13.8.2 Types of data

Variables in a study

A variable is a characteristic recorded for each patient or other unit, such as diagnosis, age or symptom score.

A dependent variable may respond to the independent variable, but it is not guaranteed to.

Levels of measurement

Three questions, asked in turn, place a variable: are the categories ordered, are the steps equal, and is there a true zero?

Numeric codes may label categories without ordering them, so coding ethnic group as 1, 2 and 3 leaves it nominal.

Nominal and binary data

• Nominal data are named categories with no inherent order. They allow classification only, whatever labels or codes record them.

• Binary (dichotomous) data fall into exactly two categories, such as relapsed or not. Binary is the more exact term for a two-category nominal variable.

• Some variables are naturally binary, but others apply a threshold to a finer measure, such as a 50% symptom reduction defining response. Applying a threshold loses information.

• Relative risk and odds ratio can only be calculated from a binary outcome, because each participant must be counted as having or not having the event.

Ordinal data

• Ordinal data are ranked categories with unequal or unknown gaps between them, such as social class or the seven grades of the Clinical Global Impression severity scale (CGI-S).

• Ordinal data remain ordinal when they are coded with numbers or entered into a regression. They suit medians and non-parametric tests better than means.

• A Likert-type item is ordinal, because its points are ranked but the spacing between adjacent points is not known to be equal.

Interval and ratio data

• Interval data have equal steps but an arbitrary zero, so differences are meaningful but ratios are not: 40 degrees Celsius is not twice as hot as 20.

• Ratio data have equal steps and a true zero that means none of the quantity, so a drug concentration of 1.0 mmol/L is twice 0.5 mmol/L.

• A summed rating-scale score at interval level supports means, standard deviations and either parametric or non-parametric tests, but it cannot carry ratio statements. Ordinal scores allow medians only.

Discrete and continuous data

This distinction is separate from the four levels.

• Discrete data are numerical data restricted to separate values, typically counts, with nothing possible in between: attendances cannot be 2.4.

• A count has a true zero, so it is discrete ratio data.

• Continuous data are measured and can take any value within a range, limited only by measurement precision, such as weight or age.

• Continuous data have equal, measurable intervals, whereas the steps of an ordinal rating scale have no known size.

Data type and analysis