Biostatistics & Research · patient case with 6 questions
Reading the evidence
demo: Journal club
chief: The practice is reviewing published evidence before making a purchasing decision and interpreting a set of student examination results.
history: Five dental students scored 64, 56, 48, 66 and 66 on an examination. A trial reports three laser devices, each with a mean difference and a 95 percent confidence interval. A separate paper reports a diagnostic test's performance.
meds: Not applicable.
findings: Laser 1: confidence interval crossing zero into negative values, lowest price. Laser 2, an erbium YAG device: confidence interval entirely above zero, mid price. Laser 3: confidence interval crossing zero, highest price.
Question 1
For the scores 64, 56, 48, 66 and 66, what are the median and the mean respectively?
Show answer and explanation
Correct answer: D. 64 and 60
- A. 66 is the mode, the most frequently occurring value, not the median.
- B. The median of 64 is right but the mean is 60, not 68.
- C. This reverses the two statistics.
- D. Correct. Sorting the values gives 48, 56, 64, 66, 66, so the middle value and therefore the median is 64. The sum is 300 and dividing by 5 gives a mean of 60. Note the order in which the question asks for them; reversing the two is the commonest error on this item.
Question 2
Which statistic expresses the probability that a result occurred by chance alone?
Show answer and explanation
Correct answer: C. The p value
- A. A confidence interval gives a range of plausible values for the true effect and conveys both direction and precision, which is more information than a p value, but it is not itself a probability of chance.
- B. Effect size expresses the magnitude of a difference and is what determines clinical relevance.
- C. Correct. The p value is the probability of obtaining a result at least as extreme as the one observed, assuming the null hypothesis is true. Conventionally a value below 0.05 is called statistically significant. It says nothing about the size of the effect or its clinical importance.
- D. Specificity is a property of a diagnostic test, not a measure of statistical significance.
Question 3
What is preferable about a confidence interval?
Show answer and explanation
Correct answer: A. A narrower interval, which indicates greater precision
- A. Correct. A narrow interval means the estimate is precise and the true value is pinned within a tight range. Width is driven mainly by sample size, so narrow intervals generally reflect larger, better-powered studies.
- B. A wide interval reflects uncertainty and imprecision. It is less useful, not more.
- C. An interval that includes the null, meaning zero for a difference or one for a ratio, indicates the result is not statistically significant.
- D. The 95 percent interval is the biomedical standard. A 90 percent interval is narrower only because it is less conservative, which is not a real gain in precision.
Question 4
Based on the confidence intervals reported, which laser should the practice purchase?
Show answer and explanation
Correct answer: C. Laser 2, the erbium YAG, whose interval lies entirely above zero
- A. Price is not evidence. Laser 3 is both the most expensive and unproven.
- B. Point estimates alone do not establish significance. Two devices can share an estimate and reach opposite conclusions depending on the width of their intervals, which is the entire lesson of this item.
- C. Correct. Only Laser 2 has an interval that excludes zero, so it is the only device with a statistically significant benefit. An interval crossing zero means the true effect could plausibly be nil or harmful. Price is a consideration only among options that actually work.
- D. A cheaper device with an interval crossing zero has not been shown to work. Buying it saves money on an ineffective purchase.
Question 5
True negatives divided by the sum of true negatives and false positives gives:
Show answer and explanation
Correct answer: C. Specificity
- A. Negative predictive value is true negatives over all negative results, and it too depends on prevalence.
- B. Sensitivity is true positives over the sum of true positives and false negatives. SnNout: a Sensitive test that is Negative rules disease out.
- C. Correct. That ratio is specificity, the proportion of genuinely disease-free people the test correctly identifies as negative. A highly specific test produces few false positives, so a positive result is convincing. The mnemonic is SpPin: a Specific test that is Positive rules disease in.
- D. Positive predictive value is true positives over all positive results, and it varies with disease prevalence.
Question 6
Which study design provides the highest level of evidence for a therapeutic question?
Show answer and explanation
Correct answer: C. A randomised controlled trial
- A. A case-control study works backwards from outcome to exposure. It suits rare diseases but is prone to recall and selection bias.
- B. A cohort study follows exposed and unexposed groups forward. It is strong for prognosis and harm but remains observational and vulnerable to confounding.
- C. Correct. Among primary studies the randomised controlled trial sits at the top, because randomisation distributes both known and unknown confounders evenly between arms and permits causal inference. Above it in the hierarchy sit only systematic reviews and meta-analyses of such trials.
- D. A case series describes patients without a comparison group and cannot support causal claims.