r

1

• r
• is sad

2
I want everyone to understand me and love me for
what I can do

• r
• is sad

3
Pearsons r
-1 ? r ? 1 -1 ? ? ? 1
Pearsons r is a function of the sum of the
cross-product of z-scores for x and y.
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Pearsons r
? zxzy
r
N
5
SampleC
SampleD
rXY
Population
rXY
SampleB
?XY
rXY
SampleE
SampleA
_
rXY
rXY
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Some uses of r

• Association of two variables
• Reliability estimates
• Validity estimates

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These are equally valid, but not equally reliable
measures of weight.
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Factors that affect r
Non-linearity Restriction of range /
variability Outliers Reliability of
measure / measurement error
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Pearsons r
-1 ? r ? 1 -1 ? ? ? 1
Pearsons r can also be interpreted as how far
the scores of Y individuals tend to deviate from
the mean of X when they are expressed in standard
deviation units.
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Pearsons r
-1 ? r ? 1 -1 ? ? ? 1
Pearsons r can also be interpreted as the
expected value of zY given a value of zX. tend to
deviate from the mean of X when they are
expressed in standard deviation units.
The expected
value of zY is zXr If you are predicting zY
from zX where there is a perfect correlation
(r1.0), then zYzX.. If the correlation is
r.5, then zY.5zX.
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The familiar t distribution, at N-2 degrees of
freedom, can be used to test the probability that
the statistic r was drawn from a population with
? 0 H0 ? XY 0 H1 ? XY ? 0 where