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2. Priority Scores and Percentiles James Onken, Ph.D. Chief, Office of Program Analysis and Evaluation NIGMS

3. Priority and Percentile Scores Priority Score = The average of individual reviewers’ scores on 1.0 - 5.0 scale (two significant digits), rounded to three significant digits, and multiplied by 100 Percentile Score = The rank of an application’s priority score, relative to all priority scores assigned in the three most recent review cycles Example:Average reviewer score = 1.53 Priority score = 153 Percentile score = 20.7 (MGA)

5. Scoring Issues How reliable are they? Are they being expressed at an appropriate level of precision? Do the average priority score and percentile provide enough information? - To applicants - To NIH staff In one way or another, all three of these issues involve score variation and what this variation means.

6. Sources of Variation in Scores Individual Reviewer Scores –True differences among applications –True differences of opinion among reviewers –Error Priority Scores –True differences among applications –Error Percentile Scores –Variation in Priority Scores –Variation in score “base” used to calculate percentiles

7. Reliability of Group Averages Reliability of individual reviewer score (r xx ): True variance True variance + Error variance Expected reliability of group average (r* xx ): r* xx =N r xx 1 + (N-1) r xx

8. Expected Reliability of Priority Scores As Function of Group Size Reviewer Reliability Group Size 51015202530 0.00.00 0.10.360.530.630.690.740.77 0.20.560.710.790.830.860.88 0.30.680.810.870.900.910.93 0.40.770.870.910.930.940.95 0.50.830.910.940.950.960.97 0.60.880.940.960.97 0.98 0.70.920.960.970.98 0.99 0.80.950.98 0.99 0.90.980.99 1.00 1.01.00

9. Misapprehension of the Advantages of Averaging “Averaging estimates is an effective way to improve accuracy when combining expert judgments, integrating group members’ judgments, or using advice to modify personal judgments... people often hold incorrect beliefs about averaging, falsely concluding that the average of two judges’ estimates would be no more accurate than the average judge. The experiments confirmed that this misconception was common across a range of tasks...” - Larrick and Soll, 2005 “Even subjects who were statistically sophisticated showed limited appreciation of the aggregation principle...” - Kunda and Nisbett, 1986

10. Describing Variation in Reviewers’ Scores Standard Deviation Range

11. Variance Indicators Grant Number PercentilePriority Score+/- 1 s.d. 10.2121115-127 20.5125118-132 31.2133125-141 41.9141133-149 52.6142121-163 62.6142137-147 73.5143137-149 85.4149140-158 96.4151139-163 106.4151144-158 117.1152144-160 127.5154145-163 138.0155147-163 148.5157151-163 1510.9160148-172 Min ScoreMax Score 110140 120140 130160 120160 120220 130150 130160 140190 130180 140170 140180 140170 140170 140170 150200

12. Variance of Proportions (Percentiles) Sampling errors in proportions are a function of: –proportion (largest around 0.5) –denominator (smaller with larger N)

13. Standard Errors of Proportions Proportion (Percentile) N (Number of Applications in Base) 255075100150200250 5+/-5+/-4+/-3+/-2 +/-1 10+/-7+/-5+/-4+/-3 +/-2 15+/-8+/-6+/-4 +/-3 +/-2 20+/-9+/-6+/-5+/-4+/-3 25+/-10+/-7+/-5 +/-4+/-3 30+/-10+/-7+/-6+/-5+/-4+/-3 35+/-11+/-7+/-6+/-5+/-4 +/-3 40+/-11+/-7+/-6+/-5+/-4 +/-3 45+/-11+/-8+/-6+/-5+/-4 +/-3 50+/-11+/-8+/-6+/-5+/-4 +/-3 55+/-11+/-8+/-6+/-5+/-4 +/-3 60+/-11+/-7+/-6+/-5+/-4 +/-3 65+/-11+/-7+/-6+/-5+/-4 +/-3

14. Round-to-Round Variation in Percentile Scores Associated with Priority Scores within the Same Study Section

15. Priority Scores Among Applications of Equivalent Relative Rank

16. Priority Score Variation Among Applications with Equivalent Relative Rank Coefficient of Variation = Standard Deviation Average Priority Score ≈ 0.10 Priority Score+/- s.d. 110+/- 11 120+/- 12 130+/- 13 140+/- 14 150+/- 15 160+/- 16 170+/- 17 180+/- 18 190+/- 19 200+/- 20 210+/- 21 220+/- 22 230+/- 23 240+/- 24 250+/- 25