# Overview — key variables & operational definitions **Independent variable (IV)** * **Nightly sleep duration (continuous and categorical):** measured as average hours of sleep per night over the 3 nights immediately preceding an exam (self-report + actigraphy where possible). Categorical bins: *Short* ≤5 hours, *Restricted* 5.1–6.9 hours, *Recommended* 7–8.9 hours, *Long* ≥9 hours. **Primary dependent variables (DVs)** * **Exam performance:** raw test score (%) on the final STEM exam (same exam for all participants or exam-score z-scores if different exams). * **Cognitive function measures:** objective lab/online tasks collected within 24 hours pre-exam: * **Sustained attention:** mean reaction time and lapses on a 10-minute Psychomotor Vigilance Task (PVT). * **Working memory:** n-back accuracy (2-back). * **Executive function / inhibitory control:** Stroop interference score (reaction time difference). * **Subjective sleepiness:** Epworth Sleepiness Scale (ESS) or Karolinska Sleepiness Scale (KSS). **Potential moderators/mediators / control variables (measured)** * Chronotype (Morningness–Eveningness Questionnaire), prior semester GPA, cumulative study hours during exam week, caffeine intake (mg/day), alcohol use, naps, mental health (PHQ-9/GAD-7), medication, circadian timing of the exam, age, sex. --- # Hypotheses (organized broad → specific). Each hypothesis is standalone, includes operational definition, directionality, rationale, suggested test, and key assumptions/confounders. --- ## Group A — Broad primary relationship between sleep duration and exam performance ### H1 (Directional, alternative) **H1 (Alt):** *Among college STEM students, greater average nightly sleep duration in the three nights before a final exam (measured in hours) will be associated with higher exam scores (percentage correct).* **Operationalization:** IV = mean hours slept (continuous); DV = exam score (%). **Rationale:** Sleep supports memory consolidation and cognitive recovery; more sleep in the immediate pre-exam window improves recall and problem solving. **Suggested test:** Linear regression (exam score ~ sleep hours + covariates). Report β, 95% CI, p-value, R². Consider nonlinearity (add quadratic term). **Assumptions/confounders:** linearity, independence, normal residuals. Control for prior GPA, study hours, caffeine, chronotype. **Null (H0):** No association between pre-exam sleep hours and exam score (β = 0). --- ## Group B — Dose-response and threshold effects ### H2a (Directional) **H2a:** *Students with short sleep (≤5 hours) in the three nights before an exam will have significantly lower mean exam scores than students with recommended sleep (7–8.9 hours).* **Operationalization:** IV categorical (Short vs Recommended); DV exam score. **Suggested test:** Independent-samples t-test or ANCOVA (if controlling covariates). If >2 groups, one-way ANOVA with post-hoc pairwise comparisons (Tukey). **Rationale:** Severe restriction markedly impairs attention and memory required for complex STEM problems. **Null (H0):** No mean difference between groups. ### H2b (Non-directional) **H2b:** *There is a nonlinear (U-shaped) relationship between sleep duration and exam scores such that both very short (≤5 h) and very long (≥9 h) sleep are associated with lower exam scores compared with recommended sleep (7–8.9 h).* **Operationalization:** IV continuous or categorical; DV exam score. **Suggested test:** Quadratic regression (add sleep² term) and/or compare group means via ANOVA. Test significance of quadratic term. **Rationale:** Extremely long sleep may indicate poor sleep quality, illness, or depression—factors that can also impair performance. **Null (H0):** Relationship is linear or no quadratic effect. --- ## Group C — Specific cognitive domains (mechanistic hypotheses) ### H3a (Directional) **H3a:** *Reduced sleep (each 1-hour decrease) in the 3 nights pre-exam will be associated with slower mean reaction times and more lapses on the PVT (poorer sustained attention).* **Operationalization:** IV = sleep hours; DV = mean RT and lapse count on PVT. **Suggested test:** Linear regression or mixed model (if multiple cognitive measures per participant). **Rationale:** Sleep loss produces measurable decrements in vigilance and attention, mediating poorer exam performance. **Null (H0):** No association. ### H3b (Directional) **H3b:** *Reduced sleep will be associated with lower working memory accuracy (2-back) and greater Stroop interference (worse executive control).* **Operationalization:** IV sleep hours; DVs = 2-back accuracy (%) and Stroop interference (ms). **Suggested test:** Multivariate ANCOVA (MANCOVA) controlling for covariates, or separate regressions with Bonferroni/FDR correction. **Rationale:** Working memory and executive control are sensitive to sleep deprivation; deficits can reduce problem-solving accuracy on complex exam items. **Null (H0):** No association. --- ## Group D — Mediators and mechanisms ### H4 (Mediational, directional) **H4:** *The relationship between pre-exam sleep duration and exam scores is mediated by sustained attention (PVT lapses): shorter sleep → more lapses → lower exam scores.* **Operationalization:** IV sleep hours; Mediator = PVT lapses; DV = exam score. **Suggested test:** Mediation analysis (e.g., PROCESS macro or structural equation model) testing indirect effect with bootstrapped CI. **Rationale:** Sleep impacts vigilance which in turn affects during-exam performance. **Null (H0):** No indirect effect through attention. --- ## Group E — Moderators (when effect differs by subgroup) ### H5a (Directional moderation) **H5a:** *Chronotype moderates the sleep–exam relationship: the negative impact of short sleep on exam scores will be stronger for evening-type students than for morning-type students when exams are scheduled in the morning.