Page 189 - Applied Statistics Using SPSS, STATISTICA, MATLAB and R

Exercises 169

freshmen in a programming course (Porto University), based on the Program ming
dataset.
Use the Levene test to check the equality of variance assumption and determine the
power of the test.

4.24 Perform the following post-hoc comparisons for the previous exercise:
a) Scheffé test.
b) “No previous knowledge” vs. “Some previous knowledge” contrast. Compare the
results with those obtained in Exercise 4.19

4.25 Consider the comparison of the bacterial counts as described in the CFU datasheet of
the Cells dataset (see Exercise 4.9) for the spleen and the liver at two weeks and at
one and two months (“time of count” categories). Using two-way ANOVA performed
on the first 5 counts of each group (“knock-out” and “control”), check the following
results:
a) In what concerns the spleen, there are no significant differences at 5% level either
for the group categories or for the “time of count” categories. There is also no
interaction between both factors.
b) For the liver there are significant differences at 5% level, both for the group
categories and for the “time of count” categories. There is also a significant
interaction between these factors as can also be inferred from the respective
marginal mean plot.
c) The test power in this last case is above 80% for the main effects.

4.26 The SPLEEN datasheet of the C ells dataset contains percent counts of bacterial load
in the spleen of two groups of mice (“knock-out” and “control”) measured by two
biochemical markers (CD4 and CD8). Using two-way ANOVA, check the following
results:
a) Percent counts after two weeks of bacterial infection exhibit significant
differences at 5% level for the group categories, the biochemical marker
categories and the interaction of these factors. However, these results are not
reliable since the observed significance of the Levene test is low (p = 0.014).
b) Percent counts after two months of bacterial infection exhibit a significant
difference (p = 0) only for the biochemical marker. This is a reliable result since
the observed significance of the Levene test is larger than 5% (p = 0.092).
c) The power in this last case is very large (p ≈ 1).

4.27 Using appropriate contrasts check the following results for the ANOVA study of
Exercise 4.24 b:
a) The difference of means for the group categories is significant with p = 0.006.
b) The difference of means for “two weeks” vs “one or two months” is significant
with p = 0.001.
c) The difference of means of the time categories for the “knock-out” group alone is
significant with p = 0.027.