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AFigure 6.12 Normal probability plot of systolic blood pressure of adult males.
look like an upside-down saucer for low values of X and a right-side-up saucer for
X greater than the mean (higher than expected for low values of X and lower than
expected for high values of X). The shape of the curve is that of an inverted S. How
the plots are made differs slightly for different statistical programs, but a straight line
is always an indication of a normal distribution.
Instead of plotting normal probability plots to illustrate whether or not the dis-
tribution of a variable is likely to be normally distributed, some statistical programs
plot normal quantile-quantile plots, often called normal 4-4 plots. Here, also, if the
points fall on or close to a straight line, the data are likely to be normally distributed.
A description of how normal q-q plots are made is given in Cleveland [1993] and a
discussion of their use is given in Fox and Long [ 19901. The statistical programs men-
tioned in this book will provide either normal probability or normal q-q plots, and Stata
has both. These two plots are interpreted in a similar fashion. The normal q-q plot
emphasizes the tails of the distribution more than the center of the distribution com-
pared to normal probability plots (see Afifi et al. [2004]).
6.5 TRANSFORMATIONS
A researcher with a variable that is not normally distributed has several options. First,
the researcher may decide that the distribution of the observations is close enough
to normality and proceed as if the data were normally distributed. Second, the re-
searcher may use some statistical methods that do not assume a normal distribution
(see Chapter 13). A third option is to transform the data so that the resulting distribu-
tion is closer to a normal distribution. Transforming the data can sometimes produce