48. Table 7.19 compares two hospitals on the outcomes of patient admissions for severe pneu- monia. Although patient status is an ordinal variable. two researchers who analyze the data treat it as an interval variable. The first researcher assigns the scores (0, 5. 10) to the three categones. The second researcher, believing that the middle category is much closer to the third category than to the first, uses the scores (0, 9. 10) Each researcher calculates the means for the two institutions and identifies the institution with the higher mean as the one having more success in treating its patients.

a) Find the two means for the scoring system used by (i) the first researcher. (ii) the sec- ond researcher. Interpret.

b) Notice that the conclusion depends on the scoring system, hence, if one uses methods for quantitative variables with ordinal data, one should take care in selecting scores.

TABLE 7.19 Patient Status Died in Released After Released After Hospital Lengthy Stay Bnef Stay Hospital A 1 29 0 Hospital B 8 8 14