MS-DS Master of Data science Research & Data Analysis 5 — Questions and Answers
Question 1: A data science team applies natural language processing to classify customer reviews. To evaluate model fairness across demographic groups, which metric should they prioritize?
- Overall accuracy
- Equalized odds across groups (Correct answer)
- Area under the ROC curve
- Root mean squared error
Correct answer: Equalized odds across groups
Equalized odds requires equal true positive and false positive rates across demographic groups, directly measuring fairness beyond aggregate performance.
Question 2: In experimental design, a Latin square design is used to control for:
- One nuisance variable
- Two nuisance variables simultaneously (Correct answer)
- Repeated measures within subjects
- Non-normality of the outcome
Correct answer: Two nuisance variables simultaneously
A Latin square balances two blocking factors (rows and columns) alongside the treatment, controlling both sources of nuisance variability.
Question 3: Which of the following best describes the curse of dimensionality in data analysis?
- Data storage limitations in high-dimensional arrays
- As features increase, the data becomes sparse and distance metrics lose meaning (Correct answer)
- Difficulty visualizing datasets with more than three variables
- Overfitting caused solely by categorical predictors
Correct answer: As features increase, the data becomes sparse and distance metrics lose meaning
In high dimensions, data points become equidistant and sparse, degrading the performance of distance-based algorithms and increasing sample size requirements.
Question 4: An analyst uses a Bonferroni correction after running 20 simultaneous hypothesis tests at α = 0.05. The corrected per-test significance level is:
- 0.05
- 0.0025 (Correct answer)
- 0.001
- 0.01
Correct answer: 0.0025
Bonferroni correction divides alpha by the number of tests: 0.05 / 20 = 0.0025, controlling the familywise error rate.
Question 5: In survival analysis, censored observations occur when:
- The event of interest has been observed for all subjects
- A subject leaves the study or the study ends before the event is observed (Correct answer)
- The time-to-event is normally distributed
- Predictor variables are missing at random
Correct answer: A subject leaves the study or the study ends before the event is observed
Censoring means the exact event time is unknown because the subject was lost to follow-up or the study concluded before the event occurred.
Question 6: A data analyst notices that residuals from a regression model show a funnel-shaped pattern when plotted against fitted values. This indicates:
- Multicollinearity
- Non-linearity of predictors
- Heteroscedasticity (Correct answer)
- Autocorrelation
Correct answer: Heteroscedasticity
A funnel-shaped residual plot indicates heteroscedasticity: the variance of residuals changes as a function of fitted values, violating OLS assumptions.
Question 7: When using information criteria to compare competing statistical models, AIC penalizes model complexity by:
- Adding the number of parameters times sample size
- Adding twice the number of estimated parameters to the negative log-likelihood (Correct answer)
- Subtracting the Bayesian prior from the likelihood
- Dividing log-likelihood by degrees of freedom
Correct answer: Adding twice the number of estimated parameters to the negative log-likelihood
AIC = 2k – 2ln(L), where k is the number of parameters; the 2k term penalizes complexity to guard against overfitting.
MS-DS Master of Data science Research & Data Analysis 5
A data science team applies natural language processing to classify customer reviews.
To evaluate model fairness across demographic groups, which metric should they prioritize?