Evidence-Based Practice for Nurses

salary values. Calculating a standard deviation provides different information
about variability. It is now apparent that the average deviation from the mean
for the experimental group is $34,842.50, which is more than double that of
the control group’s $17,073.37 deviation (see Table 13-8).

Comparing Variability When Units

of Measure Are Different

Because standard deviations are based on the mean of the data set, information
collected using different measurement scales cannot be directly compared. For
example, the mean of a sample’s age is reported in years, whereas the mean of
a sample’s weight is reported in pounds. To make comparisons among unlike
data requires that all the data means be converted to standardized units called
standardized or z scores. z scores are then used to describe the distance a score
is away from the mean per standard deviation. A z score of 1.25 means that a
data value is 1.25 standard deviations above the mean. A z score of –2.53 means
that a data value is 2.53 standard deviations below the mean. Using the z score
allows researchers to compare results of age and weight.

The coefficient of variation is a percentage used to compare standard devia-
tions when the units of measure are different or when the means of the distri-
butions being compared are far apart. The coefficient of variation is computed
by dividing the standard deviation by the mean and recording the result as a
percentage. For example, if you were to compare age and income of a sample
of nurses, you could not use range or standard deviations to discuss the vari-
ables’ comparative spread because they are measured with different units. If
the mean salary for nurses is $66,000, with a standard deviation of $6,000 and
the mean age is 32 years, with a standard deviation of 4 years, the coefficient of
variation for the salary is 9.1%, and the coefficient of variation for age is 12.5%.

KEY TERMS

z scores:

Standardized units

used to compare

data gathered

using different

measurement

scales

coefficient of

variation: A

percentage used to

compare standard

deviations when the

units of measure are

different or when

the means of the

distributions being

compared are far

apart

Control Experimental

$30,000 $15,000

$38,000 $23,000

$42,000 $42,000

$57,000 $57,000

$73,000 $103,000

SD $17,073.37 $34,842.50

TABLE 13-8 Standard Deviations of Income

13.5 Measures of Variability 347