Watson-Glaser Critical Thinking Appraisal Interpreting Evidence and Data Questions and Answers 3 — Questions and Answers
Question 1: A line graph shows that a city's annual rainfall decreased steadily from 800mm to 550mm over 20 years. Which interpretation is most appropriate?
- The city will experience a drought within five years.
- The data shows a sustained downward trend in annual rainfall over the 20-year period. (Correct answer)
- Climate change is definitely causing the reduction in rainfall.
- The city must implement water restrictions immediately.
Correct answer: The data shows a sustained downward trend in annual rainfall over the 20-year period.
A steady downward trend in the graph is a factual observation about what the data shows — predictions, causal claims, and policy prescriptions require additional evidence.
Interpreting a line graph correctly means reading the pattern accurately. A steady decline from 800mm to 550mm over 20 years is a clear downward trend. Option B describes this pattern precisely. Option A predicts a future event (drought) — time series data can show trends but predictions require statistical modeling. Option C attributes a specific cause (climate change) — while plausible, the graph shows rainfall data only; attribution requires climate attribution analysis. Option D prescribes action — policy recommendations require weighing many factors beyond a single rainfall trend graph.
Question 2: A pie chart shows that 45% of a company's revenue comes from Product A, 30% from Product B, and 25% from other products. Marketing argues that Product A should receive the most investment. Which is the best interpretation of this data for decision-making?
- Product A should definitely receive the most investment because it generates the most revenue.
- The revenue distribution shows Product A's current dominance, but investment decisions should also consider growth potential, profit margins, and market saturation. (Correct answer)
- Products B and others should receive more investment since Product A already performs well.
- The data proves Product A is the company's most important product indefinitely.
Correct answer: The revenue distribution shows Product A's current dominance, but investment decisions should also consider growth potential, profit margins, and market saturation.
Current revenue share shows what is performing now, but investment decisions also require growth potential, margins, competitive dynamics, and strategic direction — data provides one input, not the full answer.
Revenue contribution is important but not sufficient for investment decisions. Product A's 45% share reflects current performance, but investment ROI depends on marginal returns — if Product A is at market saturation, additional investment may yield diminishing returns. Product B at 30% might have higher growth potential or better profit margins. Option A treats current revenue as the sole decision criterion. Option C applies an inverse logic without justification. Option D incorrectly treats current data as a permanent state. The best interpretation acknowledges what the data shows and what additional analysis is needed before acting on it.
Question 3: A study of 200 university students finds that those who participate in extracurricular activities report higher life satisfaction scores. A dean concludes that all students should be required to join extracurricular activities. Which interpretation challenge is most important?
- 200 students is too small a sample for any conclusions.
- Students satisfied with life may self-select into extracurriculars, so the causation may be reversed. (Correct answer)
- Life satisfaction scores are subjective and therefore invalid as research data.
- University extracurricular activities are not related to life satisfaction.
Correct answer: Students satisfied with life may self-select into extracurriculars, so the causation may be reversed.
Satisfied students may be more likely to engage with activities; the causal arrow could point from satisfaction to participation, not from participation to satisfaction.
This is a reverse causation / selection bias problem. Students who are already satisfied with life, more socially confident, or more energized may be more likely to join extracurricular activities. In this case, extracurricular participation is a symptom of high satisfaction rather than a cause of it. Mandating activities based on this correlation could be ineffective or even counterproductive for students who are struggling and for whom additional obligations add stress. Option A incorrectly dismisses 200 as too small — it's sufficient for correlation studies with appropriate methodology. Option C incorrectly dismisses self-reported satisfaction as a measure. Option D contradicts research evidence on student engagement and wellbeing.
Question 4: National test score data shows that students in private schools score 20% higher on average than students in public schools. Which interpretation is best supported by this data alone?
- Private schools provide superior education to public schools.
- Private school students score higher on average, which may reflect school quality, socioeconomic factors, or student selection. (Correct answer)
- The government should defund public schools and subsidize private education.
- Students who attend private schools are more academically talented.
Correct answer: Private school students score higher on average, which may reflect school quality, socioeconomic factors, or student selection.
The score gap is a factual observation; explaining it requires considering socioeconomic background, parental education, peer effects, and selection — not just school type.
A 20% test score gap between school types is a measured fact. But interpreting what it means requires accounting for confounders: private school families typically have higher incomes, more parental education involvement, and better access to tutoring. Students who attend private schools may have been academically screened. These factors independently predict higher test scores regardless of school type. Options A and D attribute the gap to school quality or student talent without ruling out socioeconomic selection effects. Option C makes a policy leap from test score data. Option B correctly frames the gap as an observation requiring further analysis before attributing causes.
Question 5: A study reports that countries with higher social media use have higher rates of anxiety disorders. A researcher concludes that social media causes anxiety. What is the most important limitation of this conclusion?
- Social media is not used in developing countries, limiting the study's scope.
- Country-level correlation cannot establish individual-level causation, and anxious individuals may use social media more (reverse causation). (Correct answer)
- Anxiety disorders are over-diagnosed in high social media countries.
- The study should have measured depression, not anxiety.
Correct answer: Country-level correlation cannot establish individual-level causation, and anxious individuals may use social media more (reverse causation).
Ecological correlations (country-level) cannot be directly applied to individual behavior, and the possibility that anxious people use more social media as coping behavior (reverse causation) undermines the causal claim.
This question illustrates two critical data interpretation challenges: the ecological fallacy and reverse causation. The ecological fallacy occurs when country-level patterns are assumed to hold at the individual level — a country having high social media use and high anxiety rates doesn't mean the same individuals who use social media are the anxious ones. Additionally, reverse causation is plausible: people with anxiety may turn to social media for social connection or distraction, making anxiety the cause of high social media use rather than the effect. Option A makes an incorrect factual claim. Option C introduces an unsupported measurement validity claim. Option D proposes changing the research design without addressing the core interpretive limitation.
Question 6: Quarterly earnings data shows Company Z's revenue grew 8% in Q1, declined 3% in Q2, grew 5% in Q3, and declined 2% in Q4, for a net annual growth of about 8%. An analyst concludes the company had a strong year. Is this interpretation supported?
- Yes — 8% annual growth is objectively strong in any industry.
- Partially — 8% net growth is positive, but the within-year volatility suggests instability that warrants further investigation. (Correct answer)
- No — any decline in any quarter means the company performed poorly.
- Yes — quarterly fluctuations are normal and don't affect the annual conclusion.
Correct answer: Partially — 8% net growth is positive, but the within-year volatility suggests instability that warrants further investigation.
Net annual growth is a positive signal, but alternating growth and decline quarters suggest revenue instability that a simple annual figure masks — a fuller picture requires understanding the volatility.
Annual aggregate figures can mask important within-year dynamics. 8% net growth is positive on its face, but the pattern of alternating growth-decline-growth-decline suggests the company's revenue was volatile rather than steadily growing. This could indicate dependence on seasonal factors, project-based revenue recognition, client concentration, or structural challenges being temporarily masked by strong quarters. Option A adds an industry benchmark ('objectively strong') not present in the data. Option C overcorrects by treating any negative quarter as definitive failure. Option D dismisses volatility without justification. Option B correctly acknowledges what the data shows (positive net outcome) while flagging what it also reveals (instability requiring investigation).
Watson-Glaser Critical Thinking Appraisal Interpreting Evidence and Data Questions and Answers 3
A line graph shows that a city's annual rainfall decreased steadily from 800mm to 550mm over 20 years.
Which interpretation is most appropriate?