Page 173 - Applied Statistics Using SPSS, STATISTICA, MATLAB and R

4.5 Inference on More than Two Populations 153

{CON, ADI, FAD, GLA}; {ADI, FAD, GLA, MAS}; {CAR}

These results show that variable PA500 can be helpful in the discrimination of
carcinoma type tissues from other types.

Table 4.16. Scheffé test results obtained with SPSS, for the breast tissue problem
(variable PA500). Values under columns “1”, “2” and “3” are group means.
Subset for alpha = 0.05
CLASS N 1 2 3
CON 14 7.029E-02
ADI 22 7.355E-02 7.355E-02
FAD 15 9.533E-02 9.533E-02
GLA 16 0.1170 0.1170
MAS 18 0.1231
CAR 21 0.2199
Sig. 0.094 0.062 1.000

Example 4.16
Q: Taking into account the results of the previous Example 4.15, it may be asked
whether or not class {CON} can be distinguished from the three-class group {ADI,
FAD, GLA}, using variable PA500. Perform a contrast test in order to elucidate
this issue.
A: We perform the contrast corresponding to the null hypothesis:

H 0: µ CON = (µ FAD + µ GLA + µ ADI)/3,

i.e., we test whether or not the mean of class {CON} can be accepted equal to the
mean of the joint class {FAD, GLA, ADI}. We therefore use the contrast
coefficients shown in Table 4.17. Table 4.18 shows the t-test results for this
contrast. The possibility of using variable PA500 for discrimination of class
{CON} from the other three classes seems reasonable.

Table 4.17. Coefficients for the contrast {CON} vs. {FAD, GLA, ADI}.
CAR FAD MAS GLA CON ADI

0 −1 0 −1 3 −1