Question

# Organizational analyst Ann T. Gravity is examining the Peter Principle, which contends that people will rise...

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

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)

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