Small classroom market: population
The population
The applicants and programs as generated, next to what the parameters asked for, and their distributions. A line over a histogram is the requested distribution.
What to do here
- The tabs above lead to the population, the views before interviews, the applications, the match, and the lists of applicants and programs.
A saved run of the simulator: everyone who opens it sees this same market. Simulated from the assumptions in the parameters; not a prediction of any real applicant's or program's match.
The market, as generated
60 applicants for 50 positions in 8 programs: 1.200 applicants per position (requested 1.2). Programs have 2 to 13 positions (median 6.0, mean 6.25). Requested values are shown where the population was generated.
| Group | Share | Strength mean | Strength SD |
|---|---|---|---|
| non_us_img | 0.250 (0.25) | -1.13 (-1.3) | 0.85 (1.0) |
| other | 0.050 (0.04) | -0.58 (-0.5) | 0.49 (1.0) |
| us_do | 0.183 (0.18) | 0.72 (0.35) | 1.04 (1.0) |
| us_img | 0.083 (0.09) | -0.75 (-1.0) | 0.62 (1.0) |
| us_md | 0.433 (0.44) | 0.50 (0.5) | 0.84 (1.0) |
| Tier | Share | Quality mean |
|---|---|---|
| all | 1.000 (1.0) | -0.20 (0.0) |
| Attribute | Correlation with strength | Mean weight from programs |
|---|---|---|
| board_scores | 0.780 (0.8) | 0.517 (0.500) |
| honors | 0.607 (0.6) | 0.175 (0.200) |
| research | 0.618 (0.5) | 0.308 (0.300) |
| Attribute | Correlation with quality | Mean weight from applicants |
|---|---|---|
| location | -0.040 (0.0) | 0.314 (0.300) |
| program_size | -0.911 (from capacity) | 0.205 (0.200) |
| reputation | 0.836 (0.9) | 0.480 (0.500) |
Share of the common view that the attributes add beyond latent quality: 0.020 for applicants, 0.025 for programs.
Distributions
Did the generator produce the applicants asked for?
A histogram of applicant strength (z-scores) in this run. When the applicants were generated, a line shows the counts the parameters ask for: the mixture of the applicant groups' normal distributions. Bars that follow the line mean the population is what the parameters describe. The summary gives the largest deviation in standard errors; above 4, the generator did not produce what was asked. Uploaded applicants have no line: their strengths are given, not drawn.
Learn more in the helpApplicant strength: 60 applicants in 20 bins from -3.03 to 2.34; the fullest bin holds 7.
The numbers
| From | To | Count |
|---|---|---|
| -3.03 | -2.76 | 1 |
| -2.76 | -2.49 | 0 |
| -2.49 | -2.22 | 1 |
| -2.22 | -1.96 | 0 |
| -1.96 | -1.69 | 2 |
| -1.69 | -1.42 | 2 |
| -1.42 | -1.15 | 4 |
| -1.15 | -0.88 | 2 |
| -0.88 | -0.61 | 7 |
| -0.61 | -0.35 | 4 |
| -0.35 | -0.08 | 7 |
| -0.08 | 0.19 | 7 |
| 0.19 | 0.46 | 6 |
| 0.46 | 0.73 | 2 |
| 0.73 | 1.00 | 4 |
| 1.00 | 1.26 | 3 |
| 1.26 | 1.53 | 2 |
| 1.53 | 1.80 | 1 |
| 1.80 | 2.07 | 2 |
| 2.07 | 2.34 | 3 |
Did the generator produce the programs asked for?
A histogram of program quality (z-scores) in this run, with the counts the parameters ask for (the tiers' normal distributions, or one normal distribution without tiers) when the programs were generated. Bars that follow the line mean the programs are what the parameters describe. Uploaded programs have no line: their qualities are given, not drawn.
Learn more in the helpProgram quality: 8 programs in 20 bins from -1.87 to 1.77; the fullest bin holds 2.
The numbers
| From | To | Count |
|---|---|---|
| -1.87 | -1.69 | 1 |
| -1.69 | -1.51 | 0 |
| -1.51 | -1.32 | 0 |
| -1.32 | -1.14 | 0 |
| -1.14 | -0.96 | 0 |
| -0.96 | -0.78 | 1 |
| -0.78 | -0.60 | 1 |
| -0.60 | -0.42 | 1 |
| -0.42 | -0.23 | 2 |
| -0.23 | -0.05 | 0 |
| -0.05 | 0.13 | 0 |
| 0.13 | 0.31 | 0 |
| 0.31 | 0.49 | 0 |
| 0.49 | 0.68 | 0 |
| 0.68 | 0.86 | 0 |
| 0.86 | 1.04 | 0 |
| 1.04 | 1.22 | 1 |
| 1.22 | 1.40 | 0 |
| 1.40 | 1.59 | 0 |
| 1.59 | 1.77 | 1 |
How are the positions spread over programs?
How many programs have each number of positions. A long right tail means a few large programs hold many of the positions. The key numbers above give the median and the range.
Learn more in the helpPositions per program: 8 programs in 20 bins from 2.00 to 13.00; the fullest bin holds 3.
The numbers
| From | To | Count |
|---|---|---|
| 2.00 | 2.55 | 1 |
| 2.55 | 3.10 | 1 |
| 3.10 | 3.65 | 0 |
| 3.65 | 4.20 | 2 |
| 4.20 | 4.75 | 0 |
| 4.75 | 5.30 | 0 |
| 5.30 | 5.85 | 0 |
| 5.85 | 6.40 | 0 |
| 6.40 | 6.95 | 0 |
| 6.95 | 7.50 | 0 |
| 7.50 | 8.05 | 3 |
| 8.05 | 8.60 | 0 |
| 8.60 | 9.15 | 0 |
| 9.15 | 9.70 | 0 |
| 9.70 | 10.25 | 0 |
| 10.25 | 10.80 | 0 |
| 10.80 | 11.35 | 0 |
| 11.35 | 11.90 | 0 |
| 11.90 | 12.45 | 0 |
| 12.45 | 13.00 | 1 |