Every number in every paper you'll ever read, decoded with the actual diagrams, not just the vocabulary
The data type decides which test you're allowed to use. Get this step wrong and nothing downstream is valid.
| Type | Sub-type | Example | Summarize with |
|---|---|---|---|
| Qualitative | Nominal (no order) | Blood group, sex, ASA class | Counts, proportions, mode |
| Qualitative | Ordinal (ranked) | Pain score, ASA I–IV order | Median, mode |
| Quantitative | Discrete (whole) | Number of PONV episodes | Mean/median |
| Quantitative | Continuous | MAP, weight, pH | Mean ± SD (or median) |
Which average, and how scattered around it?
| Measure | Use when |
|---|---|
| Mean | Symmetric, continuous, no outliers |
| Median | Skewed data or outliers (robust to both) |
| Mode | Most frequent value; the only option for nominal data |
| SD | Spread of the raw data around the mean |
| SEM = SD / √n | Precision of the mean estimate; shrinks as sample size grows |
| IQR | Spread for skewed data, reported alongside the median |
SEM is always smaller than SD, sometimes dramatically so with a large n. Authors occasionally report SEM instead of SD because the error bars look tighter and the result looks more precise than it is. Always check which one a figure is actually showing before you interpret the spread.
Mean = median = mode, and the 68-95-99.7 rule.
If the data isn't shaped like this, don't force it: use the median plus a non-parametric test instead. As a quick tell, right-skew (a long tail to the right) pulls the mean above the median; left-skew pulls the mean below it.
The two most misquoted numbers in medicine.
| Term | What it actually means |
|---|---|
| P-value | If the null hypothesis were true, the probability of seeing a result this extreme or more. It is NOT the probability that the null hypothesis is true. |
| α (0.05) | The pre-set threshold. p < 0.05 → reject the null. |
| 95% CI | A range that, if the study were repeated many times, would contain the true population value 95% of the time. |
A tiny p-value can still describe a clinically trivial effect, especially in a huge trial. Always read the effect size and its confidence interval, not just whether "p < 0.05" is printed at the bottom of a table.
The 2×2 that every trial's design rests on, before a single patient is enrolled.
Match the test to the data. This is the table examiners love most.
| Comparison | Parametric (normal) | Non-parametric (skewed/ordinal) |
|---|---|---|
| 2 independent groups | Unpaired t-test | Mann-Whitney U |
| 2 paired / before-after | Paired t-test | Wilcoxon signed-rank |
| 3+ independent groups | One-way ANOVA | Kruskal-Wallis |
| Correlation | Pearson r | Spearman rho |
| 2 categorical variables | — | Chi-square (Fisher's if any expected cell < 5) |
With 3 or more groups, run one ANOVA (or Kruskal-Wallis), not a series of pairwise t-tests. Running multiple t-tests inflates the overall false-positive rate: each individual test carries its own 5% risk, and those risks compound across comparisons.
Sensitivity, specificity, and the prevalence trap.
| Measure | Formula | What it means |
|---|---|---|
| Sensitivity | TP / (TP+FN) | Detects disease. SnNOUT: high Sn, negative result rules OUT. |
| Specificity | TN / (TN+FP) | Excludes disease. SpPIN: high Sp, positive result rules IN. |
| PPV | TP / (TP+FP) | Positive test → truly diseased |
| NPV | TN / (TN+FN) | Negative test → truly well |
Sensitivity and specificity are properties of the test itself and don't change with prevalence. PPV and NPV do: as prevalence rises, PPV rises and NPV falls, even with the exact same test performance. The same troponin assay means something different in a chest-pain unit than it does in a low-risk outpatient screen.
The high-value extras that separate reading a paper from actually understanding it.
| Concept | Key point |
|---|---|
| LR+ = Sn / (1−Sp) | >10 large/conclusive rule-in; 5–10 moderate |
| LR− = (1−Sn) / Sp | <0.1 large/conclusive rule-out; 0.1–0.2 moderate |
| Sample size ↑ when | Smaller expected effect, more variability (SD), higher desired power, smaller α |
| Kappa (κ) | Inter-rater agreement beyond chance: 1 = perfect, 0 = chance-level |
Likelihood ratios are prevalence-independent, which is exactly what PPV and NPV are not. That makes LRs the right tool for moving from a pre-test probability (your clinical suspicion before the test) to a post-test probability (your suspicion after), regardless of how common the disease is in the population you're standing in.
This carousel is textbook biostatistics rather than a single study's findings, so the audit here is against standard conventions rather than a primary trial. Every formula, threshold, and rule of thumb (SEM, 68-95-99.7, the LR bands, Type I/II error definitions, PPV/NPV prevalence dependence) matches standard biostatistics teaching exactly. Nothing needed correcting; the additions here are the worked diagrams, since a table of definitions alone doesn't build the same intuition as seeing the shapes.