Statistical Methods for Psychology

upper 25% and the lower 25% of the distribution and taking the range of what remains. The

point that cuts off the lowest 25% of the distribution is called the first quartile,and is usu-

ally denoted as Q1.Similarly the point that cuts off the upper 25% of the distribution is

called the third quartileand is denoted Q3. (The median is the second quartile, Q2.) The

difference between the first and third quartiles (Q3 – Q1) is the interquartile range. We can

calculate the interquartile range for the data on attractiveness of faces by omitting the low-

est five scores and the highest five scores and determining the range of the remainder. In

this case the interquartile range for Set 4 would be 0.58 and the interquartile range for Set

32 would be only .11. The interquartile range plays an important role in a useful graphical

method known as a boxplot. This method will be discussed in Section 2.10.

The interquartile range suffers from problems that are just the opposite of those found

with the range. Specifically, the interquartile range discards too much of the data. If we

want to know whether one set of photographs is judged more variable than another, it may

not make much sense to toss out those scores that are most extreme and thus vary the most

from the mean.

There is nothing sacred about eliminating the upper and lower 25% of the distribution

before calculating the range. Actually, we could eliminate any percentage we wanted, as

long as we could justify that number to ourselves and to others. What we really want to do

is eliminate those scores that are likely to be errors or attributable to unusual events with-

out eliminating the variability that we seek to study.

In an earlier section we discussed the use of trimmed samples to generate trimmed

means. Trimming can be a valuable approach to skewed distributions or distributions with

large outliers. But when we use trimmed samples to estimate variability, we use a variation

based on what is called a Winsorized sample.(We create a 10% Winsorized sample, for

example, by dropping the lowest 10% of the scores and replacing them by the smallest

score that remains, then dropping the highest 10% and replacing those by the highest score

which remains, and then computing the measure of variation on the modified data.)

Section 2.8 Measures of Variability 39

1.0

Attractiveness for Set 32

Frequency

9

0

8 7 6 5 4 3 2 1

1.5 2.0 2.5 3.0 3.5 4.0

1.0

Attractiveness for Set 4

Frequency

0

3.0

2.0

1.0

1.5 2.0 2.5 3.0 3.5 4.0

Figure 2.13 Distribution of scores for attractiveness of composite

first quartile, Q1

third quartile, Q3

second
quartile, Q2

Winsorized
sample