Calculation of Pearson’s
r
with the
z
Score Formula:
A quick note at the outset  you would never calculate
r
using the
z
Score formula when
you have access to the raw scores.
Other formulas are easier to work with.
Nonetheless,
the
z
Score formula does a nice job of illustrating the mechanics of positive vs. negative
correlation, so it’s worth working through.
You can also use this to practice calculating
z
Scores and getting comfortable with multistep statistical algorithms.
Begin with the following sample data set of paired
x
and
y
scores:
x
y
6
4
8
5
6
5
7
6
4
3
5
3
8
5
9
6
4
4
After constructing a scatterplot to verify that the relationship is linear (approximating a
straight line), the next step in this case is to transform the raw scores using the
z
Score
formula.
In order to do this we first need to calculate the sample means and sample
standard deviations (using
n1
in the denominator) for each variable
x
and
y
.
Once this is
done, the product of each
z
transformed
xy
pairing is calculated.
The values you should
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 Winter '08
 Ard
 Standard Deviation, score formula

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