The result indicates that the di¤erence is statistically significant beyond the 0.01
level (ata¼ 0 :01, and for a two-sided test the cut point is 3.012 for 13 df).
Note: An SAS program would include these instructions:
DATA;
INPUT GROUP $ COTININE;
DATALINES;
U8
...
U 111
E35
...
E 208;
PROC TTEST;
CLASS GROUP;
VAR COTININE;
in which independent variable name or group follows CLASS and dependent
variable name follows VAR.
7.4 NONPARAMETRIC METHODS
Earlier we saw how to apply one- and two-samplettests to compare popula-
tion means. However, these methods depend on certain assumptions about
distributions in the population; for example, its derivation assumes that the
population(s) is (are) normally distributed. It has even been proven that these
procedures are robust; that is, they are relatively insensitive to departures from
the assumptions made. In other words, departures from those assumptions
have very little e¤ect on the results, provided that samples are large enough.
But the procedures are all sensitive to extreme observations, a few very small or
very large—perhaps erroneous—data values. In this section we learn some
nonparametric procedures, or distribution-free methods, where no assumptions
about population distributions are made. The results of these nonparametric
tests are much less a¤ected by extreme observations.
7.4.1 Wilcoxon Rank-Sum Test
The Wilcoxon rank-sum test is perhaps the most popular nonparametric pro-
cedure. The Wilcoxon test is a nonparametric counterpart of the two-samplet
test; it is used to compare two samples that have been drawn from independent
populations. But unlike thettest, the Wilcoxon test does not assume that the
underlying populations are normally distributed and is less a¤ected by extreme
observations. The Wilcoxon rank-sum test evaluates the null hypothesis that
the medians of the two populations are identical (for a normally distributed
population, the population median is also the population mean).
NONPARAMETRIC METHODS 257