Question

Organizational analyst Ann T. Gravity is examining the Peter Principle, which contends that people will rise in an organization until they reach their level of incompetence. She feels that this means that proportionately more competent people will be found at the lower level of the organization. To test this question, she decides to ask students to rate assistant professors, associate professors, and full professors. Based on these ratings, she classified the competence of professors as high, medium, or low. Interpret the accompanying table by calculating the gamma using a work table. What does the gamma tell you about Ms. Gravity’s thoughts on organization and level of incompetence?

Table 1. Competence by Academic Rank

Competence	Academic Rank
	Assistant                   Associate             Full                      Total
Low	27	38	24	89
Medium	60	91	8	159
High	106	38	8	152
Total	193	167	40	400

Answer 1

Gamma(n/2, 2) = Chi square (n)

The chi-square statistic is 76.4235. The p-value is < 0.00001. The result is significant at p < .05.

Results
	Assistant Prof	Associate Prof	Professor			Row Totals
Low	27  (42.94)  [5.92]	38  (37.16)  [0.02]	24  (8.90)  [25.62]			89
Medium	60  (76.72)  [3.64]	91  (66.38)  [9.13]	8  (15.90)  [3.93]			159
High	106  (73.34)  [14.54]	38  (63.46)  [10.21]	8  (15.20)  [3.41]			152
Column Totals	193	167	40			400  (Grand Total)