SAT Math vs EBRW Section Weighting in College Admissions

sat_section_weighting.md

SAT Math vs EBRW Section Weighting in College Admissions

Research Question

Do colleges — especially STEM-focused institutions — weight SAT Math and EBRW (Evidence-Based Reading and Writing) sections differently in admissions decisions? How much of the observed Math skew at STEM schools reflects applicant self-selection versus institutional preference? What are the implications for the simulation model?

1. Admitted Student Section Profiles

1.1 National Baseline

The 2024 national average SAT is 1024 total: 519 EBRW and 505 Math. Nationally, EBRW exceeds Math by +14 points — the general population scores higher on Reading/Writing than on Math. This makes the reversed pattern at selective colleges (Math > EBRW) even more striking.

1.2 STEM-Focused Schools

Key observation: The Math-EBRW gap ranges from +30 to +50 points at the median for STEM schools. At Caltech and Georgia Tech, the gap is largest. The gap is measured against a national baseline where Math is lower than EBRW by 14 points, making the true reversal ~44-64 points from the population norm.

MIT specifics: 100% of admitted students scored 700-800 on Math. The 25th percentile Math (780) exceeds the 75th percentile EBRW (780). MIT's Dean of Admissions explicitly stated that "performance on standardized math tests is especially predictive of student success" and that math scores "substantially improve the predictive validity of admissions decisions" — this was the primary reason MIT reinstated test requirements.

CMU specifics: CMU's School of Computer Science explicitly encourages SAT/ACT submission "with an emphasis on the math section."

1.3 HYPSM (Comprehensive Elite)

Key observation: Even at comprehensive universities (Harvard, Yale, Princeton) that are not STEM-focused, admitted students still show a Math > EBRW gap of +20 to +30 points. This is important — it suggests the Math advantage is partly a feature of extreme selectivity, not just STEM emphasis.

1.4 Ivy+ and Near-Ivy (Selected)

Northwestern's unusually large gap (+45) likely reflects its strong engineering school (McCormick).

1.5 Liberal Arts Colleges

Key observation: Even at liberal arts colleges with no engineering programs, a mild Math > EBRW gap persists (+10 to +25 points). Amherst is the notable exception with roughly balanced sections or slight EBRW advantage. This suggests a baseline Math advantage at all selective institutions, not just STEM schools.

1.6 Summary: Math-EBRW Gap by School Type

2. Empirical Evidence of Differential Weighting

2.1 College Board Predictive Validity Research

The College Board's Digital SAT Validity Study (September 2023) provides the strongest available evidence:

• SAT Math section predicts first-year math GPA and STEM GPA in a "stairstep" pattern: mean STEM GPAs rise from 3.01 (scores 400-490) to 3.68 (scores 700-800).
• SAT EBRW section predicts first-year non-math GPAs: all-but-math GPAs rose from 3.30 to 3.75 across EBRW score bands.
• Domain-specific prediction: Math section scores show sensitivity to STEM course performance; EBRW shows sensitivity to humanities/social science performance.
• STEM majors overall: SAT adds 38% more predictive power beyond HSGPA alone for STEM majors (r = .64 for SAT vs .52 for HSGPA; r = .72 combined). This is stronger than the general-population improvement.
• SAT-Math proved a stronger predictor of retention than SAT-EBRW in a multi-institution study.

Confidence: HIGH — These are large-sample (n > 200,000), multi-institution studies from College Board's own research division.

2.2 Section-Level Correlations with FYGPA (2008 national validity study)

These aggregate correlations are nearly equal. The differential validity emerges within major — Math predicts STEM GPA much better; EBRW predicts humanities/social science GPA better. The aggregate equality is an artifact of mixing majors.

Confidence: HIGH — Published peer-reviewed College Board research (ERIC ED563202).

2.3 MIT's Explicit Statement

MIT's 2022 blog post reinstating SAT/ACT requirements is the most direct evidence of institutional preference for Math sections:

"Our research shows considering performance on the SAT/ACT, particularly the math section, substantially improves the predictive validity of our admissions decisions with respect to student success at the Institute."

