? ???? ?????? ?????? ????? ?? ????1? ?? ???? ?????? ?? ????nˆρ= 1-6∑n
i=1D2i n(n2-1)????? iRiSi= 1133? ? iD2i= ??20?30 t=ˆρ1^ρ2
n2U=ˆρ
1 n-1 ?????? ??????? ????? ???? ?????t= 2.83320???? ??? ??????? ??0.01410???? ?? ??????? ?????U= 2.31181 2 4+5+6 3 2 = 10.5? T x=G∑ g=1(t3g-tg)?????? T x= 36??????? ?????ˆρ=(n3-n)-6∑n
i=1d2i-(Tx+Ty)/2 (n3-n)2-(Tx+Ty)(n3-n) +TxTy??????ˆρ=(123-12)-6×129-(36 + 0)/2
(123-12)2-(36 + 0)(123-12) + 36×0= 0.5442
ˆτ=P-Q
1 2 n(n-1)?????? 1 2 n(n-1) =(n 2)τ= 2×P[(xi-xj)×(yi-yj)>0]-1??????
S=n1∑
i=1n j=i+1ν ij ij= +1,siyi< yj -1,siyi> yj?????? i=n∑ j=i+1ν ijˆτ=S
1 2 n(n-1)=2S n(n-1)?????? ij?νi??S??????? ?????? ?? ??????j > i⇒xj> xi? ???? ??????? ? ?? ?????ν1= (-1) + (-1) + (+1) + (-1) + (-1) =-3 ???? ??????? ????? ?????? ?? ?????S=∑n1 i=1νi= (-3) + 0 + (+3) + (-2) + (+1) =-1ˆτ=2×(-1)
6×(6-1)=-0.0667
U=ˆτ
2(2n+5)
n(n-1)2(2n+ 5)??????
|U|> u1 26(6-1)
2(2×6 + 5)=-0.1879
ˆρ≈3
2τ=2
arcsinρ G x=n? ?? ??? ? ??? ???? ?????? E x=G x∑ g=1t g(tg-1)??????ˆτ=2×S
n(n-1)-Ey?????? ???? ?????? ??? ??????? ????? ??? ??????? ??X? n n n ??Y???? ????? ?????? n ???? ???? ??????? ?? ???? ?S= 19ˆτ=2×19
8(8-1)-4= 0.76061
8(8-1)
2(2×8 + 5= 2.63483
??Y???? ?????? ??????x??X?2y/x=E{(Y/X-E[Y])2}
E{(Y-E[Y])2}??????
?? ??????? ??Y??? ?? ???? ?????? ??? ???? ?? ?????? ??X?ˆη2y/x=∑
K k=1nk(¯yk-¯y)2 n i=1(yi-¯y)2??????ˆη2y/x= 1-∑
K k=1nk∑nki=1(yi-¯yk)2 n i=1(yi-¯y)2?????? r H0:η2y/x= 0
H1:η2y/x>0
H0:µ1=···=µK
H1: uneaumoinsdifferedesautres
F=^η2
K11^η2
nK=n-KK-1׈η2
1-ˆη2??????
R.C.:F > F1α(K-1,n-K)
?? ??????? ?? ???? ???? ??????? ??????? ?0.90493 n1= 6??¯y1= 6.45
T ???? ??? ????? ?F= 2.26307? r xy.z=rxy-rxzryz1-r2yz?????
?? ??????? ???? ?????? ???rxy>0? rˆrxy.z=ˆrxy-ˆrxzˆryz
1-ˆr2yz?????
???Z? r xy.z=0.88781-0.94755×0.89187 (1-0.947552)(1-0.891872)= 0.29553 H0:rxy.z= 0
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