```
Exercise 7: Nonparametric Tests
----------

Wilcoxon test
(nonparametric counterpart of the t-procedure for related pairs)
Mann-Whitney U test
(counterpart of the t-procedure for independent samples)

An experimental subject records a large number of compounds, which are
analyzed. A compound can have two forms.

The first form is:
...+vowel+t+s+word boundary+p+vowel+..., example: fietspad
The second form:
...+vowel+t+s+word boundary+b+vowel+..., example: fietsband

In total 112 compounds are recorded, 55 of the first form and 57 of the
second. For each compound the length (in ms) of the t (t_len) and the
lenth (in ms) of the s (s_len).

Now we compare the t lengths to the s lengths. The length of the s in
the compounds of the first form are compared to the length of the s in
the compounds of the second form.
(Source: research by Wouter Jansen, ATW, State University Groningen.)

The data can be found at H:\public\share\heeringa\samen.txt.
Read the ASCII data in SPSS. Define the three collumns and give them
the names "form", "t_len" and "s_len".

a. The Wilcoxon test can be used when both groups have a symmetrical
distribution. Draw a histogram for the lengths of the t and draw a
histogram for the lengths of the s.
Can the Wilcoxon test be used?

b. Is there a significant difference between the lengths of the t and
the lengths of the s? Use the Wilcoxon test. Formulate the
appropriate H_0 and H_a. Do not distinguish between the different
forms.

c. The Mann-Whitney U test can be used when the distributions of both
groups are the same. Draw a histogram for the lengths of the s in
form 1 and draw a histogram for the lengths of the s in form 2.
Can the Mann-Whitney U test be used?

d. Is there a significant difference between the lengths of the s in
form 1 and the lengths of the s in form 2? Use the Mann-Whitney U
test. Formulate the appropriate H_0 and H_a.

```