Information Technology Reference
In-Depth Information
EXCEL TIP
Step-by-Step Guide to Calculating
z
Scores
Here are the steps for transforming any set of raw scores (times, percentages, clicks,
whatever) into
z
scores:
1. Enter raw scores into a single column in Excel. For this example, we will assume
they are in column “A” and that you started on row “1”. Make sure there are no
other values in this column, such as an average at the bottom.
2. In the cell to the right of the first raw score, enter the formula:
= STANDARDIZE(A1 AVERAGEA:A STDEV(A:A))
,
(
),
3. Copy this “standardize” formula down as many rows as there are raw scores.
4. As a double check, calculate the mean and standard deviation for this
z
-score column.
The average should be 0, and the standard deviation should be 1 (both within round-
ing error).
The bottom two rows of
Table 8.7
show the mean and standard deviation for
each set of
z
scores, which should always be 0 and 1, respectively. Note that in
using
z
scores, we didn't have to make any assumptions about the maximum or
minimum values that any of the scores could have. In essence, we let each set of
scores define its own distribution and rescale them so those distributions would
each have a mean of 0 and standard deviation of 1. In this way, when they are
averaged together, each of the
z
scores makes an equal contribution to the aver-
age
z
score. Note that when averaging the
z
scores together, each of the scales
must be going the same direction—in other words, higher values should always
be better. In the case of time data, the opposite is almost always true. Since
z
scores have a mean of 0, this is easy to correct simply by multiplying the
z
score
by (-1) to reverse its scale.
If you compare the
z-
score averages in
Table 8.7
to the percentage averages in
Table 8.3
, you will find that the ordering of the participants based on those aver-
ages is nearly the same: Both techniques yield the same top three participants (9,
5, and 3) and the same bottom three participants (4, 8, and 1).
One disadvantage of using
z
scores is that you can't think of the overall
average of the
z
scores as some type of overall usability score, as by definition
that overall average will be 0. So when would you want to use
z
scores? They
mainly are useful when you want to compare one set of data to another, such
as data from iterative usability tests of different versions of a product, data from
different groups of users in the same usability test, or data from different condi-
tions or designs within the same usability test. You should also have a reason-
able sample size (e.g., at least 10 participants per condition) to use the
z
-score
method.
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