MS-DS Master of Data science Research & Data Analysis 4 — Questions and Answers
Question 1: A Likert-scale survey question (1–5) measuring satisfaction is best analyzed with which statistical approach?
- Parametric t-test assuming normality
- Mann-Whitney U test as a non-parametric alternative (Correct answer)
- Chi-square goodness-of-fit test
- Pearson correlation
Correct answer: Mann-Whitney U test as a non-parametric alternative
Ordinal Likert data often violates normality assumptions, making the Mann-Whitney U test a robust non-parametric choice for group comparisons.
Question 2: In a multiple regression model, the variance inflation factor (VIF) is used to detect:
- Heteroscedasticity
- Multicollinearity among predictors (Correct answer)
- Autocorrelation in residuals
- Outliers in the response variable
Correct answer: Multicollinearity among predictors
VIF quantifies how much a predictor's variance is inflated due to linear correlations with other predictors in the model.
Question 3: Which sampling method ensures proportional representation of subgroups within the population?
- Simple random sampling
- Cluster sampling
- Stratified random sampling (Correct answer)
- Convenience sampling
Correct answer: Stratified random sampling
Stratified random sampling divides the population into strata and samples from each proportionally, guaranteeing subgroup representation.
Question 4: A receiver operating characteristic (ROC) curve plots sensitivity against:
- Precision
- 1 – Specificity (false positive rate) (Correct answer)
- Accuracy
- F1 score
Correct answer: 1 – Specificity (false positive rate)
The ROC curve plots the true positive rate (sensitivity) on the y-axis against the false positive rate (1 – specificity) on the x-axis across all classification thresholds.
Question 5: In Bayesian inference, the posterior distribution is proportional to:
- The likelihood alone
- The prior alone
- The product of the prior and the likelihood (Correct answer)
- The marginal probability of the data
Correct answer: The product of the prior and the likelihood
Bayes' theorem states posterior ∝ likelihood × prior; the marginal likelihood acts as a normalizing constant.
Question 6: A researcher finds r = 0.92 between two variables but the relationship is explained entirely by a third variable. This is called:
- Interaction effect
- Spurious correlation (Correct answer)
- Mediation
- Suppression
Correct answer: Spurious correlation
A spurious correlation appears strong but disappears when a confounding variable is controlled, revealing no true direct relationship.
Question 7: When building a predictive model, overfitting is best identified by:
- High training accuracy and low test accuracy (Correct answer)
- Low training accuracy and high test accuracy
- Equal training and test accuracy
- Low residual sum of squares on training data
Correct answer: High training accuracy and low test accuracy
Overfitting occurs when a model memorizes training data, yielding high in-sample performance but poor generalization to unseen test data.
MS-DS Master of Data science Research & Data Analysis 4
A Likert-scale survey question (1–5) measuring satisfaction is best analyzed with which statistical approach?