250 Fundamentals of Statistics
From the two plots, there is enough graphical evidence to make us worry
that the data do not follow the normal distribution. This is a problem be-
cause now we can’t feel completely comfortable about the p values the t test
gave us. Because the assumption of normality may have been violated, we
can’t be sure that the p value is accurate.Two-Sample Data Applying a Nonparametric Test to
Paired Data
A parametric test assumes a specifi c distribution such as the normal distri-
bution, and the t test is an example. A nonparametric test does not assume
a particular distribution for the data. Most nonparametric tests are based on
ranks and not the actual data values (this frees them from assuming a par-
ticular distribution). The study of nonparametric statistics can fi ll an entire
textbook. We’ll just cover the high points and show how to apply a nonpara-
metric test to your data.The Wilcoxon Signed Rank Test
The nonparametric counterpart to the t test is the Wilcoxon Signed Rank
test. In the Wilcoxon Signed Rank test, we rank the absolute values of the
original data from smallest to largest, and then each rank is multiplied by
the sign of the original value ( 2 1, 0, or 1). In case of a tie, we assign an
average rank to the tied values. Table 6-4 shows the values of a variable,
along with the values of the signed ranks.Figure 6-15
Normal
probability
plot of the
Diff data