Applied Statistics Using SPSS, STATISTICA, MATLAB and R

220 5 Non-Parametric Tests of Hypotheses
variables describing the previous knowledge of Boole’s Algebra and binary arithmetic
are independent.
5.15 Redo Example 5.14 for the variable AB.
5.16 The FHR dataset contains measurements of foetal heart rate baseline performed by
three human experts and an automatic system. Is there evidence at the 5% level of
significance that there is no difference among the four measurement methods? Is there
evidence, at 5% level, of no agreement among the human experts?
5.17 The Culture dataset contains budget percentages spent on promoting sport activities
in samples of Portuguese boroughs randomly drawn from three regions. Based on the
sample evidence is it possible to conclude that there are no significant differences
among those three regions on how the respective boroughs assign budget percentages
to sport activities? Also perform the budget percentage comparison for pairs of regions.
5.18 Consider the flow rate data measured at Cávado and Toco Dams included in the Flow
Rate dataset. Assume that the December samples are valid random samples for that
period of the year and, furthermore, assume that one wishes to compare the flow rate
distributions at the two samples.
a) Can the comparison be performed using a parametric test?
b) Show that the conclusions of the sign test and of the Wilcoxon signed ranks test
are contradictory at 5% level of significance.
c) Estimate the power of the Wilcoxon signed ranks test.
d) Repeat the previous analyses for the January samples.
5.19 Using the McNemar Change test compare the pre and post-functional class of patients
having undergone heart valve implant using the data sample of the Heart Valve
dataset.
5.20 Determine which variables are important in the discrimination of carcinoma from other
tissue types using the Breast Tissue dataset, as well as in the discrimination
among all tissue types.
5.21 Consider the bacterial counts in the spleen contained in the Cells’ dataset and check
the following statements:
a) In general, the CD4 marker is more efficacious than the CD8 marker in the
discrimination of the knock-out vs. the control group.
b) However, in the first two weeks the CD8 marker is by far the most efficacious in
the discrimination of the knock-out vs. the control group.
c) Two months after the infection the biochemical markers CD4 and CD8 are unable
to discriminate the knock-out from the control group.
5.22 Based on the sample data included in the Clays’ dataset, compare the holocenic with
pliocenic clays according to the content of chemical oxides and show that the main
difference is in terms of alumina, Al2O3. Estimate what is the needed difference in
alumina that will correspond to an approximate power of 90%.