"Outcome of Surgery For Crooked Nose: An Objective Method of Evaluation," published in Aesthetic Plastic Surgery in 2004, explains that "Correction of a crooked nose poses one of the greatest challenges in septorhinoplasty."26 A comparison was made of results for 13 surgeries on "C-shaped" noses (bent partway down) and 14 on "I-shaped" noses (angled out from the top). For the C-shaped noses, 1 repair was termed Excellent, 6 Good, 5 Acceptable, and 1 Unsuccessful; for the I-shaped noses, 2 repairs were Excellent, 9 Good, and 3 Acceptable.
a. Are sample sizes (13 and 14) large enough to expect at least 5 in each of the the 8 category combinations (type of nose and quality of repair)?
b. The article's authors combined excellent with good, and acceptable with unsuccessful, resulting in just two categories for quality of repair. Complete the tables for observed and expected counts (to the nearest hundredth) in the various category combinations:
c. Notice that although the expected counts are not all at least 5, they do come quite close, so the chi-square procedure should give reasonably accurate results. Calculate the chi-square statistic.
d. Keeping in mind that for 2-by-2 tables the area to the right of 3.84 under the chi-square curve is 0.05, tell whether the P-value is small, not small, or borderline.
e. Is there a significant difference in repair quality for C-shaped versus I-shaped noses?
f. The researchers also looked at each nose's preoperative angle and postoperative angle. Was this a paired t, two-sample t, or F procedure?
g. In addition, the researchers compared improvements from preoperative to postoperative angle for the C-shaped noses versus the I-shaped noses. Was this a paired t, two-sample t, or F procedure?