Saral Shiksha Yojna
Courses/Behavioral Research: Statistical Methods

Behavioral Research: Statistical Methods

CG3.402
Vinoo Alluri•Monsoon 2025-26•4 credits
Sample Papers/Mock Paper 4 — All Units Mix

Mock Paper 4 — All Units Mix

Duration: 120 min • Max marks: 100

Section A — MCQ (20 × 1 = 20)

20 marks
  1. 1.Probability of two heads in two flips of a fair coin: (a) 0.25 (b) 0.5 (c) 0.75 (d) 11 m
  2. 2.Skewness of a left-skewed (negative) distribution: (a) Mean > median (b) Mean < median (c) Mean = median (d) Mode > mean1 m
  3. 3.Power = 0.80 with α = 0.05 means: (a) 80% of effects are real (b) 80% probability of correctly detecting a true effect, with 5% Type I (c) 5% Type II, 80% sensitivity (d) Always rejects H₀1 m
  4. 4.Friedman test is for: (a) Independent groups (b) Repeated-measures, non-normal data (c) Same as Kruskal-Wallis (d) Nominal data1 m
  5. 5.Variance of a discrete RV equals: (a) E(X) (b) E(X²) − [E(X)]² (c) E(X)² (d) Σx·P(x)1 m
  6. 6.Selection bias most directly threatens: (a) Internal (b) External (c) Both (d) Neither1 m
  7. 7.Cohen's d = 0.2 is: (a) Small (b) Medium (c) Large (d) No effect1 m
  8. 8.Random assignment but convenience sample → validity: (a) Strong internal, strong external (b) Strong internal, weak external (c) Weak internal, strong external (d) Weak both1 m
  9. 9.Factor with eigenvalue 0.85 in a PCA: (a) Always retained (b) Retained only if first (c) Typically not retained under Kaiser's rule (< 1) (d) Cannot exist1 m
  10. 10.95% CI for a difference: [−2, 4]. Consistent with: (a) Significant at α=.05 (b) Non-significant; CI spans 0 (c) Strong evidence for positive (d) Strong evidence for null1 m
  11. 11.Heat map of a correlation matrix is best used to: (a) Visualise mean differences (b) See patterns of pairwise correlations among many variables (c) Test for significance (d) Compute regression coefficients1 m
  12. 12.Chocolate vs Nobel prizes across countries — most likely interpretation: (a) Causal (b) Confounded by national wealth/development (c) Random fluctuation (d) Reverse causation1 m
  13. 13.An ANOVA table includes columns: (a) SS, df, MS, F, p (b) SS, n, σ, p (c) μ, σ, F (d) χ², df, p1 m
  14. 14.Correct interpretation of β₁ = 3 in regression: (a) X explains 3 units of Y (b) When X ↑ by 1, Y ↑ by 3 on average, holding other predictors constant (c) Correlation is 3 (d) Y/X = 31 m
  15. 15.Convergent validity is established when: (a) Measure correlates with conceptually unrelated measures (b) Correlates with other measures of the same construct (c) Test-retest is high (d) Items internally consistent1 m
  16. 16.Binomial → approximately normal when: (a) n small (b) p = 0 (c) np and n(1−p) both ≥ ~10 (d) Never1 m
  17. 17.Researcher peeks at p after each new participant, stops at p < .05. Actual Type I rate: (a) = 0.05 (b) Exceeds 0.05, often substantially (c) Below 0.05 (d) Unaffected1 m
  18. 18.BF₁₀ = 0.3 indicates: (a) Strong for H₁ (b) Anecdotal/weak for H₀ (1/0.3 ≈ 3.3) (c) Equivocal (d) Decisive H₀1 m
  19. 19.A bootstrap procedure: (a) Increases sample size from population (b) Resamples with replacement from the observed sample to estimate sampling distribution (c) Adds noise (d) Bayesian method1 m
  20. 20.Within-subjects task fails to control time of day. Likely issue: (a) Construct validity (b) Order/time confound (c) Type I inflation (d) Sphericity violation1 m

Section B — MSQ (10 × 2 = 20)

20 marks
  1. 1.Can be tested with χ² of independence: (a) Gender × handedness (b) Smoking × lung cancer (yes/no) (c) Height × weight (d) Treatment × recovery (yes/no) (e) IQ × age2 m
  2. 2.True about the sampling distribution of the mean: (a) Mean = μ (b) SD = σ/√n (c) Shape → Normal as n grows (CLT) (d) SD = σ (e) Variance = σ²/n2 m
  3. 3.Properties of OLS residuals: (a) Sum to zero (with intercept) (b) Orthogonal to predictors (c) Mean zero (d) Approximately normally distributed for inference (e) Variance should be constant2 m
  4. 4.Can cause low reliability: (a) Ambiguous item wording (b) Random noise (c) Heterogeneous test environment (d) Strong construct validity (e) Inconsistent rater training2 m
  5. 5.Common assumptions of parametric tests: (a) Normality (b) Homogeneity of variance (c) Interval/ratio DV (d) Independence (e) Linearity (regression)2 m
  6. 6.Sources of measurement error: (a) Random attention fluctuations (b) Equipment calibration drift (c) Rater inconsistency (d) Construct definition (e) Environment2 m
  7. 7.Strengthen statistical conclusion validity: (a) Larger n (b) Reliable measures (c) Lower noise (d) Smaller α (e) Pre-registration2 m
  8. 8.Characteristics of F: (a) Symmetric around 0 (b) Right-skewed (c) Non-negative (d) Defined by two df (e) Used in ANOVA / regression2 m
  9. 9.Warrants a non-parametric test: (a) Heavily skewed continuous data (b) Ordinal outcome (c) Tiny sample with non-normal residuals (d) Ratio data with equal variance + normality (e) Outliers that cannot be justifiably removed2 m
  10. 10.About the prior in Bayesian: (a) Reflects pre-data beliefs (b) No effect on the posterior (c) Updated via Bayes' rule (d) Should be chosen and reported transparently (e) Influences posterior more when data sparse2 m

Section C — Short descriptive (6 × 5 = 30)

30 marks
  1. 1.Distinguish independent and paired t-tests. Examples + computation difference.5 m
  2. 2.Law of large numbers vs Central Limit Theorem.5 m
  3. 3.n = 25 per group, p = .14. How does Bayesian analysis disambiguate 'no effect' vs 'underpowered'?5 m
  4. 4.One-way vs two-way ANOVA — what extra question does two-way answer?5 m
  5. 5.Differentiate construct, face, and convergent/discriminant validity.5 m
  6. 6.Andrew Gelman's 'garden of forking paths' — what is it and how does it differ from p-hacking?5 m

Section D — Long descriptive (3 × 10 = 30)

30 marks
  1. 1.Effect sizes in research. (i) Define. (ii) Compare Cohen's d, r, and η² with use cases. (iii) Why do meta-analyses depend on effect sizes? (iv) Critique reporting only 'significant'.10 m
  2. 2.Compare and contrast frequentist and Bayesian inference along: (i) philosophy, (ii) probability statements about parameters, (iii) priors, (iv) handling small/null effects, (v) practical considerations. Coin-flipping example.10 m
  3. 3.Startup A/B test: A has 1,200 visitors, 60 conversions (5.0%); B has 1,180 visitors, 84 conversions (7.1%). Walk through: (i) hypotheses, (ii) test, (iii) computation, (iv) effect size, (v) limitations + recommendations.10 m

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