- Ratio data
- Interval data
- Ordinal data
- Nominal data
Always assign the highest permissible level of measurement to a given set of observations.
It is important to understand the differences that follow because different kinds of data require different kinds of statistical tests in order to evaluate them.
- Properties: classification
- Observations reflect: differences in kind
- Examples: gender, ethnic background, political affiliation, handedness, major in college
- Properties: classification, order
- Observations reflect: differences in degree
- Examples: Likert scale categories, rankings, academic letter grade, stages in development.
- Properties: classification, order, equal intervals
- Observations reflect: measurable differences in amount
- Examples: IQ scores, degrees of temperature, magnitude estimation scales*
***Note: Ratings on a continuous 1-10 or 1-100 scale are a form of magnitude estimation and they approximate the properties of interval data. We can use the statistical tools appropriate for interval data to analyze these data because there is an underlying assumption that values given on such a rating scale are considered to have equal intervals.
- Properties: classification, order, equal intervals, true zero
- Observations reflect: measurable differences in total amount
- Examples: weight, income, family size, number of cows in a field
Shifts to more complex levels of measurement are accompanied by more informative observations that in turn permit a wider variety of interpretations and statistical analyses. Even though the numerical measurement of some non-physical characteristics (e.g., measures of intelligence, measures of satisfaction on a continuous rating scale etc.) may fail to attain the true characteristics of interval or ratio data, they are often treated as approximating at least interval data.
And the rule again: Always assign the highest permissible level of measurement to a given set of observations. Here is an example: a list of annual incomes should be designated as ratio data because $0 signifies the complete absence of income. It would be incorrect to treat annual income as interval data even though a difference of $1000 always signifies the same amount of income (equal intervals); or as ordinal data even though different incomes can always be ranked as more or less (order); or as nominal data even though different incomes always represent different classes (classification).
About the author
This article was written by Dr Philip Hodgson. Philip is an associate of Userfocus, a usability consulting and usability training company that helps organisations reduce costs and increase profits by making stuff easier to use.