Patricia Cross found that 94 percent of a sample of faculty at the University of Nebraska rated themselves as above-average teachers. 68 percent rated themselves as being in the top 25 percent.
The following is from “Not can but will college teaching be improved.” by K. Patricia Cross (1977) New Directions for Higher Education 17 pp 1-15.
To assess present attitudes [among University of Nebraska faculty] I mailed a ninety-seven-item questionnaire* [see below] to a randomly selected sample of roughly half of the faculty on the three campuses — the Lincoln campus, the urban campus at Omaha, and the Medical College in Omaha. A total of 706 responses were received (68 percent). Since some recipients did not hold teaching appointments or were for other reasons unable or unwilling to participate in the survey, this report is based on 596 completed questionnaires — 57 percent of the original sample, or approximately 29 percent of the faculty of the three campuses combined.
…
Does teaching need improvement? On this question the faculty members reveal what may as well be starkly labeled smug self-satisfaction. An amazing 94 percent rate themselves as above-average teachers, and 68 percent rank themselves in the top quarter on teaching performance. Though they are not quite as pleased with their colleagues as themselves, 60 percent are satisfied with the quality of undergraduate instruction in their department; only 5 percent are dissatisfied most of the time.
The footnote referenced above with the asterisk is:
* Appreciation is expressed to Stanley Mazur-Hart and Thomas Kess, research assistants, for their assistance with all phases of the project. For a report of the study as well as the questionnaire items and responses, see Cross 1976c.
The reference is to:
Cross, K. P. “Report to the Faculty of the University of Nebraska.” Lincoln: University of Nebraska, May 1976.
I can’t find any signs of that document online.
The text above is the full extent of the report on the 94% statistic in the Cross (1977) paper.