Page 182 - Applied Statistics Using SPSS, STATISTICA, MATLAB and R
P. 182

162      4 Parametric Tests of Hypotheses


           A: Using specific tests described in the following chapter, it is possible to show
           that variable ASTV can be assumed to approximately follow a normal distribution
           for most combinations of the factor levels. We use the subset of cases marked with
           yellow colour in the FHR-Apgar.xls file. For these cases Levene’s test yields an
           observed significance of p = 0.48; therefore, the equality of variance assumption is
           not rejected. We are then entitled to apply the two-way ANOVA test to the dataset.
              The two-way ANOVA test results, obtained with SPSS, are shown in Table 4.22
           (factors HOSP  ≡ Hospital;  APCLASS  ≡  Apgar 1 class).  We see that the null
           hypothesis is rejected for the effects and their interaction (HOSP * APCLASS).
           Thus, the test  provides evidence that the heart rate  variability index  ASTV  has
           different means according to the Hospital and to the Apgar 1 category.
              Figure 4.20 illustrates the interaction effect on the means. Category 3 of HOSP
           has quite different means depending on the APCLASS category.


           Table 4.22. Two-way ANOVA test results, obtained with SPSS, for Example 4.20.

                            Type III Sum of
           Source                            df   Mean Square     F      Sig.
                                Squares
           Model              111365.000     6     18560.833   420.881  0.000
           HOSP                3022.056      2      1511.028    34.264  0.000
           APCLASS              900.000      1      900.000     20.408  0.000
           HOSP * APCLASS      1601.167      2      800.583     18.154   0.000
           Error               1323.000      30      44.100
           Total              112688.000     36


           Example 4.21
           Q: In the previous example, the two categories of APCLASS were found to exhibit
           distinct behaviours (see Figure 4.20). Use an appropriate contrast analysis in order
           to elucidate this behaviour. Also analyse the following comparisons: hospital 2 vs. 3;
           hospital 3 vs. the others; all hospitals among them for category 1 of APCLASS.

           A: Contrasts in two-way ANOVA are carried out in a similar manner as to what
           was explained in section 4.5.2.2. The only difference is that in two-way ANOVA,
           one can specify contrast coefficients that do not sum up to zero. Table 4.23 shows
           the contrast coefficients used for the several comparisons:

           a.  The  comparison between both  categories  of APCLASS uses  symmetric
              coefficients for this variable, as in 4.5.2.2. Since this comparison treats all levels
              of HOSP in the same way, we assign to this variable equal coefficients.

           b. The comparison between hospitals 2 and 3 uses symmetric coefficients for these
              categories. Hospital 1 is removed from  the analysis by assigning  a zero
              coefficient to it.
   177   178   179   180   181   182   183   184   185   186   187