Basic Statistics

EXAMINING DATA FOR NORMALITY 73

Figure 6.9 Histogram of systolic blood pressures of adult males with normal curve.

Figure 6.1 1 is a cumulative plot of the normal distribution with = 0 and o = 1.
At p = 0, the height of the curve is 50%. This height corresponds to the area below
or to the left of the mean. (Note that since the normal distribution is symmetric,
one-half of the area lies to the left of the population mean.) In general, the height
of the cumulative distribution at any point along the X axis equals the area below
or to the left of that point under the normal curve. The cumulative plot of a normal
distribution is often described as being S shaped.
The simplest way to obtain normal probability plots is to use a statistical program.
If the data are normally distributed, the plot will be a straight line. Such plots are
usually called normal probability plots. Figure 6.12 shows a normal probability plot
for the younger adult male systolic blood pressures from Problem 5.2. The variable
X, systolic blood pressure, is shown on the horizontal axis. The expected values
of X, given that the distribution follows a standard normal distribution, is on the
vertical axis. If systolic blood pressure were normally distributed, the resulting points
would lie approximately on a straight line. In examining these plots, the user should
concentrate on the middle 90% and see if that portion is approximately a straight
line. The middle points in Figure 6.12 resemble a curve that is lower at both ends (an
upside-down saucer).
The normal probability plots for data that are skewed to the right often show the
curved pattern given in Figure 6.12. In contrast, when the normal probability plot
is curved in the opposite direction, the distribution of the variable is likely to be
skewed to the left. The latter pattern is less common in biomedical applications. If
the variable has many extreme values (high tailed), the normal probability plot will