ISAT - International Student Admissions Interpreting Scientific Data 2 — Questions and Answers
Question 1: A clinical trial: treatment group (250) shows 15% recovery, control group (250) shows 12% recovery. P-value is 0.23. What should researchers conclude?
- The drug is effective
- The difference is not statistically significant (p > 0.05), so the difference may be due to chance (Correct answer)
- The drug is ineffective and should be abandoned
- Sample size was too small
Correct answer: The difference is not statistically significant (p > 0.05), so the difference may be due to chance
P=0.23 means 23% probability of seeing this difference by chance. This exceeds the 0.05 threshold.
P=0.23 means there is a 23% chance of observing this 3-point difference even if the drug has no effect. This is too high to confidently attribute the difference to the drug.
Question 2: Plant growth under three light conditions: Red=12.4cm (SD=2.1), Blue=15.8cm (SD=1.9), White=14.2cm (SD=2.3), n=30 each. Which comparison is most likely statistically significant?
- Red vs White
- Blue vs White
- Red vs Blue (Correct answer)
- None
Correct answer: Red vs Blue
Red vs Blue has the largest mean difference (3.4cm) with relatively low standard deviations.
Red vs Blue: 3.4cm difference. Red vs White: 1.8cm. Blue vs White: 1.6cm. The largest difference with moderate variability gives the highest t-statistic.
Question 3: Ice cream sales and drowning deaths are strongly correlated (r=0.92). What is the most appropriate interpretation?
- Ice cream causes drowning
- Drowning causes ice cream purchases
- A confounding variable (temperature/season) drives both independently (Correct answer)
- Statistical error
Correct answer: A confounding variable (temperature/season) drives both independently
Hot weather increases both ice cream consumption and swimming activity, driving both variables independently.
This is a classic spurious correlation. Temperature is the confounding variable: hot weather increases both ice cream sales and drowning risk simultaneously.
Question 4: A vaccine is 90% effective. In 10,000 people (5,000 vaccinated, 5,000 not), 50 unvaccinated get the disease. How many vaccinated people would get it?
- 5 (Correct answer)
- 10
- 0
- 45
Correct answer: 5
90% effective means 10% of the unvaccinated rate. Unvaccinated rate: 50/5000=1%. Vaccinated rate: 0.1%. Expected cases: 5.
Vaccine efficacy = 1 - (risk vaccinated / risk unvaccinated). 90% efficacy means vaccinated risk = 10% of unvaccinated risk = 0.1%. Expected: 0.001 x 5000 = 5.
Question 5: Regression: y = 3.2x + 42 (x=study hours, y=score). A student studies 12 hours. What does the model predict, and what does the y-intercept mean?
- 80.4; the average student's score
- 80.4; the predicted baseline score with zero study hours (Correct answer)
- 38.4; minimum possible score
- 80.4; maximum possible score
Correct answer: 80.4; the predicted baseline score with zero study hours
y = 3.2(12) + 42 = 80.4. The y-intercept (42) represents the predicted score when x=0.
Predicted score: 3.2 x 12 + 42 = 80.4. The slope (3.2) means each hour adds 3.2 points. The y-intercept (42) represents baseline knowledge without studying.
Question 6: Treated mice (n=100): 30 developed tumors. Control (n=100): 45 developed tumors. Calculate relative risk reduction and absolute risk reduction.
- RRR=33.3%, ARR=15% (Correct answer)
- RRR=15%, ARR=33.3%
- RRR=30%, ARR=45%
- RRR=66.7%, ARR=30%
Correct answer: RRR=33.3%, ARR=15%
ARR = 45%-30% = 15%. RRR = 15%/45% = 33.3%.
ARR = control risk - treated risk = 15 percentage points. RRR = ARR/control risk = 15/45 = 33.3%. NNT = 1/0.15 = about 7.
ISAT - International Student Admissions Interpreting Scientific Data 2
A clinical trial: treatment group (250) shows 15% recovery, control group (250) shows 12% recovery.
P-value is 0.23.
What should researchers conclude?