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.