BiostatisticsTier 1Medical Sciences concept

Variable types in statistics (categorical, continuous, ordinal, nominal)

Core concept

Type	Definition	Example
Nominal (categorical)	Named groups, no order	Blood group, ethnicity, eye colour
Binary / dichotomous	Nominal with 2 levels	Sex, dead/alive, disease present/absent
Ordinal	Ordered, but intervals not equal	NYHA I-IV, mRS, pain 0-10, Likert, tumour grade
Discrete (count)	Numeric, whole numbers only	Number of exacerbations, seizures/month
Continuous	Any value in a range	Height, BP, creatinine, GFR

Interval vs ratio among continuous: ratio has a true zero (weight, kelvin) so ratios are meaningful; interval does not (degrees C, pH)
The trap: ordinal data given numeric labels are still ordinal. "Mean NYHA class 2.4" is meaningless.

Test selection follows the variable type

Outcome	Two groups	>2 groups	Association
Continuous, normal	Unpaired t-test (paired t if matched)	ANOVA	Pearson r; linear regression
Continuous, skewed / ordinal	Mann-Whitney U (Wilcoxon signed-rank if paired)	Kruskal-Wallis	Spearman rho
Categorical	Chi-square (Fisher's exact if any expected cell <5)	Chi-square	Logistic regression
Time-to-event	Log-rank	Log-rank	Cox proportional hazards

Summary statistic follows the type
- Nominal -> proportion, mode
- Ordinal or skewed -> median + IQR
- Continuous symmetric -> mean + SD
Regression choice mirrors the outcome: linear (continuous), logistic -> odds ratio (binary), Poisson -> rate ratio (counts), Cox -> hazard ratio (time-to-event)

Categorising a continuous variable loses power and creates artificial cliffs (BP 139 vs 141) - a common criticism of trial secondary analyses
Ordinal outcomes analysed as ordinal are more powerful: the shift analysis of mRS in stroke thrombectomy trials rather than dichotomising at mRS 0-2
Composite endpoints mix types and are driven by the commonest, usually softest, component - always read the components
Skewed biomarkers (ferritin, CRP, triglycerides, HIV viral load, NT-proBNP) are reported as median (IQR) or log-transformed

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