- A biochemist tests whether a new drug inhibits enzyme activity and reports: "Treatment with 10 μM drug reduced enzyme activity from 100 ± 8% to 76 ± 12% (mean ± SD, n=4 each group, p=0.045)." A colleague questions whether this represents a robust finding. What is the most valid concern about this result?
Answer: The p-value is too close to the significance threshold, and the large standard deviations relative to the effect size suggest the result may not be reproducible.
The p-value of 0.045 is just barely significant, and with relatively large SDs (8% and 12%) compared to the 24% difference, this suggests high variability that could affect reproducibility. Choice B incorrectly makes a blanket statement about sample size requirements. Choice C incorrectly dismisses SD as inappropriate. Choice D makes an unsupported assumption about what constitutes biological meaningfulness.
- A research team conducts multiple t-tests comparing protein levels between control and five different treatment groups, obtaining p-values of 0.03, 0.08, 0.01, 0.06, and 0.02. Without applying multiple comparison corrections, they conclude that treatments 1, 3, and 5 show significant effects. What is the primary statistical concern with this approach?
Answer: Multiple comparisons inflate the probability of Type I errors, so the apparent significant results may include false positives that would disappear with proper correction.
When performing multiple comparisons, the chance of finding at least one false positive increases with each test. With 5 comparisons, the family-wise error rate is much higher than 0.05, so corrections like Bonferroni should be applied. Choice A makes unsupported assumptions about sample size. Choice C incorrectly interprets p-value variation as problematic. Choice D makes a blanket incorrect statement about t-test appropriateness.
- A graduate student performs enzyme kinetics experiments and calculates 95% confidence intervals for Km values: Control enzyme Km = 15.2 μM (CI: 12.8-17.6 μM), Inhibitor-treated enzyme Km = 19.8 μM (CI: 16.1-23.5 μM). The student concludes that the inhibitor significantly increases Km. What is the primary statistical issue with this conclusion?
Answer: The conclusion inappropriately infers statistical significance from overlapping confidence intervals without performing a proper comparative test.
The confidence intervals overlap (12.8-17.6 and 16.1-23.5), and one cannot determine statistical significance just by examining whether CIs overlap. A proper statistical test (like a t-test) comparing the two Km values is needed. Choice A incorrectly suggests the CIs are too narrow. Choice C makes an unsupported assumption about sample size. Choice D incorrectly suggests a universal rule about confidence level for enzyme studies.
- A student analyzes Western blot band intensities and reports: "Protein X expression increased 2.3-fold with treatment (p < 0.001, n=3)." The instructor notes that while the p-value suggests strong statistical significance, there may be concerns about the experimental design. What is the most likely issue the instructor identified?
Answer: A sample size of n=3 provides limited statistical power and may not adequately represent biological variability, despite yielding a significant p-value.
While n=3 can sometimes yield significant p-values (especially with large effect sizes and low variability), it provides limited statistical power and may not capture biological variability adequately. The instructor likely wants more replicates for robust conclusions. Choice A incorrectly dismisses fold-change analysis. Choice C incorrectly suggests p < 0.001 is too stringent. Choice D makes an unsupported claim about required test types.
