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HS 326 study materials
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HS 326: Biostatistics and Quantitative Reasoning

HS 326 · Work through your exam, one topic at a time.

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Biostatistics and Quantitative Reasoning

Biostatistics and Quantitative Reasoning tests whether you can choose the right test, read an estimate correctly, and avoid the classic misinterpretations. HS 326 emphasizes interpretation over computation: you will rarely derive a formula, but you will be asked what a p value, a confidence interval, or a likelihood ratio actually licenses you to say.

Match the test to the data

  • Continuous, approximately normal, two independent groups: independent t-test; paired data: paired t-test.
  • Three or more group means: ANOVA with post-hoc correction.
  • Categorical data: chi-square; small expected counts: Fisher exact test.
  • Non-normal or ordinal data: Mann-Whitney, Wilcoxon, Kruskal-Wallis.
  • Association between two continuous variables: correlation for strength, regression for prediction and adjustment.
  • Time to event: Kaplan-Meier curves with log-rank test; adjusted effect as a hazard ratio.
  • Binary outcome with adjustment: logistic regression, reported as odds ratios.

What the numbers mean

A p value is the probability of data at least as extreme as observed if the null hypothesis were true; it is not the probability the null is true, nor the probability of replication. A 95 percent confidence interval gives the range of effects compatible with the data and conveys precision. Power is the pre-study probability of detecting a real effect of a stated size; underpowered studies produce wide intervals and inflated effect estimates among the results that reach significance.

Worked example

A rapid test has sensitivity 90 percent and specificity 95 percent. In a clinic where prevalence is 2 percent, the positive predictive value is (0.90 x 0.02) / [(0.90 x 0.02) + (0.05 x 0.98)] = 0.018 / 0.067, approximately 27 percent. So a positive result means roughly a one-in-four chance of disease. Raise prevalence to 30 percent and the PPV rises to about 89 percent. The lesson: sensitivity and specificity are properties of the test, but predictive values are properties of the test in a population.

Traps that cost marks

  • Interpreting PPV or NPV as fixed test characteristics independent of prevalence.
  • Confusing type I error (false positive conclusion) with type II error (missed real effect).
  • Treating a non-significant result as proof of no effect.
  • Reading an odds ratio as a risk ratio when the outcome is common.
  • Ignoring multiplicity when many endpoints are tested without correction.