MIT requires all students (regardless of major) to complete two semesters of calculus and two semesters of calculus-based physics. They found: 1. Math section is "particularly predictive" of MIT student outcomes 2. This effect persists after controlling for socioeconomic factors 3. High school grades alone are insufficient predictors

Confidence: VERY HIGH — Direct institutional statement with backing research.

2.4 CDS Section C7: Relative Importance

CDS C7 asks colleges to rate factors as Very Important / Important / Considered / Not Considered. For "standardized test scores":

• HYPSM typically rates tests as Important or Considered (not Very Important, because holistic review)
• CDS does NOT ask about Math vs EBRW weighting separately
• This means we cannot infer differential section weighting from CDS data alone

Confidence: LOW for CDS-based inference — C7 treats "standardized tests" as a single category.

3. Self-Selection vs Institutional Weighting

This is the most important question for modeling. The observed Math > EBRW gap in admitted classes could come from three sources:

3.1 Source A: Applicant Self-Selection (LARGE effect)

Students who apply to STEM schools disproportionately have strong math skills. Evidence: - National data shows students with highest test scores (especially Math) choose STEM majors at higher rates - A 2020 study across 1,389 institutions found strong correlations between average SAT percentiles and STEM graduation rates - Self-selection operates at the application stage: math-strong students disproportionately apply to MIT, Caltech, Georgia Tech

Estimated contribution to STEM school Math-EBRW gap: ~60-70%

3.2 Source B: Selectivity Effect (MODERATE effect)

Even at non-STEM selective colleges, Math > EBRW persists (+10-25 points at LACs, +20-30 at HYPS). This cannot be explained by STEM self-selection. Possible explanations: - Ceiling effects: SAT Math has a lower effective ceiling for high performers (easier to get 780+ Math than 780+ EBRW) — but this actually works against the pattern since more students hit the Math ceiling - Score distribution shape: At the extreme right tail (top 1% of test-takers), Math scores compress more toward 800 than EBRW scores do. The 99th percentile EBRW is ~770 while 99th percentile Math is ~790. - Quantitative aptitude as proxy for general cognitive ability: At the extreme right tail, Math may have higher g-loading than EBRW, making it a better discriminator

Estimated contribution to overall gap at selective schools: ~20-30%

3.3 Source C: Institutional Weighting Preference (SMALL to MODERATE effect)

Direct evidence that colleges weight Math differently: - MIT explicitly values Math section scores more - CMU's School of Computer Science emphasizes math scores - No evidence that any college explicitly weights EBRW more than Math - Most colleges claim to use the composite score

Estimated contribution: ~10-20% at STEM schools; ~0-5% at LACs

3.4 Decomposition Estimate

For a STEM-focused school like MIT (total Math-EBRW gap = +30 pts at median): - ~18-21 points from applicant self-selection (math-strong students apply) - ~6-9 points from selectivity/tail-distribution effects - ~3-6 points from institutional Math preference in admissions

For a top LAC like Williams (total gap = +20 pts at median): - ~0-5 points from self-selection (less pronounced at LACs) - ~10-15 points from selectivity/tail-distribution effects - ~0-3 points from institutional preference (minimal)

Confidence: MODERATE — This decomposition is inferred, not directly measured. No study has cleanly separated these three effects.

4. Simulation Model Calibration Recommendations

4.1 Current Model State

The simulation currently uses: - A single student.sat composite score (900-1600) - College data: sat_middle_50: [P25, P75] as composite ranges - Academic index: satS = sigmoid((student.sat - satMid) / (satSigma * 0.6)) - No section-level decomposition

4.2 Option A: Keep Composite (Recommended for now)

Rationale: The Math-EBRW gap is largely driven by self-selection and tail-distribution effects, not by admissions offices giving different weights to sections. Since our model generates students and then matches them to colleges, the self-selection effect should emerge naturally if student archetypes are well-calibrated.

What to verify: Check whether the current archetype system already produces the right Math-EBRW gap by proxy. A stem_spike student with SAT 1540 would "really" have something like Math 790 / EBRW 750 in the real world. If the model's utility function correctly steers these students toward STEM schools, the aggregate admitted profiles should look realistic without explicit section modeling.

