Measurement Scales and Data Types
What is Measurement ?
In statistics, the term measurement is used more broadly and is more appropriately termed scales of measurement. Scales of measurement refer to ways in which variables/numbers are defined and categorized.
It is important, in statistical analysis, to know about the different scales of measurement, these are:
- INTERVAL
Scale with a fixed and defined interval e.g. temperature or time. - ORDINAL
Scale for ordering observations from low to high with any ties attributed to lack of measurement sensitivity e.g. score from a questionnaire. - NOMINAL with order
Scale for grouping into categories with order e.g. mild, moderate or severe. This can be difficult to separate from ordinal. - NOMINAL without order
Scale for grouping into unique categories e.g. eye colour. - DICHOTOMOUS
As for nominal but two categories only e.g. male/female.
In addition to the classification of measurement scales, other related terms are used to describe types of data:
- CATEGORICAL vs. NUMERICAL (quantitative vs. qualitative)
Data that represent categories, such as dichotomous (two categories) and nominal (more than two categories) observations, are collectively called categorical (qualitative). Data that are counted or measured using a numerically defined method are called numerical (quantitative). - DISCRETE vs. ORDERED CATEGORICAL
Discrete data arise from observations that can only take certain numerical values, usually counts such as number of children or number of patients attending a clinic in a year. Ordered categorical data are sometimes treated as discrete data, this is wrong. For example, using the Registrar General's classification of social class, it would be wrong to say that class I is five times the socio-economic status as class V, as there is not a strict numerical relationship between these categories. It follows, therefore, that average social class is a meaningless statistic. Thus, ordered categorical data should not be treated as discrete data for statistical analysis. Discrete data may be treated as ordered categorical data in statistical analysis, but some information is lost in doing so. - CONTINUOUS
Continuous data are numerical data that can theoretically be measured in infinitely small units. For example, blood pressure is usually measured to the nearest 2mm Hg, but could be measured with much greater resolution of difference. The interval measurement scale is intended for continuous data. Sometimes continuous data are given discrete values at certain thresholds, for example age a last birthday is a discrete value but age itself is a continuous quantity; in these situations it is reasonable to treat discrete values as continuous. Remember that information is lost when continuous data are recorded only in ranges (ordered categories), and the statistical analysis of continuous data is more powerful than that of categorical data. - PERCENTAGES and RATIOS
Percentages or ratios summarise two pieces of information, namely their constituent numerator and denominator values. Simple ratios (0 to 1, i.e. the denominator is the maximum possible value that the numerator can take) can be treated as continuous data. More difficult to analyse data arise when the ratio represents a change, and the value can be negative. Ratios of observations compared with reference values, e.g. height relative to the mean of a reference population for a given sex and age, are difficult to handle as values may fall either side of 1 (100%).
Many statistical methods are appropriate only for data of certain measurement scales. When selecting a statistical method, it is essential to understand how the data to be analysed were measured. The best stage of investigation for pondering measurement scales is the design stage, at which the statistical limitations imposed by certain measurement scales may influence your choice of observations and methods of measurement.
Note that transforming data changes their measurement scales.
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