Statistical Methods for Psychology

neurosciences and health sciences, techniques like kernel density plots are becoming more

common. There are a number of technical aspects behind such plots, for example the shape

of the bumps and the bandwidth used to create them, but you now have the basic informa-

tion that will allow you to understand and work with such plots.

2.4 Stem-and-Leaf Displays

Although histograms, frequency distributions, and kernel density functions are commonly

used methods of presenting data, each has its drawbacks. Because histograms often portray

observations that have been grouped into intervals, they frequently lose the actual numeri-

cal values of the individual scores in each interval. Frequency distributions, on the other

hand, retain the values of the individual observations, but they can be difficult to use when

they do not summarize the data sufficiently. An alternative approach that avoids both of

these criticisms is the stem-and-leaf display.

John Tukey (1977), as part of his general approach to data analysis, known as

exploratory data analysis (EDA),developed a variety of methods for displaying data in vi-

sually meaningful ways. One of the simplest of these methods is a stem-and-leaf display,

which you will see presented by most major statistical software packages. I can’t start with

the reaction time data here, because that would require a slightly more sophisticated display

due to the large number of observations. Instead, I’ll use a hypothetical set of data in which

we record the amount of time (in minutes per week) that each of 100 students spends play-

ing electronic games. Some of the raw data are given in Figure 2.7. On the left side of the

figure is a portion of the data (data from students who spend between 40 and 80 minutes per

week playing games) and on the right is the complete stem-and-leaf display that results.

From the raw data in Figure 2.7, you can see that there are several scores in the 40s, an-

other bunch in the 50s, two in the 60s, and some in the 70s. We refer to the tens’ digits—

here 4, 5, 6, and 7—as the leading digits(sometimes called the most significant digits)

for these scores. These leading digits form the stem,or vertical axis, of our display. Within

the set of 14 scores that were in the 40s, you can see that there was one 40, two 41s, one

42, two 43s, one 44, no 45s, three 46s, one 47, one 48, and two 49s. The units’ digits 0, 1,

24 Chapter 2 Describing and Exploring Data

50

40

30

20

10

0

40 60

RxTime

Histogram of RxTime

80 100 120

Figure 2.6 Kernel density plot for data on reaction time

stem-and-leaf
display

leading digits

most significant
digits

stem

exploratory data
analysis (EDA)