ABSTRACT
In the last section of Chapter 2 we presented some transformations that can be applied to a set of data. In particular we said that when the mean is subtracted from each score and this difference is divided by the standard deviation of the distribution of the scores, we obtain a new standardised score named z. More formally:
z
x z
x s
.= −
=
−
µ σ
or when working with sample data l
When this standardisation (so called because the units of this new variable are standard deviations) is applied to the values of a normally distributed continuous random variable X, we obtain a new continuous random variable Z which is also normally distributed with µ = 0 and σ = 1. This distribution is called the standard normal distribution. In Figure 5.3, we performed this type of transformation to obtain the distance of IQ scores, in terms of standard deviations, from the mean.