* **Operationalization:** IV = sleep hours; Moderator = chronotype (continuous or categorical); DV = exam score; include interaction term sleep × chronotype. **Suggested test:** Hierarchical regression including interaction; simple slopes analysis. **Rationale:** Evening types may suffer more for early exams due to circadian misalignment; same sleep duration produces different functioning. **Null (H0):** No moderation by chronotype. ### H5b (Directional moderator) **H5b:** *Prior GPA moderates the sleep effect: the negative association between sleep loss and exam scores will be attenuated in students with higher prior GPA.* **Suggested test:** Regression with sleep × GPA interaction. **Rationale:** High-performing students may use compensatory strategies or have stronger baseline knowledge buffers. --- ## Group F — Acute vs cumulative sleep effects (specific design choices) ### H6 (Non-directional / comparative) **H6:** *Exam performance is differentially associated with acute short sleep (single night ≤4 h before exam) versus cumulative short sleep (averaged ≤5 h across three nights).* **Operationalization:** Compare two predictors: single-night minimum sleep and 3-night average; DV exam score. **Suggested test:** Multiple regression with both predictors included; compare standardized betas and use model comparison (AIC) to see which predicts better. **Rationale:** Some research finds cumulative restriction has larger cognitive effects, while an acute very short night may cause large immediate deficits. **Null (H0):** Neither predictor differs in explanatory power. --- # Which hypotheses are directional vs non-directional and why * **Directional hypotheses:** H1, H2a, H3a, H3b, H4, H5a, H5b — used when theory and prior evidence predict the **direction** of the effect (e.g., sleep loss reduces performance). Directional tests (one-tailed) increase power but should only be used if prior literature strongly justifies them. * **Non-directional hypotheses:** H2b, H6 — used when you expect a relationship but not a precise direction (e.g., U-shaped or comparative effects). Two-tailed tests are appropriate here. **Implication:** Choose directional tests only if you pre-register and have robust prior justification; otherwise use two-tailed tests to avoid Type I bias. --- # Recommended research designs & statistical approaches (practical choices) **Cross-sectional observational (feasible)** * Collect sleep diaries/actigraphy and cognitive tests in 100–300 STEM students during exam week. * Use multiple regression/ANCOVA, control covariates, test interactions and mediation. **Within-subjects / repeated-measures (stronger causal inference)** * Track same students across multiple exams with varying sleep (N ≥ 40–60). Use linear mixed-effects models (random intercepts for students) to separate within-person effects from between-person differences. **Experimental (gold standard but less ecologically valid)** * Randomly assign students to sleep restriction vs normal sleep before a practice exam in lab settings. Use t-tests/ANOVA and cognitive batteries. Ethical constraints around sleep deprivation and disruption to real exam performance. **Statistical tests mapped to hypotheses** * H1: Linear regression (with covariates). * H2a/H2b: ANOVA/ANCOVA; quadratic regression. * H3a/H3b: Regression or MANCOVA (multiple cognitive DVs). * H4: Mediation analysis with bootstrapped indirect effects. * H5: Interaction tests in regression/multilevel models. * H6: Model comparison using nested regression or information criteria; mixed models for repeated measures. **Power & sample size** * Expect small-to-moderate effects (Cohen's d ≈ 0.3–0.5 for severe restriction). For regression detecting R² change ~0.05 at 80% power, aim for N ≈ 150+ (rule of thumb). For within-subject designs, fewer participants needed but ensure enough repeated measures. --- # Potential confounding variables, limitations, and assumptions **Confounders to measure & control** * Prior academic ability (GPA), total study time and quality (hours + active learning), caffeine and stimulant use, alcohol, naps, chronic sleep problems (insomnia), mental health (depression/anxiety), illness, medications, exam difficulty/format, time-of-day of exam, use of sleep aids, socioeconomic status (affects housing noise), and device use before sleep. **Measurement limitations** * Self-reported sleep can be biased; whenever possible supplement with actigraphy. Cognitive tests should be validated and administered under consistent conditions. **Assumptions** * Independence of observations (if cross-sectional) — violated in repeated measures unless modeled properly. * Linearity and homoscedasticity for regression; normality for parametric tests—use transformations or robust methods if violated. * Temporal precedence for mediation: ideally measure sleep before mediator (attention) before exam outcome. **Other limitations** * Observational designs limit causal claims. Experimental manipulations improve causality but reduce ecological validity (and may be ethically constrained during real exams). * Acute exam stress may interact with sleep effects; consider measuring cortisol or subjective stress. --- # Practical checklist to include in your methods/proposal 1. **Operationalize sleep** (3-night average, actigraphy + diary). 2. **Pre-register** hypotheses and analysis plan (esp. directional tests). 3. **Collect covariates** listed above. 4. **Choose design:** within-subjects if possible; otherwise large cross-sectional sample. 5. **Use appropriate models:** mixed-effects for repeated measures, mediation for mechanisms, interaction terms for moderators. 6. **Plan sample size** with power analysis for expected effect sizes. 7. **Report effect sizes & confidence intervals,** not only p-values. 8. **Check assumptions** and run sensitivity analyses (e.g., excluding participants with extreme sleep patterns or high use of stimulants). --- If you want, I can now: * Convert these into exact, copy-paste **hypothesis statements** formatted for your proposal (H1, H0, variables, measurement), or * Draft a short statistical analysis plan mapping each hypothesis to code-ready test steps (e.g., R or Python pseudocode), or * Create a sample power analysis with assumed effect sizes to recommend sample sizes. Which of those would help you next?