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Thecorrelationcoefficientcanrangeinvaluefrom 1to
+1,andtellsyoutwothingsaboutthelinearrelationshipsbetweentwovariables:
1. Strength
Thelargertheabsolutevalueofthecoefficient,thestrongerthelinearrelationshipbetweenthevariables.
. ,
andavalueofzero(0)indicatestheabsenceofalinear
relationship.
,
moderate,orstrongcorrelationdependsonyourobjectivesand
requirements.
. .
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.
indicatesthedirectionoftherelationship.
together,thecoefficientispositive.
decreases,thecoefficientisnegative.
Wecancomputethelineofbestfit theline
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Pearsonsr Calledthecorrelationcoefficientor
,
coefficient. Thisisusedtomeasurethe
relationshipbetweentwosetsofintervalorratio
data
Spearmansrho interpretedthesameas
Pearsonsr,butisusedtomeasurerankeddata.
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Pearsons
r,
WhereN=numberofobservations
X=Xvariable,Y=Yvariable
Thus
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Pearsons r
Sub ect
ngu s c
aptitude
X
Final Score
Y XY X2
Y2
Values Needed to
Calculate r Value1 5 5 25 25 25 N 122 10 20 200 100 400 Sum of X
74
3 6 4 24 36 16 Sum of X squared 54764 8 15 120 64 225 Sum of Y
1345 4 11 44 16 121 Sum of Y squared 179566 4 9 36 16 81 Sum of XY
942
7 3 12 36 9 144 Sum of X2
536
8 10 18 180 100 324 Sum of Y2
1874
9 2 7 14 4 4910 6 2 12 36 411 7 14 98 49 196 r= 0.666831
12 9 17 153 81 289-
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Spearmansrho
Spearman's rho ngu s c
aptitude Final Score2
Values Needed to
= -1 8 10 -2 4 N 12
2 1 1 0 0 N2 144
3 6 11 -5 25 d2 1054 4 4 0 05 9 7 2 4 rho= 0.632876 9 8 1 17 11
6 5 25
-9 12 9 3 910 6 12 -6 3611 5 5 0 0
Sums -> 105
