# Presentation: 045459

## Priority Scores and Percentiles

- James Onken, Ph.D.
- Chief, Office of Program Analysis and Evaluation
- NIGMS

## 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)

## Slide 3

## 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.

## 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

## 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*

## Expected Reliability of Priority ScoresAs Function of Group Size

| Reviewer Reliability | Group Size |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- |
|  | 5 | 10 | 15 | 20 | 25 | 30 |
| 0.0 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 0.1 | 0.36 | 0.53 | 0.63 | 0.69 | 0.74 | 0.77 |
| 0.2 | 0.56 | 0.71 | 0.79 | 0.83 | 0.86 | 0.88 |
| 0.3 | 0.68 | 0.81 | 0.87 | 0.90 | 0.91 | 0.93 |
| 0.4 | 0.77 | 0.87 | 0.91 | 0.93 | 0.94 | 0.95 |
| 0.5 | 0.83 | 0.91 | 0.94 | 0.95 | 0.96 | 0.97 |
| 0.6 | 0.88 | 0.94 | 0.96 | 0.97 | 0.97 | 0.98 |
| 0.7 | 0.92 | 0.96 | 0.97 | 0.98 | 0.98 | 0.99 |
| 0.8 | 0.95 | 0.98 | 0.98 | 0.99 | 0.99 | 0.99 |
| 0.9 | 0.98 | 0.99 | 0.99 | 0.99 | 1.00 | 1.00 |
| 1.0 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |

## 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

## Describing Variation in Reviewers’ Scores

- Standard Deviation
- Range

## Variance Indicators

| Grant Number | Percentile | Priority Score  | +/- 1 s.d. |
| --- | --- | --- | --- |
| 1 | 0.2 | 121 | 115-127 |
| 2 | 0.5 | 125 | 118-132 |
| 3 | 1.2 | 133 | 125-141 |
| 4 | 1.9 | 141 | 133-149 |
| 5 | 2.6 | 142 | 121-163 |
| 6 | 2.6 | 142 | 137-147 |
| 7 | 3.5 | 143 | 137-149 |
| 8 | 5.4 | 149 | 140-158 |
| 9 | 6.4 | 151 | 139-163 |
| 10 | 6.4 | 151 | 144-158 |
| 11 | 7.1 | 152 | 144-160 |
| 12 | 7.5 | 154 | 145-163 |
| 13 | 8.0 | 155 | 147-163 |
| 14 | 8.5 | 157 | 151-163 |
| 15 | 10.9 | 160 | 148-172 |

| Min Score | Max Score |
| --- | --- |
| 110 | 140 |
| 120 | 140 |
| 130 | 160 |
| 120 | 160 |
| 120 | 220 |
| 130 | 150 |
| 130 | 160 |
| 140 | 190 |
| 130 | 180 |
| 140 | 170 |
| 140 | 180 |
| 140 | 170 |
| 140 | 170 |
| 140 | 170 |
| 150 | 200 |

## Variance of Proportions (Percentiles)

- Sampling errors in proportions are a function of:
- proportion (largest around 0.5)
- denominator (smaller with larger N)

## Standard Errors of Proportions

| Proportion (Percentile) | N (Number of Applications in Base) |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- |
|  | 25 | 50 | 75 | 100 | 150 | 200 | 250 |
| 5 | +/-5 | +/-4 | +/-3 | +/-2 | +/-2 | +/-2 | +/-1 |
| 10 | +/-7 | +/-5 | +/-4 | +/-3 | +/-3 | +/-2 | +/-2 |
| 15 | +/-8 | +/-6 | +/-4 | +/-4 | +/-3 | +/-3 | +/-2 |
| 20 | +/-9 | +/-6 | +/-5 | +/-4 | +/-3 | +/-3 | +/-3 |
| 25 | +/-10 | +/-7 | +/-5 | +/-5 | +/-4 | +/-3 | +/-3 |
| 30 | +/-10 | +/-7 | +/-6 | +/-5 | +/-4 | +/-3 | +/-3 |
| 35 | +/-11 | +/-7 | +/-6 | +/-5 | +/-4 | +/-4 | +/-3 |
| 40 | +/-11 | +/-7 | +/-6 | +/-5 | +/-4 | +/-4 | +/-3 |
| 45 | +/-11 | +/-8 | +/-6 | +/-5 | +/-4 | +/-4 | +/-3 |
| 50 | +/-11 | +/-8 | +/-6 | +/-5 | +/-4 | +/-4 | +/-3 |
| 55 | +/-11 | +/-8 | +/-6 | +/-5 | +/-4 | +/-4 | +/-3 |
| 60 | +/-11 | +/-7 | +/-6 | +/-5 | +/-4 | +/-4 | +/-3 |
| 65 | +/-11 | +/-7 | +/-6 | +/-5 | +/-4 | +/-4 | +/-3 |

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

## Priority Scores Among Applications of Equivalent Relative Rank

- Priority Scores Among Applications of Equivalent Relative Rank

## Priority Score VariationAmong Applications with Equivalent Relative Rank

- Priority Score VariationAmong 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 |