Frequency Tables and Proportions

Means and medians are for numbers. Categorical data, diagnoses, sex, smoking status, blood type, recovered-or-not, are summarized in a completely different way: by counting how many fall into each category and turning those counts into proportions and percentages. The basic tool is the frequency table. For a single categorical variable it lists each category, its count (frequency), and its percentage of the total. For example, among 200 patients: 120 non-smokers (60%), 50 ex-smokers (25%), 30 current smokers (15%). That table is the complete, honest summary, no average is possible or meaningful. A proportion is just a count divided by the total (0.15), and a percentage is that proportion times 100 (15%); they are the same information in two forms. A few related terms are worth distinguishing because they are often muddled. A proportion has the part inside the whole (smokers among all patients). A ratio compares two separate counts where the numerator is not part of the denominator (30 smokers to 120 non-smokers, a 1 to 4 ratio). A rate is a proportion with a time element (15 new infections per 1000 patient-days). Keeping these straight matters because they answer different questions and are easy to misreport. When you have two categorical variables, you build a cross-tabulation, or contingency table, which counts every combination. A 2x2 table, for instance exposure yes/no against disease yes/no, is the foundation of much of clinical epidemiology; the risk ratios and odds ratios you will meet later are all calculated from such tables. Reading one well is a core skill: always check whether percentages are calculated across rows or down columns, because 'of smokers, 40% had the disease' and 'of diseased patients, 40% smoked' are very different claims drawn from the same table. Good practice is to report both the count and the percentage, never a percentage alone. '30% improved' is far less informative than '6 of 20 (30%) improved', because a percentage from a tiny sample is fragile: 1 of 3 is 33% but means almost nothing. For categorical data the count is the evidence and the percentage is the convenience, which is why every Table 1 in a clinical paper shows categorical variables as n (%).