4.3 Option B: Add Section-Level Scores (Future Enhancement)

If section-level fidelity is desired, decompose each student's SAT:

// Generate section scores from composite
function decomposeSAT(composite, archetype) {
  // Base split: at the population level, Math ≈ EBRW - 14
  // But at high scores, Math tends to exceed EBRW

  const ARCHETYPE_MATH_BIAS = {
    stem_spike: +25,      // Strong math tilt
    humanities_spike: -15, // Verbal tilt
    arts_spike: -5,       // Slight verbal tilt
    athletic_spike: 0,    // Balanced
    well_rounded: +5,     // Slight math tilt (selectivity effect)
    average_academic: -7   // Closer to population norm
  };

  const bias = ARCHETYPE_MATH_BIAS[archetype] || 0;
  const noise = randn() * 20; // Individual variation, σ=20

  const mathShare = 0.5 + (bias + noise) / (2 * composite);
  const math = clamp(Math.round(composite * mathShare), 200, 800);
  const ebrw = composite - math;

  return { math: clamp(math, 200, 800), ebrw: clamp(ebrw, 200, 800) };
}

Then add a college-level mathWeight parameter:

// Per-college math emphasis (0.5 = equal weight, 0.7 = strong math emphasis)
const COLLEGE_MATH_WEIGHT = {
  mit: 0.60,        // Explicit math emphasis
  caltech: 0.65,    // Extreme STEM
  georgia_tech: 0.60,
  carnegie_mellon: 0.58,
  // Tier 1 HYPSM (non-MIT)
  harvard: 0.52, yale: 0.52, princeton: 0.52, stanford: 0.53,
  // LACs
  williams: 0.50, amherst: 0.48, pomona: 0.50, swarthmore: 0.51,
  // Default
  _default: 0.50
};

// Modified admission score
const w = COLLEGE_MATH_WEIGHT[collegeKey] || 0.50;
const effectiveSAT = student.satMath * w * 2 + student.satEBRW * (1 - w) * 2;

4.4 Option C: Archetype-Based SAT Modifier (Lightweight Alternative)

Instead of full section decomposition, add a STEM-school bonus for stem_spike students:

// In computeAdmissionScore, after computing satS:
if (college.stemEmphasis && student.archetype === 'stem_spike') {
  // stem_spike students get a small admissions boost at STEM schools
  // Models the implicit Math-section advantage without tracking sections
  logit += 0.15; // ~3-4 percentage point boost at baseline rates
}

This captures the net effect (institutional Math preference) without the complexity of tracking two SAT scores per student.

4.5 Recommended Parameters

4.6 Validation Target

If implementing section scores, the model should reproduce these observed gaps. The key test: do stem_spike students who enroll at MIT in the simulation have an implied Math-EBRW gap of ~+30? If the current composite model already produces realistic enrollment patterns by archetype, section-level scores may be cosmetic rather than mechanistically important.

5. Confidence Summary

Sources

• MIT Admissions Statistics
• MIT Blog: Reinstating SAT/ACT Requirement
• MIT Tests & Scores Policy
• Caltech CDS 2024-2025
• Georgia Tech SAT Scores (NextAdmit)
• Carnegie Mellon SAT Scores (NextAdmit)
• Harvard SAT Scores (NextAdmit)
• Princeton SAT Scores (NextAdmit)
• Yale CDS 2024-25
• Williams College SAT Scores (Test Ninjas)
• CMU CDS 2024-25
• College Board SAT Validity Research
• College Board Digital SAT Validity Study (September 2023)
• College Board: SAT Score Relationships with College GPA
• College Board: Relationship Between SAT Scores and Postsecondary STEM Success
• 2008 SAT National Validity Study (ERIC ED563202)
• Differential Validity and Prediction of the SAT (ERIC ED562614)
• UC SAT/ACT Study Report
• NBER Working Paper: Selection Bias in College Admissions Test Scores
• 2024 Total Group SAT Suite Annual Report
• Pomona College SAT Scores (CollegeTuitionCompare)
• Swarthmore College SAT Scores (CollegeTuitionCompare)
• Middlebury College SAT Scores (CollegeTuitionCompare)
• SAT and STEM Student Success (College Board)
• Stanford SAT Scores (NextAdmit)
• Amherst College SAT Scores (PrepScholar)