Levels of Measurement

 

In data analysis it is important to understand the type of data being analyzed before moving forward with calculations. One important distinction of data is referred to levels of measurement. This is also called levels of data and scales of measurement.

There are four basic levels of measurement:

Nominal
Ordinal
Interval
Ratio

Nominal Level of Measurement

The nominal level includes any data that can be organized by categories. Examples of nominal data include color, type, gender, names, groups, topics and just about any other characteristic used in descriptions.

Ordinal Level of Measurement

This level includes data that can be placed in order. For this reason, the level is also known as rank level of measurement. The level includes numeric and non-numeric data. A restriction I remind my students is that the users or readers of data must agree on the order – that is, the order must be recognizable. Examples include school year (1^st grade, 2^nd grade, etc.; freshman, sophomore, junior, senior); levels in a building (basement, lobby, mezzanine, 2^nd floor, 3^rd floor); survey responses (poor, good, great). Although not universal, if you see items labelled with Roman numerals, it often suggests the data is of rank order. Examples include: XXIII Olympiad, Volume III, etc.

Interval Level of Measurement

The final two levels of measurement include only numeric data. Interval level data has uniformity of length between successive units. Examples include temperature, time and dates.

Ratio Level of Measurement

The final level of measurement is the ratio level. The requirements for ratio level data are the same as the interval level but have some additional requirements. First, zero in a ratio level type of data must mean a complete lack of the item. Second, ratios of two ratio level data items must be meaningful.

To give examples of the first requirement, temperature measured in the Fahrenheit or Celsius scales are interval level but not ratio level. In both degrees F and degrees C, one can have negative values and while zero degrees F or C is cold, that temperature does not indicate a lack of thermal energy in the substance. On the other hand, in degrees Kelvin (K), zero K indicates a complete lack of thermal energy (there is no negative K in the Kelvin scale of temperature).

To give an example of the second requirement of ratio data, consider two different measurements of time: time of day and elapsed time of an event. In the first, if one were to take a ratio of 2 pm to 1 pm (time). That ratio has no meaning. While one can divide 2 by 1, the two times are simply two different points in time and their ratio doesn’t have a good meaning. Considering the second example, elapsed time of an event – if one event lasts 2 minutes and the other lasts 1 minute, the ratio of the 2 minutes to 1 minute is 2 and that is a meaningful ratio that one event took twice as long as the other.

Consequences of Using Different Levels of Measurement

Consider that you have a group of nominal data. and you wish to determine a measure of central tendency for that data. If you have nominal level data, average and medium have no meaning. However, identifying the mode (most frequently occurring item) would be useful.

If you have ordinal level data, an average could be calculated if your data is numeric. However, if the ordinal data is qualitative, an average would not be possible to calculate. With qualitative, ordinal data, the better measure is to use the medium. Determining the medium simply means placing all the data in order and taking the middle item (half the items are higher than the medium and half are below).

Moving to the interval and ratio levels of data, a good example is with temperature and ratio. In basic chemistry, we learned the relationship of pressure, temperature, volume, and quantity of gas in the relationship: PV = nRT. To use this equation, one must be measuring temperature in degrees Kelvin. Using degrees C or F will result in incorrect answers.