Statistical Methods for Psychology

we will put that off until the next chapter. For now it is sufficient to say that we will often

assume that our data are normally distributed, and superimposing a normal distribution on

the histogram will give us some idea how reasonable that assumption is.^3

Figure 2.4 was produced by SPSS and you can see that while the data are roughly de-

scribed by the normal distribution, the actual distribution is somewhat truncated on the left

and has more than the expected number of observations on the extreme right. The normal

curve is not a terrible fit, but we can do better. An alternative approach would be to create

what is called a kernel density plot.

Kernel Density Plots

In Figure 2.4 we superimposed a theoretical distribution on the data. This distribution only

made use of a few characteristics of the data, its mean and standard deviation, and did not

make any effort to fit the curve to the actual shape of the distribution. To put that a little

more precisely, we can superimpose the normal distribution by calculating only the mean

and standard deviation (to be discussed later in this chapter) from the data. The individual

data points and their distributions play no role in plotting that distribution. Kernel density

plots do almost the opposite. They actually try to fit a smooth curve to the data while at the

same time taking account of the fact that there is a lot of random noise in the observations

that should not be allowed to distort the curve too much. Kernel density plots pay no atten-

tion to the mean and standard deviation of the observations.

The idea behind a kernel density plot is that each observation might have been slightly

different. For example, on a trial where the respondent’s reaction time was 80 hundredths

of a second, the score might reasonably have been 79 or 82 instead. It is even conceivable

22 Chapter 2 Describing and Exploring Data

20

30

40

10

50

Ferquency

Reaction Times

RxTime

40 60 80 100 120

Figure 2.4 Histogram of reaction time data with normal curve superimposed

(^3) This is not the best way of evaluating whether or not a distribution is normal, as we will see in the next chapter.
However it is a common way of proceeding.
kernel density
plot