Page 188 - Applied Statistics Using SPSS, STATISTICA, MATLAB and R

168 4 Parametric Tests of Hypotheses

4.15 The FHR-Apga r dataset contains measurements, ASTV, of the percentage of time that
foetal heart rate tracings exhibit abnormal short-term variability. Use a two-sample t
test in order to compare ASTV means for pairs of Hospitals HSJ, HGSA and HUC.
State the conclusions at a 5% level of significance and study the power of the tests.

4.16 The distinction between white and red wines was analysed in Example 4.9 using
variables ASP and PHE from the Wines dataset. Perform the two-sample mean test for
all variables of this dataset in order to obtain the list of the variables that are capable of
achieving the white vs. red discrimination with 95% confidence level. Also determine
the variables for which the equality of variance assumption can be accepted.

4.17 For the variable with lowest p in the previous Exercise 4.15 check that the power of the
test is 100% and that the test guarantees the discrimination of a 1.3 mg/l mean
deviation with power at least 80%.

4.18 Perform the comparison of white vs. red wines using the GLY variable of the Wines
dataset. Also depict the situations of an RS and an AS test, computing the respective
power for α = 0.05 and a deviation of the means as large as the sample mean deviation.
Hint: Represent the test as a single mean test with µ = µ 1 – µ 2 and pooled standard
deviation.

4.19 Determine how large the sample sizes in the previous exercise should be in order to
reach a power of at least 80%.

4.20 Using the Programming dataset, compare at 5% significance level the scores
obtained by university freshmen in a programming course, for the following two
groups: “No pre-university knowledge of programming”; “Some degree of pre-
university knowledge of programming”.

4.21 Consider the comparison of the six tissue classes of the Breast Tissue dataset
studied in Example 4.15. Perform the following analyses:
a) Verify that PA500 is the only suitable variable to be used in one-way ANOVA,
according to Levene’s test of equality of variance.
b) Use adequate contrasts in order to assess the following class discriminations:
{car}, {con, adi}, {mas, fad, gla}; {car} vs. all other classes.

4.22 Assuming that in the previous exercise one wanted to compare classes {fad}, {mas}
and {con}, answer the following questions:
a) Does the one-way ANOVA test reject the null hypothesis at α = 0.005
significance level?
b) Assuming that one would perform all possible two-sample t tests at the same α =
0.005 significance level, would one reach the same conclusion as in a)?
c) What value should one set for the significance level of the two-sample t tests in
order to reject the null hypothesis in the same conditions as the one-way ANOVA
does?

4.23 Determine whether or not one should accept with 95% confidence that pre-university
knowledge of programming has no influence on the scores obtained by university