## 1.2 Levels of measurement

• Not every statistical operation can be used with every set of data, i.e. statistical operations depend on the levels of measurement

• Data can be classified into four levels of measurement (from the lowest to the highest level):

1. Nominal scale
2. Ordinal scale
3. Inetrval scale
4. Ratio scale
• Data measured using a nominal scale are qualitative (categorical). Ordering of such data is not meaningful and these data cannot be used in calculations.

• The ordinal scale data, unlike the nominal scale, can be ordered, but the difference between the data cannot be measured. Example of using the ordinal scale is a survey where the responses to questions are “excellent”, “good”, “satisfactory”, and “unsatisfactory”. They can be used to rank the observations (objects or individuals).

• The interval scale data is similar to ordinal data because it has a ordering but the distances between consecutive measurements have meaning and the data are always numerical. An example of interval data is the temperature, i.e. temperatures can be ranked, and the amounts of heat between consecutive readings, such as $$20^0$$, $$21^0$$, and $$22^0$$ are the same. In addition, with interval data, the number zero is just another measurement on the scale and does not mean the absence of the phenomenon.

• The ratio scale data have the same properties as interval data, but have an absolute zero, and the ratio of two numbers is meaningful

Interval and ratio scales belong to quantitative data (sometimes called metric data)

Nominal and ordinal scales belong to qualitative data (sometimes called non-metric data)

Example 1.4 Classify each of the following as nominal, ordinal, interval, or ratio data:

1. The number of tickets sold at a movie theater on any given night
2. Per capita incom
3. The trade balance in dollars
4. A company’s tax identification number
5. The Standard & Poor’s bond ratings
6. The response time of an emergency unit