Statistical Methods for Psychology

(Michael S) #1
Set 4(X)

Set 32(Y)

From these calculations we see that the difference in variances reflects the differences we
see in the distributions.
Although the variance is an exceptionally important concept and one of the most com-
monly used statistics, it does not have the direct intuitive interpretation we would like. Be-
cause it is based on squared deviations, the result is in squared units. Thus, Set 4 has a
mean attractiveness rating of 2.64 and a variance of 0.4293 squared unit. But squared units
are awkward things to talk about and have little meaning with respect to the data. Fortu-
nately, the solution to this problem is simple: Take the square root of the variance.

The Standard Deviation


Thestandard deviation(sor s) is defined as the positive square root of the variance and,
for a sample, is symbolized as s(with a subscript identifying the variable if necessary) or,
occasionally, as SD.^11 (The notation sis used in reference to a population standard devia-
tion). The following formula defines the sample standard deviation:

For our example,

For convenience, I will round these answers to 0.66 and 0.07, respectively.
If you look at the formula for the standard deviation, you will see that the standard
deviation, like the mean absolute deviation, is basically a measure of the average of the

sY= 3 s^2 Y= 1 0.0048=0.0689

sX= 3 s^2 X= 1 0.4293=0.6552

sX=
B

a(X^2 X)

2

N 21

=


0.0903


19


=0.0048


=


(3.13 2 3.26)^21 (3.17 2 3.26)^2 1 Á 1 (3.38 2 3.26)^2


2021


s^2 Y= a

(Y 2 Y)^2


N 21


=


8.1569


19


=0.4293


=


(1.20 2 2.64)^21 (1.82 2 2.64)^2 1 Á 1 (4.02 2 2.64)^2


2021


s^2 X=
a(X^2 X)

2

N 21

Section 2.8 Measures of Variability 41

(^11) The American Psychological Association prefers to abbreviate the standard deviation as “SD,” but everyone
else uses “s.”
standard
deviation

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