Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

PREVIEW
A common test of cognitive ability requires participants
to search through a visual display and respond to specific
targets as quickly as possible. This kind of test is
called a perceptual-speed test. Measures of perceptual
speed are commonly used for predicting performance
on jobs that demand a high level of speed and accuracy.
Although many different tests are used, a typical
example is shown in Figure 5.1. This task requires the
participant to search through the display of digit pairs as
quickly as possible and circle each pair that adds up 10.
Your score is determined by the amount of time required
to complete the task with a correction for the number of
errors that you make. One complaint about this kind of
paper-and-pencil test is that it is tedious and time consuming
to score because a researcher must also search
through the entire display to identify errors to determine
the participant’s level of accuracy. An alternative, proposed
by Ackerman and Beier (2007), is a computerized
version of the task. The computer version presents a
series of digit pairs and participants respond on a touchsensitive
monitor. The computerized test is very reliable
and the scores are equivalent to the paper-and-pencil
tests in terms of assessing cognitive skill. The advantage
of the computerized test is that the computer produces
a test score immediately when a participant finishes
the test.
Suppose that you took Ackerman and Beier’s test
and your combined time and errors produced a score of
92. How did you do? Are you faster than average, fairly
normal in perceptual speed, or does your score indicate
a serious deficit in cognitive skill? The answer is that
you have no idea how your score of 92 compares with
scores for others who took the same test. Now suppose
that you are also told that the distribution of perceptual
speed scores has a mean of μ = 86.75 and a standard
deviation of σ = 10.50. With this additional information,
you should realize that your score (X = 92) is somewhat
higher than average but not an exceptionally high score.
In this chapter we introduce a statistical procedure
for converting individual scores into z-scores, so that
each z-score is a meaningful value that identifies exactly
where the original score is located in the distribution.
As you will see, z-scores use the mean as a reference
point to determine whether the score is above or below
average. A z-score also uses the standard deviation as a
yardstick for describing how much an individual score
differs from average. For example, a z-score will tell
you if your score is above the mean by a distance equal
to two standard deviations, or below the mean by onehalf
of a standard deviation. A good understanding of
the mean and the standard deviation will be a valuable
background for learning about z-scores.
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F I G U R E 5.1
An example of a perceptual speed task.
The participant is asked to search through
the display as quickly as possible and circle
each pair of digits that add up to 10.
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