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AP Psychology Formula Sheet 2026 — Stats, Research Design & Data
APScoreHub · Updated July 5, 2026 · ✓ Verified 2026 data
AP Psychology does not provide a formula sheet. While Psych is not a math-heavy course, the FRQ section regularly requires applying descriptive statistics and research design concepts numerically. This sheet covers every formula and statistical concept that appears on the AP Psych exam.
Descriptive Statistics
| Formula / Concept | How to calculate | When tested |
|---|
| Mean (x̄) = Σx / n | Sum all values, divide by count | Most common FRQ data question |
| Median | Middle value when sorted; average of two middle values for even n | When data has outliers that skew the mean |
| Mode | Most frequent value | Rarely calculated; mostly definitional |
| Range = Max − Min | Subtract smallest from largest | Simple measure of spread |
| Standard Deviation (SD) | Measure of how spread out data is around the mean. Larger SD = more variability. (Formula not required; interpret conceptually.) | Compare variability between groups |
| Variance = SD² | Square of standard deviation | Rarely calculated on AP Psych; conceptual only |
AP Psych FRQs rarely ask you to calculate SD from scratch — they ask you to compare two SDs or interpret what a larger SD means about a dataset.
Normal Distribution & Z-Scores
| Formula / Concept | Details | When tested |
|---|
| z-score = (x − μ) / σ | x = individual score, μ = mean, σ = standard deviation | How many SDs a score is above or below the mean |
| z = 0 | Score equals the mean | Interpreting z-scores |
| z = +1 or −1 | One standard deviation above/below mean; ~68% of scores within ±1 SD | 68-95-99.7 rule |
| 68-95-99.7 Rule | 68% of data within ±1 SD; 95% within ±2 SD; 99.7% within ±3 SD | Normal distribution problems |
| Percentile from z-score | z = +1 → ~84th percentile; z = −1 → ~16th percentile; z = 0 → 50th percentile | IQ, test score, or measurement interpretation |
IQ example: Mean = 100, SD = 15. An IQ of 130 → z = (130−100)/15 = +2 → top ~2.5% of population.
Correlation & Causation
| Concept | Range / Values | What it means |
|---|
| Correlation coefficient (r) | −1.0 to +1.0 | Strength and direction of linear relationship |
| r = +1.0 | Perfect positive correlation | As X increases, Y increases proportionally |
| r = −1.0 | Perfect negative correlation | As X increases, Y decreases proportionally |
| r = 0 | No linear correlation | No predictive relationship |
| r² (coefficient of determination) | r² × 100 = % of variance explained | r = 0.7 → r² = 0.49 → 49% of Y's variance explained by X |
| Correlation ≠ Causation | — | Key concept: third variables, directionality problems |
Research Design & Experimental Concepts
| Concept | Formula / Rule | What it tests |
|---|
| Effect size = (Mean₁ − Mean₂) / SD | Cohen's d (conceptual — not calculated on AP Psych) | Practical significance vs. statistical significance |
| Statistical significance | p < 0.05 (5% chance result is due to chance) | Is the difference real or random? |
| Operational definition | Not a formula — precise, measurable statement of a variable | FRQ design questions always ask for this |
| Random assignment | Every participant has equal chance of being in any condition | Controls for confounding variables |
| Random sampling | Every member of population has equal chance of selection | Allows generalization to population |
Signal Detection Theory
| Term | Definition | On the exam |
|---|
| Absolute threshold | Minimum stimulus intensity detected 50% of the time | Definitional, not calculated |
| Difference threshold (JND) | Smallest detectable difference between two stimuli | Weber's law conceptual questions |
| Weber's Law: ΔI / I = k | JND proportional to stimulus magnitude; k = Weber fraction (constant for each sense) | Conceptual; not calculated on AP Psych |
Memory & Learning (Quantitative Concepts)
| Concept | Key Numbers | What to remember |
|---|
| Working memory capacity | 7 ± 2 items (Miller's Law) | Short-term memory span without chunking |
| Forgetting curve (Ebbinghaus) | ~50% forgotten within 1 hour; ~66% within 1 day without review | Spaced repetition rationale |
| IQ score formula | IQ = (Mental Age / Chronological Age) × 100 | Historical formula; Stanford-Binet origin |
How to Handle Data Questions on the AP Psych FRQ
- Identify the central tendency asked for — mean, median, or mode? Each is appropriate for different data types.
- Show your work — write the sum of values, then divide. Even a correct final answer without work may not earn full credit.
- Interpret, don't just calculate — "The mean score for Group A (M = 14.2) was higher than Group B (M = 11.8), suggesting that..."
- State whether difference is statistically significant — if p-value is given, state whether it meets the 0.05 threshold.
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AP Psychology Score Cutoffs (2026)
| AP Score | Composite Range |
|---|
| 5 | 113–150 |
| 4 | 90–112 |
| 3 | 65–89 |
| 2 | 40–64 |
| 1 | 0–39 |
Frequently Asked Questions
Does AP Psychology have math or formulas?
Yes, but minimally. AP Psych FRQs regularly require calculating the mean, interpreting standard deviation and correlation coefficients, and understanding z-scores. The exam does not require complex statistical calculations — the focus is on interpreting data and applying concepts correctly.
What is the most important statistical concept for AP Psych?
Correlation vs. causation is the most tested concept. Knowing when a study can establish causation (only true experiments with random assignment) vs. merely correlation (observational studies, surveys) is critical for both multiple choice and FRQ questions.
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