7.6 Table 7.21 shows the result of cross classifying a sample of people from the MBTIStep II National Sample, collected and compiled byCPPInc., on the four scales of the Myers–Briggs personality test: Extroversion/Introversion (E/I), Sensing/iNtuitive (S/N), Thinking/Feeling (T/F) and Judging/Perceiving

(J/P). The 16 cells in this table correspond to the 16 personality types: ESTJ, ESTP, ESFJ, ESFP, ENTJ, ENTP, ENFJ, ENFP, ISTJ, ISTP, ISFJ, ISFP, INTJ, INTP, INFJ, INFP.

a. Fit the loglinear model by which the variables are mutually independent.

Report the results of the goodness-of-fit test.

b. Fit the loglinear model of homogeneous association. Based on the fit, show that the estimated conditional association is strongest between the S/N and J/P scales.

c. Using the model in (b), showthat there is not strong evidence of conditional association between the E/I and T/F scale or between the E/I and J/P scales.