LEVELS OF MEASUREMENT

Knowledge about the level of measurement helps not only in interpreting the data but also in selecting the appropriate statistical procedures to analyze the data.

The four different levels of measurement, in ascending order of accuracy, are:
nominal, ordinal, interval and ratio.

• Nominal data has no order and the use of numbers to classify categories is arbitrary. Example: 1=Honda, 2=Toyota, 3=Nissan, etc. can be used to classify different Japanese car make.
  Arithmetic operations (+, -, ÷, ×) cannot be performed on nominal data.

• Ordinal data has order, but the interval between values is not interpretable. Rank data Likert scales are ordinal data. Example: 1=High School, 2=Diploma, 3= Degree, 4=Post Graduate Degree may be used to represent ranking of Academic Achievement.
  Arithmetic operations cannot be performed on ordinal data.

• Interval data has order and the interval between values is interpretable. Counts (integers) such as Years of Education and Temperatures in degrees Fahrenheit are interval data. Note that for interval data, ratios do not make sense and a zero value is not meaningful. For example, 40 degrees is not twice as hot as 20 degrees and 0 degrees does not mean ‘no temperature’.
  Only addition and subtraction can be performed on interval data.

• Ratio data are interval data with a zero value which is meaningful. Examples are Age, Length, Weight and Income. Note that A with a monthly income of Rm4,000 earns twice as much as B whose monthly salary is only Rm2,000. Also, Rm0 means no income.
  All four arithmetic operations can be performed on interval data.

We can see that there is a hierarchy in the four levels of measurement with nominal being the least accurate and ratio the most accurate. So when the phrase ‘at least ordinal’ is used, it refers to all except nominal.

Note: According to Garson, G.D. (1999), ‘Likert scales are very commonly used with interval procedures, provided the scale item has at least 5 and preferably 7 categories’. Read more.

Categorical Data and Continuous Data

It is customary to refer to nominal and ordinal data as categorical data and interval and ratio data as continuous data.

References

Garson, G.D. (2009). SPSS Tutorial. URL:http://faculty.chass.ncsu.edu/garson/PA765/datalevl.htm. Accessed: 2010-03-23. (Archived by WebCite® at http://www.webcitation.org/5oSViac3a)

Trochim, W.M.K. (2006). Web Center for Social Research Methods. URL:http://www.socialresearchmethods.net/kb/measlevl.php. Accessed: 2010-03-23. (Archived by WebCite® at http://www.webcitation.org/5oSUm5C7F)