Exploratory Data Analysis
1.3. EDA Techniques
1.3.3. Graphical Techniques: Alphabetic
188.8.131.52. Normal Probability Plot
|Normal Probability Plot for Data with Short Tails||
The following is a normal probability plot for
500 random numbers
generated from a Tukey-Lambda distribution
with the parameter equal
We can make the following conclusions from the above plot.
For data with short tails relative to the normal distribution,
the non-linearity of the normal probability plot shows up in two ways.
First, the middle of the data shows an S-like pattern. This is common
for both short and long tails. Second, the first few and the last
few points show a marked departure from the reference fitted line.
In comparing this plot to the long tail
example in the next section, the
important difference is the direction of the departure from the
fitted line for the first few and last few points. For short
tails, the first few points show increasing departure from the
fitted line above the line and last few points show increasing
departure from the fitted line below the line. For long
tails, this pattern is reversed.
In this case, we can reasonably conclude that the normal distribution does not provide an adequate fit for this data set. For probability plots that indicate short-tailed distributions, the next step might be to generate a Tukey Lambda PPCC plot. The Tukey Lambda PPCC plot can often be helpful in identifying an appropriate distributional family.